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Introduction to Research Statistical Analysis: An Overview of the Basics

Christian vandever.

1 HCA Healthcare Graduate Medical Education

Description

This article covers many statistical ideas essential to research statistical analysis. Sample size is explained through the concepts of statistical significance level and power. Variable types and definitions are included to clarify necessities for how the analysis will be interpreted. Categorical and quantitative variable types are defined, as well as response and predictor variables. Statistical tests described include t-tests, ANOVA and chi-square tests. Multiple regression is also explored for both logistic and linear regression. Finally, the most common statistics produced by these methods are explored.

Introduction

Statistical analysis is necessary for any research project seeking to make quantitative conclusions. The following is a primer for research-based statistical analysis. It is intended to be a high-level overview of appropriate statistical testing, while not diving too deep into any specific methodology. Some of the information is more applicable to retrospective projects, where analysis is performed on data that has already been collected, but most of it will be suitable to any type of research. This primer will help the reader understand research results in coordination with a statistician, not to perform the actual analysis. Analysis is commonly performed using statistical programming software such as R, SAS or SPSS. These allow for analysis to be replicated while minimizing the risk for an error. Resources are listed later for those working on analysis without a statistician.

After coming up with a hypothesis for a study, including any variables to be used, one of the first steps is to think about the patient population to apply the question. Results are only relevant to the population that the underlying data represents. Since it is impractical to include everyone with a certain condition, a subset of the population of interest should be taken. This subset should be large enough to have power, which means there is enough data to deliver significant results and accurately reflect the study’s population.

The first statistics of interest are related to significance level and power, alpha and beta. Alpha (α) is the significance level and probability of a type I error, the rejection of the null hypothesis when it is true. The null hypothesis is generally that there is no difference between the groups compared. A type I error is also known as a false positive. An example would be an analysis that finds one medication statistically better than another, when in reality there is no difference in efficacy between the two. Beta (β) is the probability of a type II error, the failure to reject the null hypothesis when it is actually false. A type II error is also known as a false negative. This occurs when the analysis finds there is no difference in two medications when in reality one works better than the other. Power is defined as 1-β and should be calculated prior to running any sort of statistical testing. Ideally, alpha should be as small as possible while power should be as large as possible. Power generally increases with a larger sample size, but so does cost and the effect of any bias in the study design. Additionally, as the sample size gets bigger, the chance for a statistically significant result goes up even though these results can be small differences that do not matter practically. Power calculators include the magnitude of the effect in order to combat the potential for exaggeration and only give significant results that have an actual impact. The calculators take inputs like the mean, effect size and desired power, and output the required minimum sample size for analysis. Effect size is calculated using statistical information on the variables of interest. If that information is not available, most tests have commonly used values for small, medium or large effect sizes.

When the desired patient population is decided, the next step is to define the variables previously chosen to be included. Variables come in different types that determine which statistical methods are appropriate and useful. One way variables can be split is into categorical and quantitative variables. ( Table 1 ) Categorical variables place patients into groups, such as gender, race and smoking status. Quantitative variables measure or count some quantity of interest. Common quantitative variables in research include age and weight. An important note is that there can often be a choice for whether to treat a variable as quantitative or categorical. For example, in a study looking at body mass index (BMI), BMI could be defined as a quantitative variable or as a categorical variable, with each patient’s BMI listed as a category (underweight, normal, overweight, and obese) rather than the discrete value. The decision whether a variable is quantitative or categorical will affect what conclusions can be made when interpreting results from statistical tests. Keep in mind that since quantitative variables are treated on a continuous scale it would be inappropriate to transform a variable like which medication was given into a quantitative variable with values 1, 2 and 3.

Categorical vs. Quantitative Variables

Both of these types of variables can also be split into response and predictor variables. ( Table 2 ) Predictor variables are explanatory, or independent, variables that help explain changes in a response variable. Conversely, response variables are outcome, or dependent, variables whose changes can be partially explained by the predictor variables.

Response vs. Predictor Variables

Choosing the correct statistical test depends on the types of variables defined and the question being answered. The appropriate test is determined by the variables being compared. Some common statistical tests include t-tests, ANOVA and chi-square tests.

T-tests compare whether there are differences in a quantitative variable between two values of a categorical variable. For example, a t-test could be useful to compare the length of stay for knee replacement surgery patients between those that took apixaban and those that took rivaroxaban. A t-test could examine whether there is a statistically significant difference in the length of stay between the two groups. The t-test will output a p-value, a number between zero and one, which represents the probability that the two groups could be as different as they are in the data, if they were actually the same. A value closer to zero suggests that the difference, in this case for length of stay, is more statistically significant than a number closer to one. Prior to collecting the data, set a significance level, the previously defined alpha. Alpha is typically set at 0.05, but is commonly reduced in order to limit the chance of a type I error, or false positive. Going back to the example above, if alpha is set at 0.05 and the analysis gives a p-value of 0.039, then a statistically significant difference in length of stay is observed between apixaban and rivaroxaban patients. If the analysis gives a p-value of 0.91, then there was no statistical evidence of a difference in length of stay between the two medications. Other statistical summaries or methods examine how big of a difference that might be. These other summaries are known as post-hoc analysis since they are performed after the original test to provide additional context to the results.

Analysis of variance, or ANOVA, tests can observe mean differences in a quantitative variable between values of a categorical variable, typically with three or more values to distinguish from a t-test. ANOVA could add patients given dabigatran to the previous population and evaluate whether the length of stay was significantly different across the three medications. If the p-value is lower than the designated significance level then the hypothesis that length of stay was the same across the three medications is rejected. Summaries and post-hoc tests also could be performed to look at the differences between length of stay and which individual medications may have observed statistically significant differences in length of stay from the other medications. A chi-square test examines the association between two categorical variables. An example would be to consider whether the rate of having a post-operative bleed is the same across patients provided with apixaban, rivaroxaban and dabigatran. A chi-square test can compute a p-value determining whether the bleeding rates were significantly different or not. Post-hoc tests could then give the bleeding rate for each medication, as well as a breakdown as to which specific medications may have a significantly different bleeding rate from each other.

A slightly more advanced way of examining a question can come through multiple regression. Regression allows more predictor variables to be analyzed and can act as a control when looking at associations between variables. Common control variables are age, sex and any comorbidities likely to affect the outcome variable that are not closely related to the other explanatory variables. Control variables can be especially important in reducing the effect of bias in a retrospective population. Since retrospective data was not built with the research question in mind, it is important to eliminate threats to the validity of the analysis. Testing that controls for confounding variables, such as regression, is often more valuable with retrospective data because it can ease these concerns. The two main types of regression are linear and logistic. Linear regression is used to predict differences in a quantitative, continuous response variable, such as length of stay. Logistic regression predicts differences in a dichotomous, categorical response variable, such as 90-day readmission. So whether the outcome variable is categorical or quantitative, regression can be appropriate. An example for each of these types could be found in two similar cases. For both examples define the predictor variables as age, gender and anticoagulant usage. In the first, use the predictor variables in a linear regression to evaluate their individual effects on length of stay, a quantitative variable. For the second, use the same predictor variables in a logistic regression to evaluate their individual effects on whether the patient had a 90-day readmission, a dichotomous categorical variable. Analysis can compute a p-value for each included predictor variable to determine whether they are significantly associated. The statistical tests in this article generate an associated test statistic which determines the probability the results could be acquired given that there is no association between the compared variables. These results often come with coefficients which can give the degree of the association and the degree to which one variable changes with another. Most tests, including all listed in this article, also have confidence intervals, which give a range for the correlation with a specified level of confidence. Even if these tests do not give statistically significant results, the results are still important. Not reporting statistically insignificant findings creates a bias in research. Ideas can be repeated enough times that eventually statistically significant results are reached, even though there is no true significance. In some cases with very large sample sizes, p-values will almost always be significant. In this case the effect size is critical as even the smallest, meaningless differences can be found to be statistically significant.

These variables and tests are just some things to keep in mind before, during and after the analysis process in order to make sure that the statistical reports are supporting the questions being answered. The patient population, types of variables and statistical tests are all important things to consider in the process of statistical analysis. Any results are only as useful as the process used to obtain them. This primer can be used as a reference to help ensure appropriate statistical analysis.

Funding Statement

This research was supported (in whole or in part) by HCA Healthcare and/or an HCA Healthcare affiliated entity.

Conflicts of Interest

The author declares he has no conflicts of interest.

Christian Vandever is an employee of HCA Healthcare Graduate Medical Education, an organization affiliated with the journal’s publisher.

This research was supported (in whole or in part) by HCA Healthcare and/or an HCA Healthcare affiliated entity. The views expressed in this publication represent those of the author(s) and do not necessarily represent the official views of HCA Healthcare or any of its affiliated entities.

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Data Science: the impact of statistics

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• Published: 16 February 2018
• Volume 6 , pages 189–194, ( 2018 )

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In this paper, we substantiate our premise that statistics is one of the most important disciplines to provide tools and methods to find structure in and to give deeper insight into data, and the most important discipline to analyze and quantify uncertainty. We give an overview over different proposed structures of Data Science and address the impact of statistics on such steps as data acquisition and enrichment, data exploration, data analysis and modeling, validation and representation and reporting. Also, we indicate fallacies when neglecting statistical reasoning.

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Data Analysis

Data science vs. statistics: two cultures?

Data Science: An Introduction

Avoid common mistakes on your manuscript.

1 Introduction and premise

Data Science as a scientific discipline is influenced by informatics, computer science, mathematics, operations research, and statistics as well as the applied sciences.

In 1996, for the first time, the term Data Science was included in the title of a statistical conference (International Federation of Classification Societies (IFCS) “Data Science, classification, and related methods”) [ 37 ]. Even though the term was founded by statisticians, in the public image of Data Science, the importance of computer science and business applications is often much more stressed, in particular in the era of Big Data.

Already in the 1970s, the ideas of John Tukey [ 43 ] changed the viewpoint of statistics from a purely mathematical setting , e.g., statistical testing, to deriving hypotheses from data ( exploratory setting ), i.e., trying to understand the data before hypothesizing.

Another root of Data Science is Knowledge Discovery in Databases (KDD) [ 36 ] with its sub-topic Data Mining . KDD already brings together many different approaches to knowledge discovery, including inductive learning, (Bayesian) statistics, query optimization, expert systems, information theory, and fuzzy sets. Thus, KDD is a big building block for fostering interaction between different fields for the overall goal of identifying knowledge in data.

Nowadays, these ideas are combined in the notion of Data Science, leading to different definitions. One of the most comprehensive definitions of Data Science was recently given by Cao as the formula [ 12 ]:

data science = (statistics + informatics + computing + communication + sociology + management) | (data + environment + thinking) .

In this formula, sociology stands for the social aspects and | (data + environment + thinking) means that all the mentioned sciences act on the basis of data, the environment and the so-called data-to-knowledge-to-wisdom thinking.

A recent, comprehensive overview of Data Science provided by Donoho in 2015 [ 16 ] focuses on the evolution of Data Science from statistics. Indeed, as early as 1997, there was an even more radical view suggesting to rename statistics to Data Science [ 50 ]. And in 2015, a number of ASA leaders [ 17 ] released a statement about the role of statistics in Data Science, saying that “statistics and machine learning play a central role in data science.”

In our view, statistical methods are crucial in most fundamental steps of Data Science. Hence, the premise of our contribution is:

Statistics is one of the most important disciplines to provide tools and methods to find structure in and to give deeper insight into data, and the most important discipline to analyze and quantify uncertainty.

This paper aims at addressing the major impact of statistics on the most important steps in Data Science.

2 Steps in data science

One of forerunners of Data Science from a structural perspective is the famous CRISP-DM (Cross Industry Standard Process for Data Mining) which is organized in six main steps: Business Understanding, Data Understanding, Data Preparation, Modeling, Evaluation, and Deployment [ 10 ], see Table  1 , left column. Ideas like CRISP-DM are now fundamental for applied statistics.

In our view, the main steps in Data Science have been inspired by CRISP-DM and have evolved, leading to, e.g., our definition of Data Science as a sequence of the following steps: Data Acquisition and Enrichment, Data Storage and Access , Data Exploration, Data Analysis and Modeling, Optimization of Algorithms , Model Validation and Selection, Representation and Reporting of Results, and Business Deployment of Results . Note that topics in small capitals indicate steps where statistics is less involved, cp. Table  1 , right column.

Usually, these steps are not just conducted once but are iterated in a cyclic loop. In addition, it is common to alternate between two or more steps. This holds especially for the steps Data Acquisition and Enrichment , Data Exploration , and Statistical Data Analysis , as well as for Statistical Data Analysis and Modeling and Model Validation and Selection .

Table  1 compares different definitions of steps in Data Science. The relationship of terms is indicated by horizontal blocks. The missing step Data Acquisition and Enrichment in CRISP-DM indicates that that scheme deals with observational data only. Moreover, in our proposal, the steps Data Storage and Access and Optimization of Algorithms are added to CRISP-DM, where statistics is less involved.

The list of steps for Data Science may even be enlarged, see, e.g., Cao in [ 12 ], Figure 6, cp. also Table  1 , middle column, for the following recent list: Domain-specific Data Applications and Problems, Data Storage and Management, Data Quality Enhancement, Data Modeling and Representation, Deep Analytics, Learning and Discovery, Simulation and Experiment Design, High-performance Processing and Analytics, Networking, Communication, Data-to-Decision and Actions.

In principle, Cao’s and our proposal cover the same main steps. However, in parts, Cao’s formulation is more detailed; e.g., our step Data Analysis and Modeling corresponds to Data Modeling and Representation, Deep Analytics, Learning and Discovery . Also, the vocabularies differ slightly, depending on whether the respective background is computer science or statistics. In that respect note that Experiment Design in Cao’s definition means the design of the simulation experiments.

In what follows, we will highlight the role of statistics discussing all the steps, where it is heavily involved, in Sects.  2.1 – 2.6 . These coincide with all steps in our proposal in Table  1 except steps in small capitals. The corresponding entries Data Storage and Access and Optimization of Algorithms are mainly covered by informatics and computer science , whereas Business Deployment of Results is covered by Business Management .

2.1 Data acquisition and enrichment

Design of experiments (DOE) is essential for a systematic generation of data when the effect of noisy factors has to be identified. Controlled experiments are fundamental for robust process engineering to produce reliable products despite variation in the process variables. On the one hand, even controllable factors contain a certain amount of uncontrollable variation that affects the response. On the other hand, some factors, like environmental factors, cannot be controlled at all. Nevertheless, at least the effect of such noisy influencing factors should be controlled by, e.g., DOE.

DOE can be utilized, e.g.,

to systematically generate new data ( data acquisition ) [ 33 ],

for systematically reducing data bases [ 41 ], and

for tuning (i.e., optimizing) parameters of algorithms [ 1 ], i.e., for improving the data analysis methods (see Sect.  2.3 ) themselves.

Simulations [ 7 ] may also be used to generate new data. A tool for the enrichment of data bases to fill data gaps is the imputation of missing data [ 31 ].

Such statistical methods for data generation and enrichment need to be part of the backbone of Data Science. The exclusive use of observational data without any noise control distinctly diminishes the quality of data analysis results and may even lead to wrong result interpretation. The hope for “The End of Theory: The Data Deluge Makes the Scientific Method Obsolete” [ 4 ] appears to be wrong due to noise in the data.

Thus, experimental design is crucial for the reliability, validity, and replicability of our results.

2.2 Data exploration

Exploratory statistics is essential for data preprocessing to learn about the contents of a data base. Exploration and visualization of observed data was, in a way, initiated by John Tukey [ 43 ]. Since that time, the most laborious part of data analysis, namely data understanding and transformation, became an important part in statistical science.

Data exploration or data mining is fundamental for the proper usage of analytical methods in Data Science. The most important contribution of statistics is the notion of distribution . It allows us to represent variability in the data as well as (a-priori) knowledge of parameters, the concept underlying Bayesian statistics. Distributions also enable us to choose adequate subsequent analytic models and methods.

2.3 Statistical data analysis

Finding structure in data and making predictions are the most important steps in Data Science. Here, in particular, statistical methods are essential since they are able to handle many different analytical tasks. Important examples of statistical data analysis methods are the following.

Hypothesis testing is one of the pillars of statistical analysis. Questions arising in data driven problems can often be translated to hypotheses. Also, hypotheses are the natural links between underlying theory and statistics. Since statistical hypotheses are related to statistical tests, questions and theory can be tested for the available data. Multiple usage of the same data in different tests often leads to the necessity to correct significance levels. In applied statistics, correct multiple testing is one of the most important problems, e.g., in pharmaceutical studies [ 15 ]. Ignoring such techniques would lead to many more significant results than justified.

Classification methods are basic for finding and predicting subpopulations from data. In the so-called unsupervised case, such subpopulations are to be found from a data set without a-priori knowledge of any cases of such subpopulations. This is often called clustering.

In the so-called supervised case, classification rules should be found from a labeled data set for the prediction of unknown labels when only influential factors are available.

Nowadays, there is a plethora of methods for the unsupervised [ 22 ] as well for the supervised case [ 2 ].

In the age of Big Data, a new look at the classical methods appears to be necessary, though, since most of the time the calculation effort of complex analysis methods grows stronger than linear with the number of observations n or the number of features p . In the case of Big Data, i.e., if n or p is large, this leads to too high calculation times and to numerical problems. This results both, in the comeback of simpler optimization algorithms with low time-complexity [ 9 ] and in re-examining the traditional methods in statistics and machine learning for Big Data [ 46 ].

Regression methods are the main tool to find global and local relationships between features when the target variable is measured. Depending on the distributional assumption for the underlying data, different approaches may be applied. Under the normality assumption, linear regression is the most common method, while generalized linear regression is usually employed for other distributions from the exponential family [ 18 ]. More advanced methods comprise functional regression for functional data [ 38 ], quantile regression [ 25 ], and regression based on loss functions other than squared error loss like, e.g., Lasso regression [ 11 , 21 ]. In the context of Big Data, the challenges are similar to those for classification methods given large numbers of observations n (e.g., in data streams) and / or large numbers of features p . For the reduction of n , data reduction techniques like compressed sensing, random projection methods [ 20 ] or sampling-based procedures [ 28 ] enable faster computations. For decreasing the number p to the most influential features, variable selection or shrinkage approaches like the Lasso [ 21 ] can be employed, keeping the interpretability of the features. (Sparse) principal component analysis [ 21 ] may also be used.

Time series analysis aims at understanding and predicting temporal structure [ 42 ]. Time series are very common in studies of observational data, and prediction is the most important challenge for such data. Typical application areas are the behavioral sciences and economics as well as the natural sciences and engineering. As an example, let us have a look at signal analysis, e.g., speech or music data analysis. Here, statistical methods comprise the analysis of models in the time and frequency domains. The main aim is the prediction of future values of the time series itself or of its properties. For example, the vibrato of an audio time series might be modeled in order to realistically predict the tone in the future [ 24 ] and the fundamental frequency of a musical tone might be predicted by rules learned from elapsed time periods [ 29 ].

In econometrics, multiple time series and their co-integration are often analyzed [ 27 ]. In technical applications, process control is a common aim of time series analysis [ 34 ].

2.4 Statistical modeling

Complex interactions between factors can be modeled by graphs or networks . Here, an interaction between two factors is modeled by a connection in the graph or network [ 26 , 35 ]. The graphs can be undirected as, e.g., in Gaussian graphical models, or directed as, e.g., in Bayesian networks. The main goal in network analysis is deriving the network structure. Sometimes, it is necessary to separate (unmix) subpopulation specific network topologies [ 49 ].

Stochastic differential and difference equations can represent models from the natural and engineering sciences [ 3 , 39 ]. The finding of approximate statistical models solving such equations can lead to valuable insights for, e.g., the statistical control of such processes, e.g., in mechanical engineering [ 48 ]. Such methods can build a bridge between the applied sciences and Data Science.

Local models and globalization Typically, statistical models are only valid in sub-regions of the domain of the involved variables. Then, local models can be used [ 8 ]. The analysis of structural breaks can be basic to identify the regions for local modeling in time series [ 5 ]. Also, the analysis of concept drifts can be used to investigate model changes over time [ 30 ].

In time series, there are often hierarchies of more and more global structures. For example, in music, a basic local structure is given by the notes and more and more global ones by bars, motifs, phrases, parts etc. In order to find global properties of a time series, properties of the local models can be combined to more global characteristics [ 47 ].

Mixture models can also be used for the generalization of local to global models [ 19 , 23 ]. Model combination is essential for the characterization of real relationships since standard mathematical models are often much too simple to be valid for heterogeneous data or bigger regions of interest.

2.5 Model validation and model selection

In cases where more than one model is proposed for, e.g., prediction, statistical tests for comparing models are helpful to structure the models, e.g., concerning their predictive power [ 45 ].

Predictive power is typically assessed by means of so-called resampling methods where the distribution of power characteristics is studied by artificially varying the subpopulation used to learn the model. Characteristics of such distributions can be used for model selection [ 7 ].

Perturbation experiments offer another possibility to evaluate the performance of models. In this way, the stability of the different models against noise is assessed [ 32 , 44 ].

Meta-analysis as well as model averaging are methods to evaluate combined models [ 13 , 14 ].

Model selection became more and more important in the last years since the number of classification and regression models proposed in the literature increased with higher and higher speed.

2.6 Representation and reporting

Visualization to interpret found structures and storing of models in an easy-to-update form are very important tasks in statistical analyses to communicate the results and safeguard data analysis deployment. Deployment is decisive for obtaining interpretable results in Data Science. It is the last step in CRISP-DM [ 10 ] and underlying the data-to-decision and action step in Cao [ 12 ].

Besides visualization and adequate model storing, for statistics, the main task is reporting of uncertainties and review [ 6 ].

3 Fallacies

The statistical methods described in Sect.  2 are fundamental for finding structure in data and for obtaining deeper insight into data, and thus, for a successful data analysis. Ignoring modern statistical thinking or using simplistic data analytics/statistical methods may lead to avoidable fallacies. This holds, in particular, for the analysis of big and/or complex data.

As mentioned at the end of Sect.  2.2 , the notion of distribution is the key contribution of statistics. Not taking into account distributions in data exploration and in modeling restricts us to report values and parameter estimates without their corresponding variability. Only the notion of distributions enables us to predict with corresponding error bands.

Moreover, distributions are the key to model-based data analytics. For example, unsupervised learning can be employed to find clusters in data. If additional structure like dependency on space or time is present, it is often important to infer parameters like cluster radii and their spatio-temporal evolution. Such model-based analysis heavily depends on the notion of distributions (see [ 40 ] for an application to protein clusters).

If more than one parameter is of interest, it is advisable to compare univariate hypothesis testing approaches to multiple procedures, e.g., in multiple regression, and choose the most adequate model by variable selection. Restricting oneself to univariate testing, would ignore relationships between variables.

Deeper insight into data might require more complex models, like, e.g., mixture models for detecting heterogeneous groups in data. When ignoring the mixture, the result often represents a meaningless average, and learning the subgroups by unmixing the components might be needed. In a Bayesian framework, this is enabled by, e.g., latent allocation variables in a Dirichlet mixture model. For an application of decomposing a mixture of different networks in a heterogeneous cell population in molecular biology see [ 49 ].

A mixture model might represent mixtures of components of very unequal sizes, with small components (outliers) being of particular importance. In the context of Big Data, naïve sampling procedures are often employed for model estimation. However, these have the risk of missing small mixture components. Hence, model validation or sampling according to a more suitable distribution as well as resampling methods for predictive power are important.

4 Conclusion

Following the above assessment of the capabilities and impacts of statistics our conclusion is:

The role of statistics in Data Science is under-estimated as, e.g., compared to computer science. This yields, in particular, for the areas of data acquisition and enrichment as well as for advanced modeling needed for prediction.

Stimulated by this conclusion, statisticians are well-advised to more offensively play their role in this modern and well accepted field of Data Science.

Only complementing and/or combining mathematical methods and computational algorithms with statistical reasoning, particularly for Big Data, will lead to scientific results based on suitable approaches. Ultimately, only a balanced interplay of all sciences involved will lead to successful solutions in Data Science.

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Acknowledgements

The authors would like to thank the editor, the guest editors and all reviewers for valuable comments on an earlier version of the manuscript. They also thank Leo Geppert for fruitful discussions.

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Weihs, C., Ickstadt, K. Data Science: the impact of statistics. Int J Data Sci Anal 6 , 189–194 (2018). https://doi.org/10.1007/s41060-018-0102-5

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In many fields, a statistical analysis forms the heart of both the methods and results sections of a manuscript. Learn how to report statistical analyses, and what other context is important for publication success and future reproducibility.

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First and foremost, the statistical methods employed in research must always be:

Appropriate for the study design

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Free of manipulation, selective reporting, or other forms of “spin”

Just as importantly, statistical practices must never be manipulated or misused . Misrepresenting data, selectively reporting results or searching for patterns  that can be presented as statistically significant, in an attempt to yield a conclusion that is believed to be more worthy of attention or publication is a serious ethical violation. Although it may seem harmless, using statistics to “spin” results can prevent publication, undermine a published study, or lead to investigation and retraction.

Supporting public trust in science through transparency and consistency

Along with clear methods and transparent study design, the appropriate use of statistical methods and analyses impacts editorial evaluation and readers’ understanding and trust in science.

In 2011  False-Positive Psychology: Undisclosed Flexibility in Data Collection and Analysis Allows Presenting Anything as Significant exposed that “flexibility in data collection, analysis, and reporting dramatically increases actual false-positive rates” and demonstrated “how unacceptably easy it is to accumulate (and report) statistically significant evidence for a false hypothesis”.

Arguably, such problems with flexible analysis lead to the “ reproducibility crisis ” that we read about today. 

A constant principle of rigorous science The appropriate, rigorous, and transparent use of statistics is a constant principle of rigorous, transparent, and Open Science. Aim to be thorough, even if a particular journal doesn’t require the same level of detail. Trust in science is all of our responsibility. You cannot create any problems by exceeding a minimum standard of information and reporting.

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While it is hard to provide statistical guidelines that are relevant for all disciplines, types of research, and all analytical techniques,  adherence to rigorous and appropriate principles remains key. Here are some ways to ensure your statistics are sound.

Define your analytical methodology before you begin Take the time to consider and develop a thorough study design that defines your line of inquiry, what you plan to do, what data you will collect, and how you will analyze it. (If you applied for research grants or ethical approval, you probably already have a plan in hand!) Refer back to your study design at key moments in the research process, and above all, stick to it.

To avoid flexibility and improve the odds of acceptance, preregister your study design with a journal Many journals offer the option to submit a study design for peer review before research begins through a practice known as preregistration. If the editors approve your study design, you’ll receive a provisional acceptance for a future research article reporting the results. Preregistering is a great way to head off any intentional or unintentional flexibility in analysis.  By declaring your analytical approach in advance you’ll increase the credibility and reproducibility of your results and help address publication bias, too. Getting peer review feedback on your study design and analysis plan before it has begun (when you can still make changes!) makes your research even stronger AND increases your chances of publication—even if the results are negative or null. Never underestimate how much you can help increase the public’s trust in science by planning your research in this way.

Imagine replicating or extending your own work, years in the future Imagine that you are describing your approach to statistical analysis for your future self, in exactly the same way as we have described for writing your methods section . What would you need to know to replicate or extend your own work? When you consider that you might be at a different institution, working with different colleagues,  using different programs, applications, resources — or maybe even adopting new statistical techniques that have emerged — you can help yourself imagine the level of reporting specificity that you yourself would require to redo or extend your work. Consider:

• Which details would you need to be reminded of? 
• What did you do to the raw data before analysis?
• Did the purpose of the analysis change before or during the experiments?
• What participants did you decide to exclude? 
• What process did you adjust, during your work? 

Even if a necessary adjustment you made was not ideal, transparency is the key to ensuring this is not regarded as an issue in the future. It is far better to transparently convey any non-optimal techniques or constraints than to conceal them, which could result in reproducibility or ethical issues downstream.

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TIP: Do you have a specific journal in mind?

Be sure to read the submission guidelines for the specific journal you are submitting to, in order to discover any journal- or field-specific policies, initiatives or tools to utilize.

Articles on statistical methods and reporting

Makin, T.R.,  Orban de Xivry, J. Science Forum: Ten common statistical mistakes to watch out for when writing or reviewing a manuscript . eLife 2019;8:e48175 (2019).  https://doi.org/10.7554/eLife.48175  

Munafò, M., Nosek, B., Bishop, D. et al. A manifesto for reproducible science . Nat Hum Behav 1, 0021 (2017). https://doi.org/10.1038/s41562-016-0021    

Writing tips

Your use of statistics should be rigorous, appropriate, and uncompromising in avoidance of analytical flexibility. While this is difficult, do not compromise on rigorous standards for credibility!

• Remember that trust in science is everyone’s responsibility.
• Keep in mind future replicability.
• Consider preregistering your analysis plan to have it (i) reviewed before results are collected to check problems before they occur and (ii) to avoid any analytical flexibility.
• Follow principles, but also checklists and field- and journal-specific guidelines.
• Consider a commitment to rigorous and transparent science a personal responsibility, and not simple adhering to journal guidelines.
• Be specific about all decisions made during the experiments that someone reproducing your work would need to know.
• Consider a course in advanced and new statistics, if you feel you have not focused on it enough during your research training.

Don’t

• Misuse statistics to influence significance or other interpretations of results
• Conduct your statistical analyses if you are unsure of what you are doing—seek feedback (e.g. via preregistration) from a statistical specialist first.
• How to Write a Great Title
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Simplifying Debiased Inference via Automatic Differentiation and Probabilistic Programming

Published 5/14/2024

We introduce an algorithm that simplifies the construction of efficient estimators, making them accessible to a broader audience. 'Dimple' takes as input computer code representing a parameter of interest and outputs an efficient estimator. Unlike standard approaches, it does not require users to derive a functional derivative known as the efficient influence function. Dimple avoids this task by applying automatic differentiation to the statistical functional of interest. Doing so requires expressing this functional as a composition of primitives satisfying a novel differentiability condition. Dimple also uses this composition to determine the nuisances it must estimate. In software, primitives can be implemented independently of one another and reused across different estimation problems. We provide a proof-of-concept Python implementation and showcase through examples how it allows users to go from parameter specification to efficient estimation with just a few lines of code.

Estimating the Effects of Political Pressure on the Fed: A Narrative Approach with New Data

This paper combines new data and a narrative approach to identify shocks to political pressure on the Federal Reserve. From archival records, I build a data set of personal interactions between U.S. Presidents and Fed officials between 1933 and 2016. Since personal interactions do not necessarily reflect political pressure, I develop a narrative identification strategy based on President Nixon's pressure on Fed Chair Burns. I exploit this narrative through restrictions on a structural vector autoregression that includes the personal interaction data. I find that political pressure shocks (i) increase inflation strongly and persistently, (ii) lead to statistically weak negative effects on activity, (iii) contributed to inflationary episodes outside of the Nixon era, and (iv) transmit differently from standard expansionary monetary policy shocks, by having a stronger effect on inflation expectations. Quantitatively, increasing political pressure by half as much as Nixon, for six months, raises the price level more than 8%.

I thank Juan Antolin-Diaz, Jonas Arias, Boragan Aruoba, Miguel Bandeira, Francesco Bianchi, Allan Drazen, Leland Farmer, Yuriy Gorodnichenko, Amy Handlan, Fatima Hussein, Hanno Lustig, Fernando Martin, Emi Nakamura, Evgenia Passari, Jon Steinsson and Sarah Zubairy for detailed discussions. Seminar and conference participants at UC Berkeley, Stanford SITE, the NBER Monetary Economics Spring Meeting 2024, the Federal Reserve Board, the Boston Fed, Philadelphia Fed, Minneapolis Fed, Richmond Fed, St. Louis Fed, Texas A&M University, and the University of Maryland provided very useful suggestions. I am grateful to Seho Kim, Ko Miura and Daniel Schwindt for excellent research assistance. The views expressed herein are those of the author and do not necessarily reflect the views of the National Bureau of Economic Research.

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Experimental R&D Value Added Statistics for the U.S. and States Now Available

Research and development activity accounted for 2.3 percent of the U.S. economy in 2021, according to new experimental statistics released today by the Bureau of Economic Analysis. R&D as a share of each state’s gross domestic product, or GDP, ranged from 0.3 percent in Louisiana and Wyoming to 6.3 percent in New Mexico, home to federally funded Los Alamos National Laboratory and Sandia National Laboratories.

These statistics are part of a new Research and Development Satellite Account  BEA is developing in partnership with the National Center for Science and Engineering Statistics of the National Science Foundation . The statistics complement BEA’s national data on R&D investment  and provide BEA’s first state-by-state numbers on R&D.

The new statistics, covering 2017 to 2021, provide information on the contribution of R&D to GDP (known as R&D value added), compensation, and employment for the nation, all 50 states, and the District of Columbia. In the state statistics, R&D is attributed to the state where the R&D is performed.

Some highlights from the newly released statistics:

R&D activity is highly concentrated in the United States. The top ten R&D-producing states account for 70 percent of U.S. R&D value added. California alone accounts for almost a third of U.S. R&D. Other top R&D-producing states include Washington, Massachusetts, Texas, and New York.

Treating R&D as a sector allows for comparisons with other industries and sectors of the U.S. economy. For instance, R&D’s share of U.S. value added in 2021 is similar to hospitals (2.4 percent) and food services and drinking places (2.2 percent).

Eighty-five percent of R&D value added is generated by the business sector, followed by government, and nonprofit institutions serving households.

Within the business sector, the professional, scientific, and technical services industry accounts for 40 percent of business R&D value added.    Information (15 percent), chemical manufacturing (12 percent), and computer and electronic product manufacturing (11 percent) also account for sizable shares.

Visit the R&D Satellite Account on BEA’s website for the full set of experimental statistics and accompanying information. To help refine the methodology and presentation of these statistics, BEA is seeking your feedback. Please submit comments to  [email protected] .

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Wang named 2024 Fellow of American Statistical Association

Friday, May 17, 2024 • Greg Pederson :

Xinlei “Sherry” Wang, director for research in the Division of Data Science at The University of Texas at Arlington, has been named a 2024 Fellow of the American Statistical Association (ASA).

Wang, who is also the Jenkins Garret Endowed Professor of Statistics and Data Science, was selected for outstanding contributions in developing and applying statistical and computational methods for complex data challenges; for excellence in mentoring Ph.D. students and junior researchers; and for exceptional leadership of data science programs.

ASA is the world’s largest community of statisticians. It was founded in 1839 and is the second-oldest, continuously operating professional association in the country. ASA Fellows have been designated for nearly 100 years, and only up to one-third of one percent of the total association membership can be elected as fellows each year.

“I am honored to be elected an ASA Fellow and recognized by my profession,” Wang said. “I'm truly grateful for the support I've received from my department, college, and university since I joined UTA, which undoubtedly contributed to this achievement.

“This recognition is a testament to the incredible collaborations I've had with students and colleagues throughout my career. I'm especially grateful to my academic advisor, Dr. Edward George [professor emeritus of statistics and data science at the University of Pennsylvania], and my former professor and career mentor, Dr. Lynne Stokes [professor emerita of statistical science at Southern Methodist University], for their unwavering support throughout my career.

“Additionally, I'd like to thank Dr. Steven Ma [professor and chair of biostatistics at Yale University] for the entire nomination process and Dr. Tamara Brown [UTA provost and senior vice president for academic affairs] for her strong endorsement."

Wang joined UTA in January 2023 as director of the College of Science’s newly created Center for Data Science Research and Education (CDSRE). She and her colleagues launched the College’s first graduate degree in data science, the M.S. in Applied Statistics and Data Science (ASDS), in Fall 2023.

In January 2024, College of Science Dean Morteza Khaledi appointed Wang as director for research of a new Division of Data Science, which serves as a hub to organize, provide infrastructure support, and facilitate growth in instructional and research programs involving data science. The DDS houses the College’s bachelor’s and master’s programs in data science, as well as the CDSRE.

“Dr. Wang is very deserving of this honor of being named an ASA Fellow,” Khaledi said. “This recognition is a testament to her outstanding scholarship. She has played a major role in building and advancing our data science program in the College of Science, and we’re very fortunate to have her here at UTA.”

Wang received a B.S. degree in Automatic Control from the University of Science and Technology of China in 1997 and an M.A. degree in Statistics at the University of Pittsburgh in 1998. She earned a Ph.D. in Decision Science and Statistics from the McCombs School of Business at UT Austin in 2002.

She joined the faculty at SMU in 2003 as an assistant professor in the Department of Statistical Sciences. She was promoted to associate professor in 2009 and to full professor in 2015. Her research was funded by major grants from the National Science Foundation, National Institutes of Health, and the Cancer Prevention and Research Institute of Texas. At SMU she was named a Gerald J. Ford Senior Research Fellow (2020) and received the Dean’s Research Council Award (2022).

She has authored or co-authored more than 90 papers in refereed publications and made more than 75 presentations at conferences and seminars around the world. She has directed Ph.D. dissertations for 19 students, with seven more in progress.

Wang has been an ASA member since 1999 and has served the ASA in various capacities, including as vice president (2009–10) and president (2010–11) of the North Texas Chapter. She will be formally recognized as a 2024 Fellow at an awards ceremony at the 2024 Joint Statistical Meetings (JSM) in Portland, Oregon, in August. JSM is the is the largest gathering of statisticians and data scientists in North America and is held jointly with 13 organizations, including ASA.

The UTA College of Science, a Carnegie R1 research institution, is preparing the next generation of leaders in science through innovative education and hands-on research and offers programs in Biology, Chemistry & Biochemistry, Data Science, Earth & Environmental Sciences, Health Professions, Mathematics, Physics and Psychology. To support educational and research efforts visit the  giving page , or if you're a prospective student interested in beginning your #MaverickScience journey visit our  future students page .

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Innovative Statistics Project Ideas for Insightful Analysis

Table of contents

• 1.1 AP Statistics Topics for Project
• 1.2 Statistics Project Topics for High School Students
• 1.3 Statistical Survey Topics
• 1.4 Statistical Experiment Ideas
• 1.5 Easy Stats Project Ideas
• 1.6 Business Ideas for Statistics Project
• 1.7 Socio-Economic Easy Statistics Project Ideas
• 1.8 Experiment Ideas for Statistics and Analysis
• 2 Conclusion: Navigating the World of Data Through Statistics

Diving into the world of data, statistics presents a unique blend of challenges and opportunities to uncover patterns, test hypotheses, and make informed decisions. It is a fascinating field that offers many opportunities for exploration and discovery. This article is designed to inspire students, educators, and statistics enthusiasts with various project ideas. We will cover:

• Challenging concepts suitable for advanced placement courses.
• Accessible ideas that are engaging and educational for younger students.
• Ideas for conducting surveys and analyzing the results.
• Topics that explore the application of statistics in business and socio-economic areas.

Each category of topics for the statistics project provides unique insights into the world of statistics, offering opportunities for learning and application. Let’s dive into these ideas and explore the exciting world of statistical analysis.

Top Statistics Project Ideas for High School

Statistics is not only about numbers and data; it’s a unique lens for interpreting the world. Ideal for students, educators, or anyone with a curiosity about statistical analysis, these project ideas offer an interactive, hands-on approach to learning. These projects range from fundamental concepts suitable for beginners to more intricate studies for advanced learners. They are designed to ignite interest in statistics by demonstrating its real-world applications, making it accessible and enjoyable for people of all skill levels.

Need help with statistics project? Get your paper written by a professional writer Get Help Reviews.io 4.9/5

AP Statistics Topics for Project

• Analyzing Variance in Climate Data Over Decades.
• The Correlation Between Economic Indicators and Standard of Living.
• Statistical Analysis of Voter Behavior Patterns.
• Probability Models in Sports: Predicting Outcomes.
• The Effectiveness of Different Teaching Methods: A Statistical Study.
• Analysis of Demographic Data in Public Health.
• Time Series Analysis of Stock Market Trends.
• Investigating the Impact of Social Media on Academic Performance.
• Survival Analysis in Clinical Trial Data.
• Regression Analysis on Housing Prices and Market Factors.

Statistics Project Topics for High School Students

• The Mathematics of Personal Finance: Budgeting and Spending Habits.
• Analysis of Class Performance: Test Scores and Study Habits.
• A Statistical Comparison of Local Public Transportation Options.
• Survey on Dietary Habits and Physical Health Among Teenagers.
• Analyzing the Popularity of Various Music Genres in School.
• The Impact of Sleep on Academic Performance: A Statistical Approach.
• Statistical Study on the Use of Technology in Education.
• Comparing Athletic Performance Across Different Sports.
• Trends in Social Media Usage Among High School Students.
• The Effect of Part-Time Jobs on Student Academic Achievement.

Statistical Survey Topics

• Public Opinion on Environmental Conservation Efforts.
• Consumer Preferences in the Fast Food Industry.
• Attitudes Towards Online Learning vs. Traditional Classroom Learning.
• Survey on Workplace Satisfaction and Productivity.
• Public Health: Attitudes Towards Vaccination.
• Trends in Mobile Phone Usage and Preferences.
• Community Response to Local Government Policies.
• Consumer Behavior in Online vs. Offline Shopping.
• Perceptions of Public Safety and Law Enforcement.
• Social Media Influence on Political Opinions.

Statistical Experiment Ideas

• The Effect of Light on Plant Growth.
• Memory Retention: Visual vs. Auditory Information.
• Caffeine Consumption and Cognitive Performance.
• The Impact of Exercise on Stress Levels.
• Testing the Efficacy of Natural vs. Chemical Fertilizers.
• The Influence of Color on Mood and Perception.
• Sleep Patterns: Analyzing Factors Affecting Sleep Quality.
• The Effectiveness of Different Types of Water Filters.
• Analyzing the Impact of Room Temperature on Concentration.
• Testing the Strength of Different Brands of Batteries.

Easy Stats Project Ideas

• Average Daily Screen Time Among Students.
• Analyzing the Most Common Birth Months.
• Favorite School Subjects Among Peers.
• Average Time Spent on Homework Weekly.
• Frequency of Public Transport Usage.
• Comparison of Pet Ownership in the Community.
• Favorite Types of Movies or TV Shows.
• Daily Water Consumption Habits.
• Common Breakfast Choices and Their Nutritional Value.
• Steps Count: A Week-Long Study.

Business Ideas for Statistics Project

• Analyzing Customer Satisfaction in Retail Stores.
• Market Analysis of a New Product Launch.
• Employee Performance Metrics and Organizational Success.
• Sales Data Analysis for E-commerce Websites.
• Impact of Advertising on Consumer Buying Behavior.
• Analysis of Supply Chain Efficiency.
• Customer Loyalty and Retention Strategies.
• Trend Analysis in Social Media Marketing.
• Financial Risk Assessment in Investment Decisions.
• Market Segmentation and Targeting Strategies.

Socio-Economic Easy Statistics Project Ideas

• Income Inequality and Its Impact on Education.
• The Correlation Between Unemployment Rates and Crime Levels.
• Analyzing the Effects of Minimum Wage Changes.
• The Relationship Between Public Health Expenditure and Population Health.
• Demographic Analysis of Housing Affordability.
• The Impact of Immigration on Local Economies.
• Analysis of Gender Pay Gap in Different Industries.
• Statistical Study of Homelessness Causes and Solutions.
• Education Levels and Their Impact on Job Opportunities.
• Analyzing Trends in Government Social Spending.

Experiment Ideas for Statistics and Analysis

• Multivariate Analysis of Global Climate Change Data.
• Time-Series Analysis in Predicting Economic Recessions.
• Logistic Regression in Medical Outcome Prediction.
• Machine Learning Applications in Statistical Modeling.
• Network Analysis in Social Media Data.
• Bayesian Analysis of Scientific Research Data.
• The Use of Factor Analysis in Psychology Studies.
• Spatial Data Analysis in Geographic Information Systems (GIS).
• Predictive Analysis in Customer Relationship Management (CRM).
• Cluster Analysis in Market Research.

Conclusion: Navigating the World of Data Through Statistics

In this exploration of good statistics project ideas, we’ve ventured through various topics, from the straightforward to the complex, from personal finance to global climate change. These ideas are gateways to understanding the world of data and statistics, and platforms for cultivating critical thinking and analytical skills. Whether you’re a high school student, a college student, or a professional, engaging in these projects can deepen your appreciation of how statistics shapes our understanding of the world around us. These projects encourage exploration, inquiry, and a deeper engagement with the world of numbers, trends, and patterns – the essence of statistics.

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Household Debt Rose by $184 Billion in Q1 2024; Delinquency Transition Rates Increased Across All Debt Types

NEW YORK — The Federal Reserve Bank of New York’s Center for Microeconomic Data today issued its Quarterly Report on Household Debt and Credit . The report shows total household debt increased by $184 billion (1.1%) in the first quarter of 2024, to $17.69 trillion. The report is based on data from the New York Fed’s nationally representative Consumer Credit Panel .

The New York Fed also issued an accompanying Liberty Street Economics blog post examining credit card utilization and its relationship with delinquency. The Quarterly Report also includes a one-page summary of key takeaways and their supporting data points.

“In the first quarter of 2024, credit card and auto loan transition rates into serious delinquency continued to rise across all age groups,” said Joelle Scally, Regional Economic Principal within the Household and Public Policy Research Division at the New York Fed. “An increasing number of borrowers missed credit card payments, revealing worsening financial distress among some households.”

Mortgage balances rose by $190 billion from the previous quarter and was $12.44 trillion at the end of March. Balances on home equity lines of credit (HELOC) increased by $16 billion, representing the eighth consecutive quarterly increase since Q1 2022, and now stand at $376 billion. Credit card balances decreased by $14 billion to $1.12 trillion. Other balances, which include retail cards and consumer loans, also decreased by $11 billion. Auto loan balances increased by $9 billion, continuing the upward trajectory seen since 2020, and now stand at $1.62 trillion.

Mortgage originations continued increasing at the same pace seen in the previous three quarters, and now stand at $403 billion. Aggregate limits on credit card accounts increased modestly by $63 billion, representing a 1.3% increase from the previous quarter. Limits on HELOC grew by $30 billion and have grown by 14% over the past two years, after 10 years of observed declines.

Aggregate delinquency rates increased in Q1 2024, with 3.2% of outstanding debt in some stage of delinquency at the end of March. Delinquency transition rates increased for all debt types. Annualized, approximately 8.9% of credit card balances and 7.9% of auto loans transitioned into delinquency. Delinquency transition rates for mortgages increased by 0.3 percentage points yet remain low by historic standards.

Household Debt and Credit Developments as of Q1 2024

*Change from Q4 2023 to Q1 2024 ** Change from Q1 2023 to Q1 2024

Flow into Serious Delinquency (90 days or more delinquent)

About the Report

The Federal Reserve Bank of New York’s Household Debt and Credit Report provides unique data and insight into the credit conditions and activity of U.S. consumers. Based on data from the New York Fed’s Consumer Credit Panel , a nationally representative sample drawn from anonymized Equifax credit data, the report provides a quarterly snapshot of household trends in borrowing and indebtedness, including data about mortgages, student loans, credit cards, auto loans and delinquencies. The report aims to help community groups, small businesses, state and local governments and the public to better understand, monitor, and respond to trends in borrowing and indebtedness at the household level. Sections of the report are presented as interactive graphs on the New York Fed’s  Household Debt and Credit Report web page  and the full report is available for download.

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Covid-19 accelerated the digitalisation of payments

Key takeaways.

• The Covid-19 pandemic has boosted the use of digital and contactless payments.
• Cash in circulation reached a decade high due to a surge in demand for high-value banknotes, suggesting that cash was increasingly held as a store of value rather than for making payments.
• The pandemic has added to the motivations of central banks to develop central bank digital currencies (CBDCs).

Summary of latest developments 1

The Covid-19 pandemic accelerated the digitalisation of payments. The latest Red Book Statistics from the BIS Committee on Payments and Market Infrastructures (CPMI) show that consumers have shifted from physical cash to digital and contactless payment instruments at a rate unprecedented since the start of the Red Book Statistics. At the same time, and as in earlier stress episodes, the value of cash in circulation surged.

Non-cash payments

The pandemic 2 has made a marked impact on non-cash payments. 3 In particular, the total value of non-paper-based or digital credit transfers grew strongly in both advanced economies (AEs) and emerging market and developing economies (EMDEs). These payments include transfers initiated via online banking, a mobile banking app or an automated transfer. As a result, the growth in total credit transfer usage was so strong that the share of non-cash payments in total GDP sharply increased across the globe ( Graph 1 left-hand panel). This, together with a decline in the share of private consumption expenditure in GDP suggests a meaningful move away from cash payments.

In addition to the decline in cash payments, the growth in the number of card payments lost momentum or even declined in various jurisdictions ( Graph 1 centre panel). The shift away from cash and cards towards digital credit transfers is probably driven by a combination of ongoing trends and Covid-19-related developments. The latter include (i) the worldwide migration to working-from-home; (ii) temporary shutdowns of shops, hotels and restaurants; (iii) some merchants refusing cash payments; 4 (iv) the surge in e-commerce; 5 (v) the growth in digital person-to-person payments; 6 and (vi) the distribution of Covid-19 benefit payments by governments. 7

In all jurisdictions from which the CPMI collects contactless card data, the share of contactless payments in total card transactions increased in 2020 at its highest rate since 2015 ( Graph 1 right-hand panel). 8 This may be explained by public fears of contagion 9 and associated policy measures. For example, banks and card companies in many countries raised their value limits for contactless card payments in response to the pandemic. 10

In 2020, on average, AE residents made close to twice as many cashless payments as residents of EMDEs. Yet, both groups of countries are similar in that most of these payments were made using a debit or credit card ( Graph 1 centre panel). Also, as credit transfers are more often used for settling payments of higher value, all over the world, credit transfers accounted for the largest share of cashless payments in terms of value ( Graph 1 left-hand panel).

Click here for an interactive version of this graph

Cash withdrawals and cash holdings

The decline in cash usage during the Covid-19 pandemic is also reflected in the cash withdrawals data. Compared with 2019, both the number and value of cash withdrawals dropped in 2020 in most countries ( Graph 2 left-hand panel). Consumers made between 10 and 25 cash withdrawals on average in most CPMI jurisdictions in 2020. Generally, the total number of cash withdrawals declined by 23%, exceeding the 10% decline in value. This suggests that consumers took out cash less frequently, but when they did, they withdrew larger amounts (see also Graph 2 centre panel). The decline in the number of withdrawals might be due to fewer commuting and shopping trips 11 during the pandemic and a tendency to avoid the use of automated teller machines (ATMs) or to visit bank branches because of fear of being infected with the virus. 12 However, country differences in withdrawals are large, with five annual withdrawals in China and India and 50 in Saudi Arabia ( Graph 2 right-hand panel). In terms of value, cash withdrawals were the lowest in Sweden and the Netherlands (3% and 4% of GDP, respectively) and highest in China and Russia (39% and 26%, respectively).

The increase in the average withdrawal value globally is probably driven, in part, by the public's desire to hold cash for precautionary reasons, as the value of coins and banknotes in circulation outside banks surged in many jurisdictions in 2020. Even in jurisdictions where the value of cash in circulation had been declining prior to the pandemic, the outstanding cash value grew further or stabilised in 2020 ( Graph 3 left-hand panel). In particular, the demand for high-value denominations, which are typically held as a store of value, increased further, and more strongly than for other notes and coins ( Graph 3 centre and right-hand panel). Apparently, cash was increasingly held as a store of value rather than used for transactional purposes. This suggests that consumers accumulated cash as a precautionary measure, for example against potential disruptions to the availability of payment infrastructures or potential bank closures. Similar cash hoarding behaviour was observed during earlier crises or periods of uncertainty, such as the Y2K episode or the Great Financial Crisis. 13 Moreover, in some jurisdictions the surge in cash in circulation could be explained partly by the increase in aggregate disposable household income due to Covid-19-related income support measures and tax and loan repayment deferrals, and by falling interest rates, which further reduced the opportunity costs of holding cash in a physical form instead of in a bank account. 14

The role of cash post-pandemic

How long these changes in cash usage will persist after the pandemic is unclear. As a means of payment, cash lost ground to digital and contactless methods of payment in 2020, while the demand for cash as a store of value rose precipitously. An ECB survey of all euro area countries showed that 87% of the respondents who had made fewer payments in cash during the pandemic would continue to do so when the coronavirus crisis is over. 15 Whether the pandemic will have a similar prolonged effect on cash hoarding remains to be seen. Earlier research shows that the growth in cash holdings has slowed after a crisis or period of uncertainty had passed. 16

Although it changed the public's payment behaviour, the pandemic does not appear to have affected the public's perception of cash being a safe haven. Many central banks are exploring the potential of and need for a digital form of cash, a retail central bank digital currency (retail CBDC) that would provide consumers with the same protection as cash does today, while allowing them to make payments without carrying physical banknotes and coins. A 2020 BIS survey among more than 60 central banks (Boar and Wehrli (2021)) showed that the pandemic added to the motivations of central banks to develop retail CBDCs, especially with the aim of giving access to central bank money during times of emergency and of complementing cash and in-person payment methods when social distancing is required. Since then, retail CBDCs have been launched in the Bahamas, the Eastern Caribbean and Nigeria, and retail CBDC pilots are under way in 14 other jurisdictions. 17 Whether a retail CBDC, if issued, will change the use of cash in its physical form, either as a means of payment or as a store of value, will depend on central bank decisions as to the CBDC's design and the perceived value for households and businesses. These decisions and the degree and speed of adoption may differ among jurisdictions depending on their current payment infrastructures and instruments.

This commentary was written by Anneke Kosse and Robert Szemere. We are grateful to Ilaria Mattei and Ismail Mustafi for their excellent research assistance and we would like to thank Bilyana Bogdanova, Jenny Hancock, Stijn Claessens, Tara Rice and Takeshi Shirakami for their valuable comments.

Auer, R, G Cornelli and J Frost (2020a): " Covid-19, cash, and the future of payments ", BIS Bulletin , no 3, April.

--- (2021): " Rise of the central bank digital currencies: drivers, approaches and technologies ", updated data set, October.

Auer, R, J Frost, T Lammer, T Rice and A Wadsworth (2020b): "Inclusive payments for the post-pandemic world", SUERF Policy Note , no 193, September.

Akana, T (2021): "Changing US consumer payment habits during the COVID-19 crisis", Journal of Payments Strategy & Systems , vol 15, no 3, pp 234–43.

Alfonso, V, C Boar, J Frost, L Gambacorta and J Liu (2021): " E-commerce in the pandemic and beyond ", BIS Bulletin , no 36, 12 January.

Boar, C and A Wehrli (2021): " Ready, steady, go? – Results of the third BIS survey on central bank digital currency ", BIS Papers , no 114, January.

ECB (2020): " Study on the payment attitudes of consumers in the euro area (SPACE) ", December.

Chen, H, M Stratheam and M Voia (2021): "Consumer cash withdrawal behaviour: branch networks and online financial innovation", Bank of Canada, Staff Working Papers , no 28, June.

Guttmann, R, C Pavlik, B Ung and G Wang (2021): " Cash demand during Covid-19 ", RBA Bulletin , March.

IMF (2021): " Policy response to Covid-19 Policy Tracker ", last updated on 2 July.

Judson, R (2017): "The death of cash? Not so fast: demand for U.S. currency at home and abroad, 1990–2016", Conference Paper for International Cash Conference 2017 – War on Cash: Is there a Future for Cash?, April.

NFCW (2021): " Table: Contactless payment transaction limit increases around the world ", last updated on 27 August.

Rösl, G and F Seitz (2021): " Cash and crises: No surprises by the virus ", IMFS Working Paper Series , no150.

Visa (2021): " The Visa Back to business study 2021 Outlook ".

1     This commentary is based on the CPMI Red Book data published for 27 jurisdictions for the period 2012–20. Advanced economies (AEs) refer to Australia, Belgium, Canada, the euro area, France, Germany, Italy, Japan, the Netherlands, Spain, Sweden, Switzerland, the United Kingdom and the United States. Emerging market and developing countries (EMDEs) refer to Argentina, Brazil, China, Hong Kong SAR, India, Indonesia, Korea, Mexico, Russia, Saudi Arabia, Singapore, South Africa and Turkey. In the case of missing observations, data are estimated using the average growth rate of all other countries.

2    Covid-19 was first identified in December 2019 and declared a global pandemic by the World Health Organization (WHO) on 11 March 2020.

3    Non-cash payments refer to payments made using a payment instrument other than cash, such as payment cards, credit transfers, direct debits and cheques. With the exception of payments made using a cheque or paper-based credit transfer, all non-cash payments are digital payments.

4    See, for example, ECB (2020).

5    See Alfonso et al (2021).

6    For example, in the United States, person-to-person and mobile payments increased by 6% and 8%, respectively, during 2020 and the first months of 2021 (Akana (2021)).

7    IMF (2021).

8    Data on contactless card payments have been collected since 2012 but for most countries in the sample, data are available only from 2014.

9     According to ECB (2020), on average, 38% of respondents in the euro area avoided cash for fear of being infected with Covid-19 using banknotes and coins.

10    See NFCW (2021).

11    Chen et al (2021) demonstrate how some consumers try to minimise the time costs of withdrawing cash by making cash withdrawals opportunistically, eg on their commute to work.

12    See, for example, Auer et al (2020a) and (2020b).

13    See, for example, Judson (2017) and Rösl and Seitz (2021).

14    Guttmann et al (2021).

15    See ECB (2020). Similarly, a recent survey conducted by Visa showed that 65% of respondents planned to use contactless card payments as much or even more than before they were vaccinated, while 16% expected to revert to their previous payment habits (Visa (2021)).

16    See, for example, Judson (2017) and Rösl and Seitz (2021).

17    See Auer et al (2021).

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• Half of Latinas Say Hispanic Women’s Situation Has Improved in the Past Decade and Expect More Gains

Government data shows gains in education, employment and earnings for Hispanic women, but gaps with other groups remain

Table of contents.

• Assessing the progress of Hispanic women in the last 10 years
• Views of Hispanic women’s situation in the next 10 years
• Views on the gender pay gap
• Latinas’ educational attainment
• Latinas’ labor force participation
• Latinas’ earnings
• Latinas as breadwinners in their relationships
• Bachelor’s degrees among Latinas
• Labor force participation rates among Latinas
• Occupations among working Latinas
• Earnings among Latinas
• Latinas as breadwinners in 2022
• Appendix: Supplemental charts and tables
• Acknowledgments
• The American Trends Panel survey methodology
• Methodology for the analysis of the Current Population Survey

This report explores Latinas’ economic and demographic progress in the last two decades – and their perceptions of that progress – using several data sources.

The first is a Pew Research Center survey of 5,078 Hispanic adults, including 2,600 Hispanic women. Respondents were asked whether U.S. Latinas saw progress in their situation in the last decade, whether they expected any in the future decade, and how big a problem the U.S. gender pay gap is. The survey was conducted from Nov. 6 to 19, 2023, and includes 1,524 respondents from the American Trends Panel (ATP) and an additional 3,554 from Ipsos’ KnowledgePanel .

Respondents on both panels are recruited through national, random sampling of residential addresses. Recruiting panelists by mail ensures that nearly all U.S. adults have a chance of selection. This gives us confidence that any sample can represent the whole population, or in this case the whole U.S. Hispanic population. (For more information, watch our Methods 101 explainer on random sampling.) For more information on this survey, refer to the American Trends Panel survey methodology and the topline questionnaire .

The second data source is the U.S. Census Bureau’s and Bureau of Labor Statistics’ 2003, 2008, 2013, 2018 and 2023 Current Population Survey (CPS) Monthly and Annual Social and Economic Supplement (ASEC) data series, provided through the Integrated Public Use Microdata Series (IPUMS) from the University of Minnesota.

The CPS Monthly microdata series was used only to calculate median hourly earnings for those ages 25 to 64 years old and who were not self-employed. Medians were calculated for the whole year by considering all wages reported in that year, regardless of month. Median wages were then adjusted to June 2023 dollars using the Chained Consumer Price Index for All Urban Consumers for June of each year. For more information on the demographic analysis, refer to the methodology for the analysis of the Current Population Survey .

The terms  Hispanic  and  Latino  are used interchangeably in this report.

The terms Latinas and Hispanic women are used interchangeably throughout this report to refer to U.S. adult women who self-identify as Hispanic or Latino, regardless of their racial identity.

Foreign born  refers to persons born outside of the 50 U.S. states or the District of Columbia. For the purposes of this report, foreign born also refers to those born in Puerto Rico. Although individuals born in Puerto Rico are U.S. citizens by birth, they are grouped with the foreign born because they are born into a Spanish-dominant culture and because on many points their attitudes, views and beliefs are much closer to those of Hispanics born outside the U.S. than to Hispanics born in the 50 U.S. states or D.C., even those who identify themselves as being of Puerto Rican origin.

The terms  foreign born  and  immigrant  are used interchangeably in this report. Immigrants are also considered first-generation Americans.

U.S. born  refers to persons born in the 50 U.S. states or D.C.

Second generation  refers to people born in the 50 U.S. states or D.C. with at least one immigrant parent.

Third or higher generation  refers to people born in the 50 U.S. states or D.C., with both parents born in the 50 U.S. states or D.C.

Throughout this report, Democrats are respondents who identify politically with the Democratic Party or those who are independent or identify with some other party but lean toward the Democratic Party. Similarly, Republicans are those who identify politically with the Republican Party and those who are independent or identify with some other party but lean toward the Republican Party.

White, Black  and  Asian each include those who report being only one race and are not Hispanic.

Civilians are those who were not in the armed forces at the time of completing the Current Population Survey.

Those participating in the labor force either were at work; held a job but were temporarily absent from work due to factors like vacation or illness; were seeking work; or were temporarily laid off from a job in the week before taking the Current Population Survey. In this report, the labor force participation rate is shown only for civilians ages 25 to 64.

The phrases living with children or living with their own child describe individuals living with at least one of their own stepchildren, adopted children or biological children, regardless of the children’s ages. The phrases not living with children or not living with their own child describe individuals who have no children or whose children do not live with them.

Occupation and occupational groups describe the occupational category of someone’s current job, or – if unemployed – most recent job. In this report we measure occupation among civilians participating in the labor force. Occupational groups are adapted from the U.S. Census Bureau’s occupation classification list from 2018 onward .

Hourly earnings , hourly wages and hourly pay all refer to the amount an employee reported making per hour at the time of taking the Current Population Survey where they were employed by someone else. Median hourly wages were calculated only for those ages 25 to 64 who were not self-employed. Calculated median hourly wages shared in this report are adjusted for inflation to 2023. (A median means that half of a given population – for example, Hispanic women – earned more than the stated wage, and half earned less.)

Breadwinners refer to those living with a spouse or partner, both ages 25 to 64, who make over 60% of their and their partner’s combined, positive income from all sources. Those in egalitarian relationships make 40% to 60% of the combined income. For those who make less than 40% of the combined income, their spouse or partner is the breadwinner . This analysis was conducted among both opposite-sex and same-sex couples.

Half of Latinas say the situation of Hispanic women in the United States is better now than it was 10 years ago, and a similar share say the situation will improve in the next 10 years.

Still, 39% of Latinas say that the situation has stayed the same, and 34% say it will not change in the next 10 years. Two-thirds (66%) say the gender pay gap – the fact that women earn less money, on average, than men – is a big problem for Hispanic women today, according to new analysis of Pew Research Center’s National Survey of Latinos.

At 22.2 million, Latinas account for 17% of all adult women in the U.S. today. Their population grew by 5.6 million from 2010 to 2022, the largest numeric increase of any major female racial or ethnic group. 1

Latinas’ mixed assessments reflect their group’s gains in education and at work over the last two decades, but also stalled progress in closing wage gaps with other groups.

• Hispanic women are more likely to have a bachelor’s degree today (23% in 2023) than they were in 2013 (16%). More Hispanic women than ever are also completing graduate degrees .
• Hispanic women have increased their labor force participation rate by 4 percentage points, from 65% in 2013 to 69% in 2023.
• The median hourly wage of Hispanic women has increased by 17% in the last decade. In 2023, their median hourly wage was $19.23, up from $16.47 in 2013 (in 2023 dollars).

Despite this progress, Hispanic women’s pay gaps with their peers haven’t significantly improved in recent years:

• The gender pay gap among Hispanics persists with no significant change. In 2023, Hispanic women earned 85 cents (at the median) for every dollar earned by Hispanic men, compared with 89 cents per dollar in 2013 (and 87 cents per dollar in 2003).
• Hispanic women continue to lag non-Hispanic women in earnings , with no significant improvement in the past decade. In 2023, the median Hispanic woman made 77 cents for each dollar earned by the median non-Hispanic woman, compared with 75 cents per dollar in 2013.
• The pay gap between Hispanic women and White men has changed only slightly . In 2023, Hispanic women earned 62 cents of every dollar earned by non-Hispanic White men, up from 59 cents per dollar in 2013.

In addition, Hispanic women lag Hispanic men and non-Hispanic women in labor force participation, and they lag non-Hispanic women in educational attainment. Read more in Chapter 2 .

Among Latinas who are employed, about half (49%) say their current job is best described as “just a job to get them by.” Fewer see their job as a career (30%) or a steppingstone to a career (14%).

Pew Research Center’s bilingual 2023 National Survey of Latinos – conducted Nov. 6-19, 2023, among 5,078 Hispanic adults, including 2,600 Hispanic women – explores what it’s like to be a Latina in the U.S. today. This report uses findings from our 2023 survey as well as demographic and economic data from the Current Population Survey.

The following chapters take a closer look at:

• How Latinas view the progress and future situation of Hispanic women in the U.S.
• What government data tells us about Latinas’ progress in the labor market, earnings and educational attainment
• How Latinas’ educational and economic outcomes vary

For additional survey findings on what it means to be a Latina in the U.S. today and the daily pressures they face, read our report “A Majority of Latinas Feel Pressure To Support Their Families or To Succeed at Work.”

• Latinas’ population size and growth rate from 2010 to 2022 were calculated using the 2010 and 2022 American Community Surveys, accessed through IPUMS. The rest of the demographic analysis in this post uses data from the Current Population Survey. ↩

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Why writing by hand beats typing for thinking and learning

Jonathan Lambert

If you're like many digitally savvy Americans, it has likely been a while since you've spent much time writing by hand.

The laborious process of tracing out our thoughts, letter by letter, on the page is becoming a relic of the past in our screen-dominated world, where text messages and thumb-typed grocery lists have replaced handwritten letters and sticky notes. Electronic keyboards offer obvious efficiency benefits that have undoubtedly boosted our productivity — imagine having to write all your emails longhand.

To keep up, many schools are introducing computers as early as preschool, meaning some kids may learn the basics of typing before writing by hand.

But giving up this slower, more tactile way of expressing ourselves may come at a significant cost, according to a growing body of research that's uncovering the surprising cognitive benefits of taking pen to paper, or even stylus to iPad — for both children and adults.

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In kids, studies show that tracing out ABCs, as opposed to typing them, leads to better and longer-lasting recognition and understanding of letters. Writing by hand also improves memory and recall of words, laying down the foundations of literacy and learning. In adults, taking notes by hand during a lecture, instead of typing, can lead to better conceptual understanding of material.

"There's actually some very important things going on during the embodied experience of writing by hand," says Ramesh Balasubramaniam , a neuroscientist at the University of California, Merced. "It has important cognitive benefits."

While those benefits have long been recognized by some (for instance, many authors, including Jennifer Egan and Neil Gaiman , draft their stories by hand to stoke creativity), scientists have only recently started investigating why writing by hand has these effects.

A slew of recent brain imaging research suggests handwriting's power stems from the relative complexity of the process and how it forces different brain systems to work together to reproduce the shapes of letters in our heads onto the page.

Your brain on handwriting

Both handwriting and typing involve moving our hands and fingers to create words on a page. But handwriting, it turns out, requires a lot more fine-tuned coordination between the motor and visual systems. This seems to more deeply engage the brain in ways that support learning.

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"Handwriting is probably among the most complex motor skills that the brain is capable of," says Marieke Longcamp , a cognitive neuroscientist at Aix-Marseille Université.

Gripping a pen nimbly enough to write is a complicated task, as it requires your brain to continuously monitor the pressure that each finger exerts on the pen. Then, your motor system has to delicately modify that pressure to re-create each letter of the words in your head on the page.

"Your fingers have to each do something different to produce a recognizable letter," says Sophia Vinci-Booher , an educational neuroscientist at Vanderbilt University. Adding to the complexity, your visual system must continuously process that letter as it's formed. With each stroke, your brain compares the unfolding script with mental models of the letters and words, making adjustments to fingers in real time to create the letters' shapes, says Vinci-Booher.

That's not true for typing.

To type "tap" your fingers don't have to trace out the form of the letters — they just make three relatively simple and uniform movements. In comparison, it takes a lot more brainpower, as well as cross-talk between brain areas, to write than type.

Recent brain imaging studies bolster this idea. A study published in January found that when students write by hand, brain areas involved in motor and visual information processing " sync up " with areas crucial to memory formation, firing at frequencies associated with learning.

"We don't see that [synchronized activity] in typewriting at all," says Audrey van der Meer , a psychologist and study co-author at the Norwegian University of Science and Technology. She suggests that writing by hand is a neurobiologically richer process and that this richness may confer some cognitive benefits.

Other experts agree. "There seems to be something fundamental about engaging your body to produce these shapes," says Robert Wiley , a cognitive psychologist at the University of North Carolina, Greensboro. "It lets you make associations between your body and what you're seeing and hearing," he says, which might give the mind more footholds for accessing a given concept or idea.

Those extra footholds are especially important for learning in kids, but they may give adults a leg up too. Wiley and others worry that ditching handwriting for typing could have serious consequences for how we all learn and think.

What might be lost as handwriting wanes

The clearest consequence of screens and keyboards replacing pen and paper might be on kids' ability to learn the building blocks of literacy — letters.

"Letter recognition in early childhood is actually one of the best predictors of later reading and math attainment," says Vinci-Booher. Her work suggests the process of learning to write letters by hand is crucial for learning to read them.

"When kids write letters, they're just messy," she says. As kids practice writing "A," each iteration is different, and that variability helps solidify their conceptual understanding of the letter.

Research suggests kids learn to recognize letters better when seeing variable handwritten examples, compared with uniform typed examples.

This helps develop areas of the brain used during reading in older children and adults, Vinci-Booher found.

"This could be one of the ways that early experiences actually translate to long-term life outcomes," she says. "These visually demanding, fine motor actions bake in neural communication patterns that are really important for learning later on."

Ditching handwriting instruction could mean that those skills don't get developed as well, which could impair kids' ability to learn down the road.

"If young children are not receiving any handwriting training, which is very good brain stimulation, then their brains simply won't reach their full potential," says van der Meer. "It's scary to think of the potential consequences."

Many states are trying to avoid these risks by mandating cursive instruction. This year, California started requiring elementary school students to learn cursive , and similar bills are moving through state legislatures in several states, including Indiana, Kentucky, South Carolina and Wisconsin. (So far, evidence suggests that it's the writing by hand that matters, not whether it's print or cursive.)

Slowing down and processing information

For adults, one of the main benefits of writing by hand is that it simply forces us to slow down.

During a meeting or lecture, it's possible to type what you're hearing verbatim. But often, "you're not actually processing that information — you're just typing in the blind," says van der Meer. "If you take notes by hand, you can't write everything down," she says.

The relative slowness of the medium forces you to process the information, writing key words or phrases and using drawing or arrows to work through ideas, she says. "You make the information your own," she says, which helps it stick in the brain.

Such connections and integration are still possible when typing, but they need to be made more intentionally. And sometimes, efficiency wins out. "When you're writing a long essay, it's obviously much more practical to use a keyboard," says van der Meer.

Still, given our long history of using our hands to mark meaning in the world, some scientists worry about the more diffuse consequences of offloading our thinking to computers.

"We're foisting a lot of our knowledge, extending our cognition, to other devices, so it's only natural that we've started using these other agents to do our writing for us," says Balasubramaniam.

It's possible that this might free up our minds to do other kinds of hard thinking, he says. Or we might be sacrificing a fundamental process that's crucial for the kinds of immersive cognitive experiences that enable us to learn and think at our full potential.

Balasubramaniam stresses, however, that we don't have to ditch digital tools to harness the power of handwriting. So far, research suggests that scribbling with a stylus on a screen activates the same brain pathways as etching ink on paper. It's the movement that counts, he says, not its final form.

Jonathan Lambert is a Washington, D.C.-based freelance journalist who covers science, health and policy.

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