DSRT 734: How to Choose an Inferential Statistical Test

Start with the inferential question, not the test menu

A method-selection chart is useful only after the research target is explicit. Is the analysis estimating one population value, comparing groups, testing change within the same units, studying association between categorical variables, or modeling a quantitative outcome? The same dataset can answer different questions with different methods, so variable names alone do not determine the procedure.

Write the target in parameter language. Examples include a population mean, a difference in means, a population proportion, a difference in proportions, an odds relationship, a correlation, or a regression coefficient. Then ask whether estimation, hypothesis testing, prediction, or explanation is the principal goal. This prevents the analyst from selecting a method merely because it is familiar or because software places it prominently in a menu.

Use the outcome variable to narrow the method family

A quantitative outcome may support methods that compare means or model continuous variation, provided the design and assumptions fit. A binary or multicategory outcome requires procedures that respect categorical information. Counts, rates, bounded scales, and strongly skewed measurements may need special treatment because their distributions and variance patterns differ from those of an unbounded continuous response.

The explanatory side matters too. A categorical explanatory variable defines groups or conditions. A quantitative predictor supports analysis of how the outcome changes across predictor values. Multiple predictors invite regression modeling, but adding variables should follow the research design and a reasoned model, not a search for a favorable result.

Count the groups and identify dependence

A one-sample procedure compares a sample parameter with a reference value. A two-sample procedure compares separate groups. A paired procedure analyzes linked observations such as before-and-after measurements from the same units or deliberately matched pairs. Analysis of variance provides a framework for comparing means across more than two conditions and for richer designs, but its model and assumptions must match the data.

Do not confuse two rows with two independent observations. Repeated measures, clusters, teams, organizations, and matched units create dependence. Using an independent-samples method on paired or clustered data can misstate uncertainty. The design—not the number of spreadsheet columns—determines whether observations contribute independent information.

One-sample, independent two-sample, and paired procedures

A one-sample t procedure can estimate or test a population mean relative to a reference when its conditions are reasonable. An independent two-sample t procedure addresses a difference between two population means from separate groups. A paired t procedure addresses the mean of within-pair differences. The paired analysis is not simply a two-sample analysis with smaller groups; the difference score is the observational unit.

For proportions, corresponding one- and two-sample methods depend on binary outcomes and adequate sampling conditions. Small samples or sparse events may require exact or specialized approaches. Always pair the method name with the target parameter and observation structure so the reader can see why it answers the research question.

When analysis of variance enters the decision

Analysis of variance evaluates structured differences in quantitative outcomes across multiple groups or conditions through a model of explained and unexplained variation. A significant omnibus result indicates evidence that not all modeled means are equal; it does not identify every pairwise difference. Planned contrasts or multiple-comparison procedures must fit the research question and account for the family of comparisons.

ANOVA is not exempt from design constraints. Independence, error structure, variance behavior, distributional diagnostics, balance, and influential observations matter. Factorial designs can estimate main effects and interactions, but an interaction changes how main effects should be interpreted. Repeated-measures or clustered designs require methods that represent within-unit dependence rather than an ordinary one-way analysis.

Use chi-square methods for categorical count structures

Chi-square goodness-of-fit methods compare observed category counts with a specified distribution. Chi-square tests of independence examine whether two categorical variables are associated in a contingency table. The data for the calculation are counts, even when percentages are displayed. Expected cell counts, independence of observations, category definitions, and sampling design affect validity.

A significant chi-square result establishes evidence of association, not its direction, practical importance, or causal origin. Follow with transparent proportions and an appropriate measure of association. When expected counts are too sparse, combining categories without a substantive rationale can distort the question; an exact method or a different model may be more defensible.

Distinguish correlation from regression

Correlation summarizes the direction and strength of association between two variables under a chosen correlation model. Simple linear regression models the expected quantitative outcome as a function of a predictor and estimates an intercept, slope, and residual variation. Multiple regression extends that model to more predictors, but its coefficients are conditional on the included variables and coding.

Neither correlation nor regression automatically establishes causation. Linearity, independence, residual behavior, influential points, measurement quality, omitted variables, and the range of observed data matter. Prediction beyond the observed predictor range is extrapolation and can be unreliable even when the fitted line looks strong. Choose the method based on the intended estimate and design, not because one produces a smaller p-value.

Consider nonparametric alternatives for the right reason

Nonparametric methods can be useful when the inferential target, scale, distribution, sample size, outliers, or model conditions make a standard parametric procedure unsuitable. Examples include rank-based comparisons and permutation approaches. They do not remove every assumption, and they may target a different population quantity than the parametric method they are said to replace.

Do not choose a nonparametric method simply because a normality test crossed a threshold, and do not assume it always tests medians. Examine the shape, measurement scale, design, estimand, sample size, and robustness of the candidate procedure. State what the chosen method actually estimates or tests.

Treat assumptions as questions about the data-generating process

Assumptions are not a box to check after the result is known. Independence comes mainly from design. Distributional and variance conditions can be examined through plots, residuals, domain knowledge, and sensitivity analysis. Expected counts matter for contingency tables. Linearity and residual structure matter for linear models. Outliers can be errors, valid extreme cases, or evidence that the model is incomplete.

A formal assumption test is only one piece of evidence and can be underpowered in small samples or overly sensitive in large samples. Explain why the method is reasonable, what diagnostics show, and whether an alternative produces a materially different conclusion. If the design violates a core condition, changing the method cannot always repair the inference.

Illustrative example: choosing among comparison methods

A fictional organization measures decision time in minutes for analysts using three training formats. If different analysts are independently assigned to the three formats and the outcome is quantitative, an ANOVA model may address whether the population mean decision times differ, subject to design and model checks. If the same analysts try all three formats, ordinary one-way ANOVA would ignore within-person dependence; a repeated-measures approach or another method representing that structure is needed.

If the outcome were instead whether each analyst completed the decision within a quality threshold, the outcome would be binary and a mean-comparison method would no longer match the question. If the research target were the relationship between experience in years and decision time, regression or correlation might enter the framework. The example uses invented conditions and is not an official B03 assignment.

A practical test-selection sequence

First state the population parameter or relationship. Second classify the outcome. Third count groups or conditions and identify whether observations are independent, paired, repeated, or clustered. Fourth identify the explanatory-variable structure and whether adjustment is part of the research question. Fifth list assumptions and the evidence available to assess them. Sixth decide whether the desired output is an estimate, comparison, association, prediction, or model coefficient. Finally, compare candidate methods and explain why the selected procedure best represents the design.

Related DSRT 734 questions

• DSRT 734: Choosing a T-Test for Two Independent Branches
• DSRT 734: Comparing Three Product Weights in JASP
• DSRT 734: Comparing Midterm and Final Exam Scores in JASP
• DSRT 734: Testing Baseball and Football Throwing Distances for Correlation
• DSRT 734: Choosing a Test for Disease Prevalence by Gender
• DSRT 734: Testing Gender and COVID Diagnosis in JASP
• DSRT 734: Choosing a Test From the Blue Versus White Scatterplot — Item 14
• DSRT 734: Choosing a Test From the Blue Versus White Scatterplot — Item 15
• DSRT 734: Testing Two Variables for Correlation in JASP
• DSRT 734: Comparing Teacher Evaluations Before and After Training
• DSRT 734: Comparing Homework Hours Across Three Student Teams
• DSRT 734: Testing the Relationship Between Reading Time and GPA
• DSRT 734: Choosing a Test for Gender and Disease
• DSRT 734: Comparing Grades From Different Students Across Two Years
• DSRT 734: Testing Hospital Rank Against Physician Count
• DSRT 734: Choosing a Test From the Blue Versus White Scatterplot — Item 23
• DSRT 734: Comparing Employee Knowledge Before and After Training in JASP
• DSRT 734: Testing Chronic Disease Prevalence by Gender in JASP

Related DSRT 734 resources

• DSRT 734 Inferential Statistics in Decision-Making at University of the Cumberlands
• DSRT 734: From a Research Question to Hypotheses and Study Design
• DSRT 734: Interpreting P-Values, Confidence Intervals, and Effect Sizes