Topic hub
Inferential Statistics
Hypothesis tests, confidence intervals, p-values, and the reasoning for drawing conclusions about a population from a limited sample.
Chi-Square Distribution: Shape, Table & Density
The chi-square distribution explained: shape, formula, and how to read the chi square value table. Covers the chi squared probability density function.
Chi-Square Test Formula, Examples & How to Use It
Learn the chi-square test formula, chi squared equation, and step-by-step worked examples to test independence or goodness-of-fit with categorical data.
Confidence Interval Formula: Calculate a 95% CI
Learn the confidence interval formula and how to calculate a 95% CI step by step, with a fully worked example, calculator embed, and common-mistake guide.
Effect Size: What It Means & How to Interpret It
Understand what effect size means in statistics, how to calculate Cohen's d for group comparisons, and how to interpret effect sizes in statistical research.
Kruskal-Wallis Analysis of Variance: Formula & Uses
Learn the Kruskal-Wallis analysis of variance: formula, step-by-step example, assumptions, and when to use it over one-way ANOVA.
Mann-Whitney U Test: Formula & When to Use It
Learn the Mann-Whitney U test formula, how it ranks values to compare two independent groups, and when to use this Wilcoxon rank-sum alternative to the t-test.
Null Hypothesis: Definition, Examples & How to State It
A null hypothesis states there is no effect or difference. Learn what is a null hypothesis, see null hypothesis examples, and how to state one.
One-Way ANOVA: When and How to Use It
Learn when and how to use one-way ANOVA to compare means across three or more groups. Step-by-step formula, worked example, assumptions, and FAQ.
P-Value: What It Is & How to Calculate It
A p value is the probability of a result as extreme as yours if the null hypothesis is true. Learn the p-value formula and how to calculate p value.
Paired T-Test: Formula, Equation & Worked Example
The paired t-test formula tests differences in related measurements; this guide also covers the two-sample t-test equation with fully worked examples.
Paired vs. Independent T-Test: Which One Do You Need?
Learn when to use a t-test and paired t-test vs. an independent t-test, with worked examples, the decision rule, and step-by-step formulas for each.
Post-Hoc Tests: Tukey, Bonferroni & When to Use Them
Post-hoc tests identify which group means differ after a significant ANOVA. Compare Tukey HSD, Bonferroni, Scheffé, and Dunnett with worked examples.
Statistical Power: What It Means and How to Calculate It
Learn what statistical power means, how to calculate it, and why 0.80 is the standard target. Includes a fully worked example and power analysis guide.
Test Statistic: Formula, Critical Values & df
A test statistic is the number a hypothesis test produces to compare a sample result against a critical value and decide whether to reject the null hypothesis.
Two-Way ANOVA: Main Effects and Interaction Effects
Learn two-way ANOVA step by step: test two factors at once, understand main effects and interaction effects, and read a full worked numeric example.
Type I and Type II Errors: Definition and Examples
Learn what type I and type II errors are in hypothesis testing, how they differ, and how to reduce them. Includes worked examples and a comparison table.
Which Statistical Test Should You Use? A Decision Guide
Learn which statistical test to use based on your data type, research question, and sample size. Covers t-test, ANOVA, chi-square, regression, and more.
Z-Score: Formula, How to Calculate & What It Means
A z score measures standard deviations from the mean. Learn the z score formula, how to calculate z score step-by-step, and how to read a z-score chart.