How to Choose the Right Statistical Test: A Decision Flowchart for Every Common Scenario

You can identify the correct statistical test by answering three questions about your data: **Question 1: What is your research question?** Are you comparing groups (is there a difference?), testing a relationship (are these variables associated?), or predicting an outcome (can X predict Y)? **Question 2: What type of data do you have?** Continuous/numerical (height, weight, test scores, income), categorical/nominal (gender, treatment group, yes/no), or ordinal (Likert scales, rankings)? **Question 3: How many groups or variables?** One group vs a known value, two groups, three+ groups, or two continuous variables? The answers map directly to specific tests: - Comparing 2 group means (continuous data): independent samples t-test - Comparing 3+ group means (continuous data): one-way ANOVA - Comparing 2 related/paired means: paired t-test - Testing association between 2 categorical variables: chi-square test of independence - Testing relationship between 2 continuous variables: Pearson correlation - Predicting a continuous outcome from one or more predictors: linear regression - Predicting a categorical outcome (yes/no): logistic regression Snap a photo of any stats problem and StatsIQ identifies the correct test, explains why that test applies, and walks through the solution step by step.

Here is the full flowchart. Start at the top and follow the branches. **Branch 1: Comparing group means (continuous dependent variable)** → How many groups? 2 groups → Are they independent or paired? Independent → Independent t-test. Paired/matched → Paired t-test. 3+ groups → One-way ANOVA. If significant, follow with post-hoc tests (Tukey HSD) to determine which groups differ. 2+ groups with 2+ factors → Two-way (factorial) ANOVA. **Branch 2: Testing association between categorical variables** → Both variables categorical? Yes → Chi-square test of independence (or Fisher's exact test if any expected cell count < 5). One categorical, one continuous → go to Branch 1 (the categorical variable defines your groups). **Branch 3: Testing relationship between continuous variables** → 2 continuous variables, testing strength of linear relationship → Pearson correlation (r). Testing whether one variable predicts another → Simple linear regression. Multiple predictors → Multiple regression. Non-linear relationship → consider transformation or non-parametric (Spearman rank correlation). **Branch 4: Predicting a categorical outcome** → Outcome is binary (yes/no, pass/fail) → Logistic regression. Outcome has 3+ categories → Multinomial logistic regression. **Branch 5: Non-parametric alternatives (when normality is violated)** → Instead of independent t-test → Mann-Whitney U test. Instead of paired t-test → Wilcoxon signed-rank test. Instead of one-way ANOVA → Kruskal-Wallis test. Instead of Pearson correlation → Spearman rank correlation. StatsIQ identifies which branch your problem falls on and selects the correct test automatically — it even checks whether parametric assumptions are met and recommends the non-parametric alternative when needed.

Parametric tests (t-test, ANOVA, Pearson correlation, linear regression) assume the data is approximately normally distributed and has equal variances across groups. When these assumptions are violated, the test may produce unreliable p-values and misleading conclusions. How to check normality: visual inspection (histogram should be roughly bell-shaped, Q-Q plot points should fall near the diagonal line) and formal tests (Shapiro-Wilk test — if p < 0.05, normality is rejected). In practice, parametric tests are robust to mild violations of normality, especially with larger samples (n > 30 per group). The Central Limit Theorem means that sample means are approximately normal even when the underlying data is not — so t-tests and ANOVA remain valid with mild skew if sample sizes are adequate. When to switch to non-parametric: the data is severely skewed or has extreme outliers that cannot be justified, sample sizes are small (n < 15 per group) AND the data is non-normal, the data is ordinal (rankings, Likert scales) rather than truly continuous, or the variances are dramatically unequal across groups (Levene's test p < 0.05). The trade-off: non-parametric tests make fewer assumptions but have less statistical power — they are less likely to detect a real effect. This means a non-parametric test might give you p = 0.08 (not significant) where the parametric equivalent would give p = 0.03 (significant). Only switch to non-parametric when the parametric assumptions are clearly violated, not just because you are unsure. StatsIQ checks normality and equal variances for you when solving problems — if assumptions are violated, it recommends the appropriate non-parametric alternative and explains why.

Scenario 1: A researcher wants to know if a new medication reduces blood pressure more than a placebo. 50 patients are randomly assigned to medication (n=25) or placebo (n=25). Blood pressure (mmHg) is measured after 8 weeks. → Comparing 2 independent group means with a continuous DV → Independent t-test. Scenario 2: A survey asks 200 people their political party (Democrat, Republican, Independent) and whether they support a specific policy (yes/no). Is there an association between party and policy support? → Two categorical variables → Chi-square test of independence. Scenario 3: A professor wants to know if study hours predict exam scores. She measures hours studied and exam score (0-100) for 40 students. → Predicting a continuous outcome from a continuous predictor → Simple linear regression (or Pearson correlation if she only wants the strength of association). Scenario 4: Patients rate their pain before and after physical therapy on a 1-10 scale. Is there a significant reduction? → Two related measurements (same patients, before/after) with ordinal data → Wilcoxon signed-rank test (non-parametric alternative to paired t-test, because Likert pain scales are ordinal, not truly continuous). Scenario 5: Three different teaching methods are compared. Students are randomly assigned to Method A (n=20), Method B (n=20), or Method C (n=20). Final exam scores are compared. → Comparing 3 independent group means → One-way ANOVA. If significant, follow with Tukey HSD to determine which methods differ. The pattern: identify the research question type, check the data type, count the groups/variables, verify assumptions, and the test chooses itself. StatsIQ applies this exact logic — snap a photo of any scenario and it walks through each decision point.