AI Prompts for Statistical Testing and Hypothesis Building

Choosing the right statistical test is half the battle; running it correctly and interpreting it honestly is the other half. AI can guide you through all three — if you describe your data and your question with enough detail. This topic shows you how to prompt for trustworthy statistical analysis without slipping into p-hacking or misuse.

1. Introduction

Statistical testing is easy to do badly. The wrong test, the wrong assumption, the wrong correction for multiple comparisons — any one of these turns a confident claim into noise. AI can dramatically speed up the work, but only if you treat it as a competent statistician who needs to be briefed. The prompt patterns in this topic focus on choosing the right test for your data, running it with the right assumptions, and writing up the result in a way that does not overstate what the evidence supports.

2. The Concept Explained

Every test has a domain: the kind of question it answers, the kind of data it expects, and the assumptions it makes. A two-sample t-test compares means of continuous outcomes between two independent groups, assuming roughly normal distributions and similar variances. Chi-square tests independence of two categorical variables. ANOVA generalises t-tests to three or more groups. Mann-Whitney U handles non-normal continuous data. Regression handles multivariate relationships. The hardest part of running a test correctly is not the calculation — it is the diagnosis: which test is appropriate here.

Think of it like a doctor matching a treatment to a diagnosis. The prescription is easy once the diagnosis is right. AI can suggest both — but you must describe the symptoms (data shape, group structure, what you're trying to learn).

3. The Problem Without This Technique

Run a statistical test on my data and tell me if it's significant.

Act as a senior statistician using scipy and statsmodels.

Data: DataFrame ab_test_df, ~32,000 rows, one row
per user randomised at session start.
Columns:
  user_id (int), variant (str: 'A'|'B'),
  session_revenue_gbp (float, range 0..420,
  heavy right skew, ~37% zeros).

Question: did variant B increase mean revenue per
user compared to variant A?

Tasks:
1. Recommend the appropriate test given the
   distribution and propose a non-parametric backup.
2. Run a Welch's t-test AND a bootstrap difference
   in means (10k resamples) for robustness.
3. Report: effect size in £ (B - A), 95% CI,
   p-value, and an interpretation paragraph.
4. Add a one-line caveat about the ~37% zero
   inflation and whether a two-part model would
   be more appropriate.
5. Return runnable Python code.

4. The Solution

The pattern is: data brief → question → ask for test selection → run with assumptions → report effect size and CI → caveat. The single most important habit is to let AI propose the test before you ask it to run one. A two-step prompt — first "which test fits?", then "run it" — produces more honest analysis than a one-shot "run a t-test for me".

Always demand an effect size and confidence interval alongside any p-value. P-values without effect sizes are misleading; effect sizes without uncertainty are equally misleading. Prompt: "Report effect size, 95% CI, and p-value. Lead with the effect size."

5. Step-by-Step Breakdown

1. Describe the outcome. Continuous or categorical, mean or rate, distribution shape, zero-inflation. The distribution drives the test choice.
2. Describe the group structure. Two groups, three or more, paired, repeated measures, hierarchical. Each one suggests a different test.
3. State the hypothesis in plain words. "Does variant B increase revenue?" "Are churn rates the same across regions?" Avoid double-barrelled questions.
4. Ask for test selection first, then execution. A two-step conversation prevents jumping to a wrong-but-familiar test.
5. Demand assumption checks. Normality, equal variances, independence, sample size adequacy. Each violated assumption may demand a non-parametric alternative.
6. Report effect size, CI, and p-value together. Always. Lead with the effect size — that is the business-relevant number.

Tip: When running multiple tests, ask AI to apply a multiple-comparison correction (Bonferroni, Holm, or Benjamini-Hochberg). The correction choice depends on whether you care more about avoiding false positives or false negatives.

6. Practice Exercises

7. Key Takeaways