Choosing the Right Statistical Test for Your Data Analysis

Introduction

Selecting the correct statistical test is one of the most critical decisions you’ll make as a data analyst. The right test validates your hypotheses, ensures reproducibility, and prevents misleading conclusions. Yet with dozens of parametric and non‑parametric options available, analysts often feel overwhelmed. This article walks you through a systematic, decision‑tree‑style approach to choosing the appropriate test for your data, highlights common pitfalls, and provides practical examples relevant to business, health, and social‑science contexts. By the end, you’ll have a clear checklist you can apply to any analysis project.

1. Clarify the Research Question and Data Structure

1.1 Define the objective

• Descriptive: Summarise a variable (e.g., average sales per region).
• Comparative: Test differences between groups (e.g., conversion rates of two landing pages).
• Associative: Examine relationships (e.g., correlation between advertising spend and revenue).
• Predictive: Model outcomes (e.g., logistic regression for churn prediction).

1.2 Identify the type of data

Data type	Description	Typical examples
Categorical (nominal)	Names or labels with no intrinsic order	Gender, product category, country
Ordinal	Categories with a meaningful rank	Survey Likert scores, education level
Continuous (interval/ratio)	Measurable numeric values	Revenue, temperature, time‑to‑event

Knowing whether your variable is categorical or continuous narrows the pool of viable tests dramatically.

2. Determine the Comparison Framework

Comparison type	When to use	Typical tests
One‑sample	Compare a single sample mean/proportion to a known value	One‑sample t‑test, One‑sample proportion z‑test
Independent‑samples	Compare two or more unrelated groups	Independent t‑test, ANOVA, Mann‑Whitney U, Kruskal‑Wallis
Paired‑samples	Repeated measures on the same subjects (before‑after)	Paired t‑test, Wilcoxon signed‑rank, Repeated‑measures ANOVA
Correlation/association	Examine relationship between two variables	Pearson r, Spearman ρ, Chi‑square test of independence
Regression	Model one variable as a function of others	Linear regression, Logistic regression, Poisson regression

3. Count the Groups or Variables

• Two groups → t‑tests (parametric) or Mann‑Whitney U (non‑parametric).
• Three or more groups → ANOVA (parametric) or Kruskal‑Wallis (non‑parametric).
• Multiple predictors → Multiple regression, MANOVA, or Generalised Linear Models.

4. Check Test Assumptions

Assumption	Why it matters	How to assess
Normality	Parametric tests assume the data (or residuals) follow a normal distribution.	Shapiro‑Wilk test, Q‑Q plots, histograms.
Homogeneity of variances	ANOVA and t‑tests assume equal variances across groups.	Levene’s test, Bartlett’s test, visual box‑plots.
Independence	Violation leads to inflated Type I error.	Study design (randomisation, lack of clustering).
Linearity (for regression)	Relationship must be approximately linear.	Scatter plots, residual plots.
Sample size	Small samples reduce power; large samples may mask non‑normality.	Power analysis (e.g., G*Power) or rule‑of‑thumb (≥30 per group for t‑test).

If any assumption is violated, consider a non‑parametric alternative, data transformation, or a robust test (e.g., Welch’s t‑test for unequal variances).

5. Decision‑Tree Walkthrough

Below is a condensed decision tree you can embed in your analysis notebook (see Figure 1).

Start
│
├─ Is the outcome variable categorical?
│   ├─ Yes → Use Chi‑square (independence) or Fisher’s exact (small counts)
│   └─ No (continuous)
│
├─ Number of groups?
│   ├─ 1 → One‑sample t‑test (normal) / Wilcoxon signed‑rank (non‑normal)
│   ├─ 2 → Independent t‑test (normal, equal var) /
│   │       Welch’s t‑test (unequal var) /
│   │       Mann‑Whitney U (non‑normal)
│   └─ ≥3 → ANOVA (normal, equal var) /
│           Welch ANOVA (unequal var) /
│           Kruskal‑Wallis (non‑normal)
│
├─ Are the samples paired/repeated?
│   ├─ Yes → Paired t‑test (normal) / Wilcoxon signed‑rank (non‑normal)
│   └─ No → Continue above
│
├─ Do you need to assess association?
│   ├─ Both continuous → Pearson r (normal) / Spearman ρ (non‑normal)
│   └─ One continuous, one categorical → Point‑biserial r / t‑test
│
└─ Modelling required?
    ├─ Linear relationship → Linear regression
    ├─ Binary outcome → Logistic regression
    └─ Count data → Poisson or Negative Binomial regression

Figure 1: Simplified decision tree for test selection (adapted from Statology, 2024).

6. Practical Examples

6.1 Business: A/B Test of Two Landing Pages

• Question: Does page B increase conversion rate compared with page A?
• Data: Binary outcome (converted / not converted) for 1,200 visitors per page.
• Test: Two‑proportion z‑test (or Chi‑square if sample > 5 per cell).
• Assumptions: Independence of visitors, sufficient sample size (≥30 per cell).
• Result interpretation: p‑value < 0.05 → reject H₀, conclude a statistically significant lift.

6.2 Health: Comparing Blood Pressure Across Three Diets

• Question: Do low‑salt, Mediterranean, and DASH diets lead to different systolic BP reductions?
• Data: Continuous BP change, 45 participants per diet (randomised).
• Assumptions: Normality (Shapiro‑Wilk p > 0.10), homogeneity (Levene p > 0.05).
• Test: One‑way ANOVA (F = 5.23, p = 0.007).
• Post‑hoc: Tukey HSD identifies Mediterranean vs. low‑salt as significantly different.

6.3 Social Science: Relationship Between Education Level (Ordinal) and Income (Continuous)

• Question: Is higher education associated with higher annual income?
• Data: Ordinal education (high school, bachelor, master, doctorate) and income in £.
• Assumptions: Income not normally distributed (skewed).
• Test: Kruskal‑Wallis (χ² = 22.4, p < 0.001) followed by Dunn’s pairwise comparisons.

7. Frequently Overlooked Pitfalls

1. Multiple testing – Running many tests inflates Type I error. Apply Bonferroni or Benjamini‑Hochberg corrections.
2. Data dredging – Formulating hypotheses after looking at the data invalidates p‑values; pre‑register analyses when possible.
3. Ignoring effect size – A statistically significant result may have a trivial practical impact; report Cohen’s d, odds ratio, or η².
4. Mismatched test and data scale – Using a t‑test on ordinal Likert scores can be misleading; consider non‑parametric alternatives.
5. Over‑reliance on p‑values – Complement with confidence intervals and Bayesian metrics where appropriate.

8. Quick Reference Cheat‑Sheet

Scenario	Variable type(s)	Groups	Recommended test(s)	Key assumption
Compare a single mean to a target	Continuous	1	One‑sample t‑test / Wilcoxon signed‑rank	Normality (t)
Two independent means	Continuous	2	Independent t‑test / Welch’s t / Mann‑Whitney U	Normality + equal variances (t)
Three+ independent means	Continuous	≥3	One‑way ANOVA / Welch ANOVA / Kruskal‑Wallis	Normality + homoscedasticity (ANOVA)
Paired measurements	Continuous	2 (paired)	Paired t‑test / Wilcoxon signed‑rank	Normality of differences
Binary outcome vs. group	Categorical + binary	2	Chi‑square / Fisher’s exact / Two‑proportion z	Expected counts ≥5 (χ²)
Correlation of two continuous variables	Continuous	–	Pearson r / Spearman ρ	Normality (Pearson)
Predicting continuous Y	Continuous + predictors	–	Linear regression (multiple)	Linearity, homoscedasticity, normal residuals
Predicting binary Y	Binary + predictors	–	Logistic regression	Independent observations, linear logit

9. Implementing the Workflow in Python (or R)

Below is a concise Python snippet that demonstrates the decision‑tree logic for a common “compare two means” scenario. Replace the placeholders with your data.

import pandas as pd
import scipy.stats as stats
import statsmodels.api as sm
import seaborn as sns
import matplotlib.pyplot as plt

# Load data
df = pd.read_csv('experiment.csv')          # columns: group, value

# Visual checks
sns.boxplot(x='group', y='value', data=df)
plt.show()

# Normality test per group
for g in df['group'].unique():
    w, p = stats.shapiro(df.loc[df.group == g, 'value'])
    print(f'{g}: Shapiro‑Wilk p={p:.3f}')

# Variance homogeneity
levene = stats.levene(*[df.loc[df.group == g, 'value'] for g in df['group'].unique()])
print('Levene p =', levene.pvalue)

# Choose test
if all(p > 0.05 for p in [stats.shapiro(df.loc[df.group == g, 'value']).pvalue for g in df['group'].unique()]) \
   and levene.pvalue > 0.05:
    # Parametric ANOVA
    model = sm.formula.ols('value ~ C(group)', data=df).fit()
    anova = sm.stats.anova_lm(model, typ=2)
    print(anova)
else:
    # Non‑parametric Kruskal‑Wallis
    kw = stats.kruskal(*[df.loc[df.group == g, 'value'] for g in df['group'].unique()])
    print('Kruskal‑Wallis H =', kw.statistic, ', p =', kw.pvalue)

A similar workflow can be built in R using shapiro.test(), leveneTest(), aov(), and kruskal.test().

10. Reporting Your Findings

A transparent report should contain:

1. Research question & hypotheses
2. Data description (sample size, missing values, variable types)
3. Assumption checks (including test statistics and plots)
4. Chosen statistical test with justification
5. Effect size (Cohen’s d, η², odds ratio)
6. Confidence intervals for estimates
7. Interpretation in the context of the business or scientific problem
8. Limitations and suggestions for further analysis

Example sentence:

“A one‑way ANOVA revealed a significant effect of diet on systolic blood‑pressure reduction (F(2,132) = 5.23, p = 0.007, η² = 0.07). Post‑hoc Tukey tests indicated that the Mediterranean diet produced a greater mean reduction (‑8.4 mmHg) than the low‑salt diet (‑4.1 mmHg, p = 0.02).”

Conclusion

Choosing the right statistical test is less about memorising a long list of formulas and more about following a logical workflow: define the question, classify the data, map the comparison type, verify assumptions, and then select the test that aligns with those conditions. The decision‑tree framework presented here, combined with practical checks for normality, variance homogeneity, and effect size, equips data analysts at any experience level to make robust, reproducible choices.

Remember to:

• Document every step – future you (or a reviewer) will thank you.
• Report effect sizes alongside p‑values for real‑world relevance.
• Re‑evaluate assumptions when new data arrive or when you subset the dataset.

Armed with this systematic approach, you can confidently turn raw data into trustworthy insights that drive business decisions, scientific discovery, and policy formulation.

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