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08 – Statistical Tests

📘 RIDE User Manual – Panel 8: Statistical Tests

📊 Purpose of the Panel

The Statistical Tests panel allows users to run hypothesis tests on their data to determine:

  • Differences between groups
  • Associations between categorical variables
  • Normality of distributions

Users can choose from 6 popular tests depending on data type, assumptions, and goals.

Recommended Reading

🧭 User Workflow

  1. Upload Dataset
    Choose from:

    • Initial DataFrame
    • Imputed, Encoded, or Scaled DataFrame

  2. Choose a Statistical Test
    Options include:

    • 2-Sample T-Test
    • ANOVA
    • Chi-Square Test
    • Mann-Whitney U Test
    • Wilcoxon Signed-Rank Test
    • Kruskal-Wallis Test

  3. Select Group & Value Columns
    Based on the test chosen, select a categorical column (for grouping) and a numerical column (for values).

  4. Visualize Distributions (Optional)
    Choose to view histograms, box plots, or group distributions.

  5. Run the Test
    Get test statistics, p-values, interpretation, and AI-generated summaries if OpenAI API is enabled.

🧪 Statistical Test Explanations with Formulas & Use Cases

1. 2-Sample T-Test

  • Purpose: Compares means of two independent groups.
  • Assumptions: Normal distribution, equal variances.
    • Formula \(t = \frac{\bar{x}_1 - \bar{x}_2}{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}}\)
    • \(\bar{x}_1\) and \(\bar{x}_2\) are the sample means
    • \(s_1^2\) and \(s_2^2\) are the sample variances
    • \(n_1\) and \(n_2\) are the sample sizes

  • Example: Compare exam scores between two sections of students.

  • Two-Sample T-Test

  • The Two-Sample t-Test
  • Two Sample t-test: Definition, Formula, and Example

2. ANOVA (Analysis of Variance)

  • Purpose: Compares means of 3 or more independent groups.
  • Assumptions: Normal distribution, equal variances.
  • Formula:
    • \[F = \frac{\text{Between-group variance}}{\text{Within-group variance}} = \frac{MS_{between}}{MS_{within}}\]
    • The \(F\)-statistic compares \(MS_{between}\) to \(MS_{within}\)
    • \(MS_{between}\) represents the between-group variance
    • \(MS_{within}\) represents the within-group variance

  • Example: Compare customer satisfaction across 4 product lines.

  • Analysis of Variance (ANOVA) Guide with Examples

  • Analysis of Variance Tutorial

3. Chi-Square Test

4. Mann-Whitney U Test

  • Purpose: Non-parametric alternative to T-test (for non-normal data).
  • Assumptions: Independent samples, ordinal/numeric values.
  • Formula:
    \(U = n_1 n_2 + \frac{n_1(n_1+1)}{2} - R_1\)
    • where \(R_1\) is the sum of ranks in group 1.

  • Example: Compare ratings of two movies.

  • Mann-Whitney U-Test

  • The Mann-Whitney U Test

5. Wilcoxon Signed-Rank Test

  • Purpose: Non-parametric test for paired data.
  • Assumptions: Symmetric distribution of differences.
  • Formula Wilcoxon Signed-Rank Test \(W = \sum_{i=1}^{n} [sgn(x_{2,i} - x_{1,i}) \cdot R_i]\)
    • where \(R_i\) is the rank of the absolute difference, and \(sgn()\) is the sign function.

  • Example: Compare before/after treatment scores for same patients.

  • How to Conduct a Wilcoxon Signed Rank Test

  • Wilcoxon signed-rank test

6. Kruskal-Wallis H Test

  • Purpose: Non-parametric ANOVA (3+ groups, not normally distributed).
  • Kruskal-Wallis H Test
  • Formula:
  • \[H = \frac{12}{n(n+1)} \sum \frac{R_i^2}{n_i} - 3(n+1)\]
    • where \(R_i\) is the sum of ranks in group \(i\), \(n_i\) is the sample size of group \(i\), and \(n\) is the total sample size.

  • Example: Compare time spent on app across multiple age groups.

  • Kruskal-Wallis-Test

🔍 Summary Table

Test Parametric? Groups Data Type Use When
T-Test Yes 2 Numeric Comparing two groups (normal)
ANOVA Yes ≥3 Numeric Comparing ≥3 groups (normal)
Chi-Square No ≥2 Categorical Check relationships
Mann-Whitney U No 2 Numeric (Ordinal) Two groups, not normal
Wilcoxon No Paired Numeric (Ordinal) Paired samples, not normal
Kruskal-Wallis No ≥3 Numeric (Ordinal) ≥3 groups, not normal