How It Works

Understand when and how to use each statistical test in Indexly.

How the Inference Engine Works

The dispatcher routes your request based on --test.

Each test:

  • Has defined input requirements
  • Applies correct statistical assumptions
  • Returns structured output
  • Can auto-reroute if assumptions fail

Test Selection Guide

Command Selection Table

Goal Command Required arguments Notes
Pearson correlation with CI --test correlation --x one_column --y outcome Uses Fisher Z CI; tune CI with --alpha.
Spearman rank correlation --test corr-spearman --x one_column --y outcome Use for monotonic or ordinal relationships.
Lagged Pearson correlation --test corr-lag --x predictor --y shifted_outcome --lag shifts y before computing Pearson r.
Correlation matrix --test corr-matrix --x col1 col2 col3 Optional --correction bonferroni|holm|bh applies to matrix p-values.
Independent two-group comparison --test ttest --y outcome --group category With --auto-route, uses Welch for unequal variance and Mann-Whitney for non-normal samples.
Bayesian two-group comparison --test bayes-ttest --y outcome --group category Reports BF10 as evidence for the alternative over the null.
Paired before/after comparison --test paired-ttest --x before after Reports paired t-test, Cohen’s dz, and mean-difference CI.
Three or more group means --test anova --y outcome --group category With --auto-route, uses Kruskal for non-normal groups and Welch ANOVA for unequal variances.
Tukey posthoc comparisons --test anova-posthoc --y outcome --group category Tukey HSD controls family-wise error; optional extra correction adds p_corrected.
Linear regression --test ols --y outcome --x predictors... Supports categorical predictors, interactions, HC3 robust covariance, and bootstrap CIs.
Mixed-effects model --test mixed --y outcome --x predictors... --group subject Builds y ~ x1 + x2 with random intercepts by --group.
Nonparametric two-group test --test mannwhitney --y outcome --group category Alternative to independent t-test for ordinal or non-normal data.
Nonparametric 3+ group test --test kruskal --y outcome --group category Reports epsilon-squared effect size.
Mean confidence interval --test ci-mean --y outcome Uses t-distribution.
Proportion confidence interval --test ci-proportion --y binary_column Uses a Wald interval; best for large samples away from 0/1 extremes.
Mean-difference confidence interval --test ci-diff --y outcome --group category Requires exactly two groups; uses Welch degrees of freedom.

Correlation Tests

Test When to Use Command Example
correlation Linear relationship between two continuous variables --test correlation --x height --y weight
corr-spearman Monotonic relationship (non-normal data) --test corr-spearman --x rank --y score
corr-lag Time-shifted correlation --test corr-lag --x sales --y revenue --lag 2
corr-matrix Multiple variable correlation overview --test corr-matrix --x col1 col2 col3

Pearson CI uses Fisher Z-transform.

Example:

indexly infer-csv health.csv --test correlation --x cholesterol --y age --use-raw
indexly infer-csv survey.csv --test corr-matrix --x sleep steps mets --correction bh

T-Tests

Test When to Use Required Arguments
ttest Compare two independent groups --y outcome --group category
paired-ttest Same subjects measured twice --x before after

Example:

indexly infer-csv trial.csv --test ttest --y blood_pressure --group treatment
indexly infer-csv trial.csv --test ttest --y blood_pressure --group treatment --auto-route
indexly infer-csv trial.csv --test paired-ttest --x before after --bootstrap
indexly infer-csv trial.csv --test bayes-ttest --y blood_pressure --group treatment

ANOVA

Test Purpose
anova Compare means across 3+ groups
anova-posthoc Tukey HSD pairwise comparisons

Supports:

  • Assumption checks
  • Optional correction (--correction bonferroni)
  • Auto rerouting

Routing behavior:

  • Non-normal groups with --auto-route → Kruskal-Wallis
  • Normal groups with unequal variance and --auto-route → Welch ANOVA
  • Normal groups with equal variance → classical one-way ANOVA
  • Significant classical ANOVA with 3+ groups runs Tukey HSD posthoc automatically

Example:

indexly infer-csv study.csv --test anova --y score --group group_name
indexly infer-csv study.csv --test anova --y score --group group_name --auto-route
indexly infer-csv study.csv --test anova-posthoc --y score --group group_name

Nonparametric Tests

Test Alternative To
mannwhitney Independent t-test
kruskal ANOVA

Use when:

  • Data not normal
  • Small sample size
  • Ordinal variables

Regression

Test Description
ols Ordinary Least Squares regression
mixed Mixed-effects model

Supports:

  • Interaction terms
  • Bootstrap coefficients
  • Assumption validation

Example:

indexly infer-csv dataset.csv --test ols --y outcome --x age income --interaction age income
indexly infer-csv dataset.csv --test ols --y outcome --x age income --bootstrap
indexly infer-csv repeated.csv --test mixed --y score --x week dose --group participant_id

Confidence Intervals

Test Description
ci-mean CI for single mean (t-distribution)
ci-proportion CI for binomial proportion
ci-diff CI for mean difference

Example:

indexly infer-csv survey.csv --test ci-mean --y satisfaction
indexly infer-csv survey.csv --test ci-mean --y satisfaction --alpha 0.01
indexly infer-csv survey.csv --test ci-proportion --y completed
indexly infer-csv trial.csv --test ci-diff --y score --group treatment

Advanced Controls

Auto Rerouting 

--auto-route

Automatically switches to a nonparametric test if assumptions fail. For ANOVA, unequal variances route to Welch ANOVA instead of Kruskal when group normality is acceptable.

Bootstrap 

--bootstrap

Uses bootstrap confidence intervals where supported.

Multiple Comparison Correction 

--correction bonferroni
--correction holm
--correction bh

Applies correction where supported. For corr-matrix, corrections apply to the pairwise matrix p-values. For anova-posthoc, Tukey HSD already controls family-wise error; an explicit correction adds a conservative p_corrected column.

Output Structure

All tests return a unified structure:

  • Statistic
  • P-value
  • Effect size (when applicable)
  • Confidence interval
  • Interpretation
  • Metadata
  • Optional additional tables

Formatted Inference Output

Summary

The inference engine is:

  • Statistically rigorous
  • CLI-native
  • Assumption-aware
  • Modular
  • Extensible

You can phrase it like this:

The next section will demonstrate a complete workflow using:

  • analyze-csv
  • infer-csv
  • Report export

If you’d like to understand the statistical concepts behind these commands first, you can review the mathematical foundation section before continuing.