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

Correlation Tests

Test When to Use Command Example
correlation Linear relationship between two continuous variables --test correlation --x height weight
corr-spearman Monotonic relationship (non-normal data) --test corr-spearman --x rank score
corr-lag Time-shifted correlation --test corr-lag --x sales revenue
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

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

ANOVA

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

Supports:

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

Example:

indexly infer-csv study.csv --test anova --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

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

Advanced Controls

Auto Rerouting 

--auto-route

Automatically switches to a nonparametric test if assumptions fail.

Bootstrap 

--bootstrap

Uses bootstrap confidence intervals where supported.

Multiple Comparison Correction 

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

Applies correction to post-hoc or ANOVA outputs.

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.