@tpmjs/tools-effect-size-suite

Calculate multiple effect size measures (Cohen's d, Hedge's g, Glass's delta) for comparing two groups.

Overview

Effect sizes quantify the magnitude of difference between two groups in standardized units. Unlike p-values (which tell you if a difference exists), effect sizes tell you how large the difference is, making them essential for practical significance and meta-analysis.

This tool calculates three common effect size measures:

• Cohen's d: Uses pooled standard deviation from both groups
• Hedge's g: Bias-corrected version of Cohen's d for small samples
• Glass's delta: Uses only the control group's standard deviation (useful when variances differ)

Installation

npm install @tpmjs/tools-effect-size-suite

Usage with AI SDK

import { effectSizeSuiteTool } from '@tpmjs/tools-effect-size-suite';
import { generateText } from 'ai';

const result = await generateText({
  model: yourModel,
  tools: { effectSize: effectSizeSuiteTool },
  toolChoice: 'required',
  prompt: 'Compare treatment group [78, 82, 85, 79, 88] vs control [72, 68, 70, 65, 71]',
});

Direct Usage

import { effectSizeSuiteTool } from '@tpmjs/tools-effect-size-suite';

const result = await effectSizeSuiteTool.execute({
  group1: [78, 82, 85, 79, 88], // Treatment group
  group2: [72, 68, 70, 65, 71], // Control group
});

console.log(result);
// {
//   cohensD: 2.156,
//   hedgesG: 1.942,
//   glassDelta: 2.289,
//   interpretation: {
//     cohensD: 'large',
//     hedgesG: 'large',
//     glassDelta: 'large'
//   },
//   groupStats: {
//     group1: { mean: 82.4, sd: 3.975, n: 5 },
//     group2: { mean: 69.2, sd: 2.863, n: 5 },
//     meanDifference: 13.2
//   }
// }

Parameters

• group1 (required): Array of numeric values for first group (minimum 2 values)
• group2 (required): Array of numeric values for second group (minimum 2 values)

Note: Group 2 is treated as the "control" for Glass's delta calculation.

Returns

{
  cohensD: number;        // Cohen's d effect size
  hedgesG: number;        // Hedge's g (bias-corrected)
  glassDelta: number;     // Glass's delta
  interpretation: {
    cohensD: string;      // 'negligible' | 'small' | 'medium' | 'large'
    hedgesG: string;
    glassDelta: string;
  };
  groupStats: {
    group1: { mean, sd, n };
    group2: { mean, sd, n };
    meanDifference: number;
  };
}

Effect Size Interpretation

Following Cohen's (1988) conventions:

Which Effect Size to Use?

Cohen's d

Best for: Most common use case, balanced designs with similar sample sizes

Formula: d = (M₁ - M₂) / SDpooled

Use when:

• Sample sizes are similar
• Variances are roughly equal
• Standard choice for meta-analysis

Hedge's g

Best for: Small samples (n < 20 per group)

Formula: g = d × correction_factor

Use when:

• Small sample sizes (provides unbiased estimate)
• Otherwise same as Cohen's d

Glass's delta

Best for: Different variances, experimental vs control comparison

Formula: Δ = (M₁ - M₂) / SD₂

Use when:

• Treatment may change variance
• Clear control group exists
• Comparing to a standard/baseline

Example Use Cases

Clinical trial comparison:

const trial = await effectSizeSuiteTool.execute({
  group1: [145, 138, 142, 149, 140], // Blood pressure after treatment
  group2: [158, 162, 155, 160, 157], // Blood pressure control group
});
// Large negative effect = treatment reduced blood pressure

Educational intervention:

const education = await effectSizeSuiteTool.execute({
  group1: [88, 92, 85, 90, 87], // Test scores with new method
  group2: [78, 82, 80, 79, 81], // Test scores traditional method
});
// Positive effect = new method improved scores

A/B testing with different variances:

const abTest = await effectSizeSuiteTool.execute({
  group1: [5.2, 8.1, 6.4, 9.2, 7.1], // Version B (high variance)
  group2: [4.1, 4.3, 4.0, 4.2, 4.1], // Version A (stable baseline)
});
// Use Glass's delta when treatment changes variance

Important Notes

1. Direction matters: Positive effect size means group1 > group2
2. Small samples: Use Hedge's g for n < 20 per group
3. Assumptions:
   • Data should be reasonably continuous
   • Extreme outliers can distort effect sizes
   • Groups should be independent
4. Statistical significance: Effect size ≠ statistical significance
   • Large effect with small n may not be significant (p > 0.05)
   • Small effect with large n may be significant but not meaningful

Formulas

Pooled Standard Deviation:

SDpooled = √[((n₁-1)×SD₁² + (n₂-1)×SD₂²) / (n₁+n₂-2)]

Cohen's d:

d = (M₁ - M₂) / SDpooled

Hedge's g:

g = d × [1 - 3/(4N - 9)]
where N = n₁ + n₂

Glass's delta:

Δ = (M₁ - M₂) / SD₂

References

• Cohen, J. (1988). Statistical Power Analysis for the Behavioral Sciences (2nd ed.)
• Hedges, L. V. (1981). Distribution theory for Glass's estimator of effect size. Journal of Educational Statistics, 6(2), 107-128
• Lakens, D. (2013). Calculating and reporting effect sizes. Frontiers in Psychology, 4, 863

License

MIT