Effect size calculator
Open Effect size calculator on Happytails.ai. This view has the same page content and links, with explicit tool capabilities. Read the processing notes before using a tool.
Tool capabilities
{
"id": "effect-size-calculator",
"category": "calculators",
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"requirements": "Runs locally in your browser; nothing is uploaded. Group sizes are whole numbers of at least 2 (pairs at least 2, correlation sample size at least 4), means and SDs are plain decimals within plus or minus 1,000,000,000,000, counts are whole numbers up to 1,000,000,000 and the confidence level is from 0.5 to 0.9999. Downloads: a JSON report and a CSV table of measures, estimates, limits and methods.",
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{
"key": "n2",
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"value": "30",
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"help": "Whole number of at least 2. Group 2 is the comparison group for Glass delta.",
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"help": "Whole number of at least 2.",
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{
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"label": "Mean of the differences",
"value": "1.7",
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"help": "First measurement minus second.",
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"help": "Greater than zero.",
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{
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{
"key": "sdSecond",
"label": "SD of the second measurement (optional)",
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"help": "Enter both measurement SDs for d_av, or leave both blank to skip it.",
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{
"key": "correlation",
"label": "Correlation between measurements (optional)",
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"help": "Between -1 and 1; leave blank to skip d_rm.",
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{
"key": "a",
"label": "Group 1 events",
"value": "15",
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"help": "Whole number of zero or more.",
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"two-by-two"
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{
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"help": "Whole number of zero or more.",
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"help": "Whole number of zero or more.",
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"help": "Whole number of zero or more.",
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{
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{
"key": "df1",
"label": "Effect degrees of freedom",
"value": "2",
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"help": "Whole number of at least 1.",
"showWhen": {
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{
"key": "df2",
"label": "Error degrees of freedom",
"value": "45",
"type": "text",
"maxLength": 40,
"help": "Whole number of at least 1.",
"showWhen": {
"mode": [
"f-statistic"
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},
{
"key": "r",
"label": "Correlation r",
"value": "0.42",
"type": "text",
"maxLength": 40,
"help": "Strictly between -1 and 1.",
"showWhen": {
"mode": [
"correlation"
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},
{
"key": "sampleSize",
"label": "Sample size",
"value": "50",
"type": "text",
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"help": "Whole number of at least 4.",
"showWhen": {
"mode": [
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"registrationFamily": "statistical-analysis-reference",
"input": false,
"note": "Runs on your device. Enter summaries for one input type; intervals use the noncentral t or F distribution where noted, and the JSON report and CSV hold every measure.",
"experience": {
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"inputMaxLength": 1000000,
"inputMode": "text",
"label": "Summary values",
"placeholder": "Enter values in the form fields",
"help": "This calculator reads the form fields below; there is no text box. Up to 1,000,000 characters. Review the settings before running.",
"helpParts": [
"This calculator reads the form fields below; there is no text box.",
"Up to 1,000,000 characters.",
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}Page guide
Turn group summaries, paired differences, 2 x 2 counts or a published t, F or r into standardized effect sizes with confidence intervals. Every measure is labelled with the groups and standard deviation it uses.
How to use Effect size calculator
- Choose the input type that matches what you have: two groups, paired differences, event counts or a test statistic.
- Enter the summary values and the confidence level.
- Calculate, then read each measure with its interval and the standard deviation it divides by.
- Download the JSON report or the CSV table of every measure.
Useful next steps
Which d is which
d_s divides the mean difference by the pooled SD of two independent groups (Cohen 1988). Hedges g multiplies it by the exact small-sample correction J. Glass delta uses the SD of group 2 only. For paired data, d_z divides the mean difference by the SD of the differences, d_av by the average of the two SDs (enter both, or leave both blank to skip it) and d_rm adjusts d_z for the correlation (Lakens 2013, Frontiers in Psychology 4:863). These measures are not interchangeable, so report which one you used.
How the intervals are found
Intervals for d_s, d_z and d from a t statistic invert the noncentral t distribution (Steiger and Fouladi 1997), computed accurately even for very large effects; the g interval multiplies those limits by J. A normal-approximation interval from the Hedges and Olkin (1985) variance is also listed. The partial eta squared interval inverts the noncentral F distribution with N = df1 + df2 + 1. Odds and risk ratios use log intervals (Woolf 1955; Katz et al. 1978), the risk difference a Wald interval, and r a Fisher z interval.
Assumptions and limits
Group SDs are sample SDs with n - 1. If any 2 x 2 cell is zero, 0.5 is added to every cell before ratios are computed, and the report says so. Conversions such as d to r or d to a log odds ratio (Chinn 2000, Statistics in Medicine 19:3127) assume roughly normal data. The d to r conversion allows unequal group sizes: r = d / sqrt(d^2 + a) with a = (n1 + n2)^2 / (n1 n2) (Borenstein et al. 2009, Introduction to Meta-Analysis, chapter 7). An effect size describes these data; it does not show importance or cause.