Effect Size Calculator (Cohen's d) Formula

Understand the math behind the effect size calculator (cohen's d). Each variable explained with a worked example.

Use the Effect Size Calculator (Cohen's d)

Formulas Used

Cohen's d

cohens_d = abs(mean1 - mean2) / pooled_sd

Pooled Standard Deviation

pooled_sd_out = pooled_sd

Mean Difference

mean_diff = abs(mean1 - mean2)

Variables

VariableDescriptionDefault
mean1Group 1 Mean78
mean2Group 2 Mean72
sd1Group 1 Std Deviation10
sd2Group 2 Std Deviation12
pooled_sdDerived value= sqrt((pow(sd1, 2) + pow(sd2, 2)) / 2)calculated

How It Works

How Cohen's d Measures Effect Size

Cohen's d quantifies the difference between two group means in standard deviation units, providing a measure of practical significance independent of sample size.

Formula

d = Mean_1 - Mean_2 / SD_pooled

Where SD_pooled = sqrt((SD_1^2 + SD_2^2) / 2)

Interpretation

  • Small effect: d = 0.2
  • Medium effect: d = 0.5
  • Large effect: d = 0.8

    • In education research, an effect size of 0.4 or higher is generally considered practically significant.

    Worked Example

    Treatment group scored mean 78 (SD = 10), control group scored mean 72 (SD = 12).

    mean1 = 78mean2 = 72sd1 = 10sd2 = 12
    1. 01Pooled SD = sqrt((100 + 144) / 2) = sqrt(122) = 11.05
    2. 02Mean difference: |78 - 72| = 6
    3. 03Cohen's d = 6 / 11.05 = 0.543
    4. 04Interpretation: Medium effect size

    Frequently Asked Questions

    Why not just use p-values?

    P-values indicate statistical significance but not practical importance. A large sample can make a tiny difference statistically significant.

    What is a meaningful effect size in education?

    Hattie suggests d = 0.4 as the threshold for a worthwhile intervention in education (the "hinge point").

    Can effect size be negative?

    This calculator reports the absolute value. A negative d would simply mean Group 2 scored higher than Group 1.

    Ready to run the numbers?

    Open Effect Size Calculator (Cohen's d)