The Effect Size Index Calculator helps researchers and students calculate Cohen’s d, a statistical measure that shows the standardized difference between two means. This calculator is commonly used in psychology, education, medicine, and social science research to evaluate the strength or impact of a treatment or intervention.
By using this tool, you can easily compare results across different studies, regardless of the original scales used. This is important when interpreting the practical significance of results, especially in experiments or group comparisons.
This calculator falls under the Statistical Analysis and Research Tools category.
formula of Effect Size Index Calculator
Formula:
d = (M1 - M2) / SD_pooled
Explanation of Variables and Calculations
d:
This is Cohen’s d, the effect size index. It shows how different two groups are by standardizing the mean difference using their variability. A higher d value indicates a stronger effect.
M1:
Mean (average) of the first group.
M2:
Mean (average) of the second group.
SD_pooled:
Pooled standard deviation, combining the variability of both groups. It is calculated as:
SD_pooled = sqrt( [ ((n1 - 1) * SD1^2) + ((n2 - 1) * SD2^2) ] / (n1 + n2 - 2) )
SD1:
Standard deviation of the first group.
SD2:
Standard deviation of the second group.
n1:
Sample size of the first group.
n2:
Sample size of the second group.
SD1^2 and SD2^2:
These are the variances (standard deviation squared) of both groups.
sqrt:
Square root function, applied to calculate SD_pooled.
This formula allows you to determine if the observed difference is small, medium, or large, using the scale commonly accepted in research:
- Small effect size: 0.2
- Medium effect size: 0.5
- Large effect size: 0.8 or higher
Table of Common Effect Size Benchmarks
| Effect Size (d) | Interpretation |
|---|---|
| 0.0 - 0.19 | Very small |
| 0.20 - 0.49 | Small |
| 0.50 - 0.79 | Medium |
| 0.80 - 1.19 | Large |
| 1.20 - 1.99 | Very large |
| 2.0 and above | Huge |
This table helps users quickly understand the magnitude of their calculated effect size without needing extra context.
Example of Effect Size Index Calculator
Imagine you conducted an experiment on two groups:
- Group 1 (n1 = 25):
Mean = 85, SD = 10 - Group 2 (n2 = 25):
Mean = 75, SD = 12
Step 1: Calculate SD_pooled
SD_pooled = sqrt( [ ((25 - 1) * 10^2) + ((25 - 1) * 12^2) ] / (25 + 25 - 2) )
SD_pooled = sqrt( [ 2400 + 3456 ] / 48 )
= sqrt(5856 / 48) = sqrt(122) ≈ 11.05
Step 2: Calculate d
d = (85 - 75) / 11.05 = 10 / 11.05 ≈ 0.91
Result:
The effect size is approximately 0.91, which is considered large. This means there is a strong difference between the two groups.
Most Common FAQs
A: It depends on the context. Generally, 0.2 is small, 0.5 is medium, and 0.8 or more is large. The larger the effect size, the stronger the difference between groups.
A: The pooled SD gives a more accurate measure of variability when two groups are compared, especially if their sizes and standard deviations are not the same.
A: No. There are others like Hedges’ g, Glass’s Δ, and eta-squared, but Cohen’s d is one of the most widely used for comparing two means.