The Effect Size Index Calculator helps researchers and students calculate 科恩的, 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.
此计算器属于 Statistical Analysis and Research Tools 类别。
formula of Effect Size Index Calculator
分子式：
d = (M1 - M2) / SD_pooled
Explanation of Variables and Calculations
d:
这是 科恩的, the effect size index. It shows how different two groups are by standardizing the mean difference using their variability. A higher d值 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:
平方根运算 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) | 解释 |
|---|---|
| 0.0 - 0.19 | 很小 |
| 0.20 - 0.49 | S小号 |
| 0.50 - 0.79 | 中等 |
| 0.80 - 1.19 | L大号 |
| 1.20 - 1.99 | 很大 |
| 2.0及以上 | 巨大 |
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
结果：
The effect size is approximately 0.91, which is considered 大. This means there is a strong difference between the two groups.
最常见的常见问题解答
A: It depends on the context. Generally, 0.2小, 0.5 中等及 0.8 or more is large. The larger the effect size, the stronger the difference between groups.
答： 合并标准差 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 赫奇斯的 g, Glass’s Δ及 eta-squared, but Cohen’s d is one of the most widely used for comparing two means.