Bootstrap Effect Size Calculator

Calculator Inputs

Group A Name

Group B Name

Data Entry Mode

Design

Effect Size Metric

Confidence Level (%)

Bootstrap Iterations

Random Seed

Interpretation Note

Effect size direction is always calculated as Group B minus Group A.

Group A Values

Use commas, spaces, semicolons, or new lines.

Group B Values

For paired data, place matching observations in the same order.

Example Data Table

Raw sample example for quick testing

Observation	Group A	Group B
1	12	18
2	15	20
3	14	19
4	16	21
5	13	17
6	17	22
7	14	20
8	15	19
9	18	23
10	16	21

Formula Used

Mean Difference:
Mean Difference = Mean(B) − Mean(A)

Cohen's d for independent groups:
d = (Mean(B) − Mean(A)) / s_pooled
s_pooled = √[ ((n_A−1)s_A² + (n_B−1)s_B²) / (n_A+n_B−2) ]

Hedges' g:
g = d × J, where J = 1 − 3 / (4(n_A+n_B) − 9)

Glass's Δ:
Δ = (Mean(B) − Mean(A)) / s_A
This uses Group A as the reference standard deviation.

Paired Cohen's dz:
dz = Mean(Differences) / SD(Differences)

Bootstrap confidence interval:
Repeatedly resample the data with replacement, recalculate the effect size, then take percentile cutoffs at α/2 and 1−α/2.

How to Use This Calculator

Choose raw samples or summary statistics.
Name the two groups for clearer reports.
Select independent or paired design.
Pick an effect size metric matching your study goal.
Enter confidence level, iterations, and optional seed.
Click the calculate button to show results above the form.
Inspect the point estimate, interval, and bootstrap distribution plot.
Export the summary as CSV or PDF when needed.

Frequently Asked Questions

1) What does a bootstrap effect size show?

It shows the magnitude of the difference between two groups and the uncertainty around that magnitude. Bootstrapping repeatedly resamples the data, giving a data-driven confidence interval for the chosen effect metric.

2) When should I use Hedges' g instead of Cohen's d?

Use Hedges' g when sample sizes are modest and you want a small-sample bias correction. It is often preferred for reporting standardized differences in studies with limited observations.

3) What is the difference between independent and paired designs?

Independent designs compare separate groups. Paired designs compare linked observations, such as before-and-after scores on the same subjects. The paired option resamples matched pairs together.

4) Why can the bootstrap interval differ from a textbook formula?

Bootstrap intervals are built from the empirical resampling distribution, not only from theoretical assumptions. They can better reflect skewed or irregular data when classic formulas are less reliable.

5) How many bootstrap iterations should I use?

Three thousand to five thousand iterations usually gives stable percentile intervals for routine work. Larger runs can improve stability, especially for publication-quality estimates or noisy datasets.

6) Can I use summary statistics instead of raw values?

Yes. Summary mode works from sample size, mean, and standard deviation. It uses a normal-data approximation to generate a parametric bootstrap distribution because the original observations are not available.

7) What does a negative effect size mean here?

A negative value means Group B is lower than Group A because the calculator always computes Group B minus Group A. The sign reflects direction, while the absolute size reflects magnitude.

8) Should I report only the effect size?

Report the effect size together with its confidence interval, study design, sample sizes, and the exact metric used. That combination gives readers both magnitude and uncertainty.