Calculator
This calculator assumes independent two group studies and consistent effect direction across studies.
Example Data Table
| Study | Treatment Mean | Treatment SD | Treatment n | Control Mean | Control SD | Control n |
|---|---|---|---|---|---|---|
| Study A | 14.2 | 4.8 | 48 | 11.6 | 4.5 | 46 |
| Study B | 21.1 | 6.2 | 55 | 18.7 | 5.9 | 57 |
| Study C | 9.4 | 3.1 | 36 | 8.0 | 2.9 | 34 |
About This Meta Analysis T Test Calculator
This tool combines study level evidence from independent two group comparisons and turns each study into a standardized effect size. It is useful when different studies report means and standard deviations or when they only report a t statistic with group sizes. The calculator then combines those study estimates into one pooled result.
You can compare fixed effect and random effects models, inspect study weights, review heterogeneity, and interpret the pooled outcome with confidence intervals. The table and graph help you see whether studies point in the same direction and whether one study has unusual influence on the combined estimate.
This design is especially practical for education, psychology, medicine, social science, and experimental work where researchers often compare treatment and control groups. It gives a fast summary, but careful review of study design, bias, and outcome definitions should still happen before publication or decision making.
Formula Used
For means and SDs:
Pooled SD = √[ ((n1 - 1)SD12 + (n0 - 1)SD02) / (n1 + n0 - 2) ]
Cohen d = (Mean1 - Mean0) / Pooled SD
For t statistic input:
Cohen d = t × √(1 / n1 + 1 / n0)
Small sample correction:
Hedges g = J × d, where J = 1 - 3 / (4df - 1)
Sampling variance:
Var(d) = (n1 + n0) / (n1n0) + d2 / (2df)
Fixed weight = 1 / Variance
Random weight = 1 / (Variance + τ²)
Pooled effect = Σ(weight × effect) / Σ(weight)
Q = Σ[weight × (effect - pooled effect)2]
I² = max(0, (Q - df) / Q) × 100
τ² is estimated here with the DerSimonian and Laird method.
How to Use This Calculator
- Choose whether your studies are entered by means and SDs or by t statistic and group sizes.
- Select Hedges g or Cohen d as the study effect metric.
- Pick the summary model. Random effects is usually preferred when studies differ in design or population.
- Enter one row per study. Keep the treatment minus control direction consistent across all rows.
- Click calculate to view pooled effect, heterogeneity, weights, confidence interval, graph, CSV export, and PDF export.
FAQs
1. What does this calculator combine?
It combines study level two group comparisons into a single pooled effect size. Each study contributes an effect estimate and variance, then the model weights and summarizes them into one result.
2. When should I use fixed effect versus random effects?
Use fixed effect when studies are very similar and seem to estimate one common effect. Use random effects when studies differ in settings, participants, measures, or methods and heterogeneity is expected.
3. Can I enter only t values instead of means and SDs?
Yes. Switch to the t statistic mode and enter each study’s t value plus both group sizes. The calculator converts that information into a standardized effect size automatically.
4. Why is Hedges g often preferred?
Hedges g adjusts Cohen d for small sample bias. When studies have limited sample sizes, that correction usually gives a more conservative and more stable standardized estimate.
5. What does I² tell me?
I² estimates how much of the observed variation is due to real between study differences rather than sampling noise. Larger values suggest more heterogeneity and a stronger case for random effects interpretation.
6. What if one study has a much larger weight?
A heavily weighted study can strongly influence the pooled estimate. Check its variance, sample size, and design quality. Sensitivity checks are useful before making a final conclusion.
7. Can a negative pooled effect still be useful?
Yes. A negative sign simply shows direction based on your coding. It may indicate lower outcomes in treatment than control or the reverse, depending on setup.
8. Does this replace a full systematic review?
No. It summarizes numerical evidence quickly, but it does not evaluate bias, missing data, publication bias, outcome comparability, or protocol quality. Those steps still matter.