Calculator Inputs
Example Data Table
This sample uses effect sizes and standard errors. Ratio measures should usually be entered on the log scale.
| Study | Effect Size | Standard Error | Precision | Standard Normal Deviate |
|---|---|---|---|---|
| Study A | 0.18 | 0.07 | 14.2857 | 2.5714 |
| Study B | 0.11 | 0.05 | 20.0000 | 2.2000 |
| Study C | 0.28 | 0.11 | 9.0909 | 2.5455 |
| Study D | 0.05 | 0.04 | 25.0000 | 1.2500 |
| Study E | 0.31 | 0.13 | 7.6923 | 2.3846 |
Formula Used
Precision: \( x_i = 1 / SE_i \)
Standard normal deviate: \( y_i = Effect_i / SE_i \)
Egger regression model: \( y_i = \beta_0 + \beta_1 x_i + \epsilon_i \)
Intercept test: \( t = \beta_0 / SE(\beta_0) \)
Degrees of freedom: \( df = k - 2 \)
Decision rule: compare the two-tailed p value with the selected alpha level.
How to Use This Calculator
- Collect each study effect and its standard error.
- Use log transformed values for odds ratios, risk ratios, and hazard ratios.
- Paste one study per line using study name, effect, and standard error.
- Select the confidence level and alpha value.
- Press the calculate button.
- Review the intercept, p value, confidence interval, chart, and diagnostics.
- Export CSV or PDF files for your meta-analysis notes.
Egger Regression Test for Meta Analysis
What This Test Shows
Egger regression checks small study effects in a review. It asks whether smaller studies show stronger or weaker results than larger studies. This pattern can suggest publication bias, selective reporting, chance imbalance, or real clinical differences. The test should support judgment. It should not replace careful review.
How The Model Works
The calculator uses each study effect and standard error. It converts the effect into a standard normal deviate. It also converts standard error into precision. Then it fits a simple regression line. The intercept is the key diagnostic value. When that intercept is far from zero, the funnel pattern may be asymmetric.
Reading The Output
A small p value suggests evidence of asymmetry. Many reviewers use 0.05 as a guide. Yet the result depends on study count, effect scale, standard errors, and heterogeneity. Egger testing is usually weak with fewer than ten studies. It may also overreact when between study variation is large. Compare the result with a funnel plot and subject knowledge.
Preparing Your Data
Use this tool after extracting comparable effects. For odds ratios, risk ratios, or hazard ratios, enter log transformed effects. For mean differences, enter effects on one consistent scale. Standard errors must be positive. Avoid mixing raw ratios with log ratios. That mistake can change the intercept and p value.
Output And Reports
The output gives the intercept, standard error, confidence interval, t statistic, degrees of freedom, p value, slope, residual error, and R squared. The chart plots precision against the standard normal deviate. The fitted line shows how the model reads the evidence. CSV and PDF exports help document your review. Keep the exported report with your notes. It records assumptions, included studies, and calculated values for later checking. This makes updates easier when new studies are added or corrections are needed during peer review later.
Final Review Advice
No single test proves bias. Treat Egger regression as one signal among several. Consider study quality, search coverage, trial registration, missing outcomes, and sensitivity analyses before drawing a final conclusion. Report both statistical and clinical context so readers understand the practical meaning clearly.
FAQs
1. What does Egger regression test?
It tests whether the regression intercept differs from zero. A large departure can suggest funnel plot asymmetry or small-study effects in a meta-analysis.
2. What data do I need?
You need one effect estimate and one standard error for each study. The effects should be comparable and measured on the same scale.
3. Should I enter odds ratios directly?
No. For odds ratios, risk ratios, and hazard ratios, enter the log transformed value with its standard error. Do not mix raw and log values.
4. How many studies are recommended?
Ten or more studies are usually preferred. With fewer studies, the test can be weak, unstable, or misleading.
5. What does a significant p value mean?
It suggests evidence of funnel asymmetry. It does not prove publication bias. Other causes include heterogeneity, chance, and methodological differences.
6. What is the standard normal deviate?
It is the study effect divided by its standard error. Egger regression uses it as the outcome in the linear model.
7. What does precision mean here?
Precision is one divided by the standard error. Larger studies often have smaller standard errors and higher precision values.
8. Can I export the results?
Yes. Use the CSV button for study diagnostics. Use the PDF button for a concise report with the main interpretation.