Calculator
Enter a direct z-statistic, or let the page calculate it from a biological value, reference mean, and reference standard deviation.
Example Data Table
Illustrative biology-style values using a shared sample size of 36 for effect size conversion.
| Biological Measure | Observed Value | Reference Mean | Reference SD | Z Score | Effect Size r |
|---|---|---|---|---|---|
| Leaf chlorophyll concentration | 27.4 | 24.0 | 2.0 | 1.70 | 0.28 |
| Zebrafish serum glucose | 101.0 | 110.0 | 8.0 | -1.13 | -0.19 |
| Root length after treatment | 15.8 | 13.5 | 1.5 | 1.53 | 0.26 |
| Mouse hemoglobin level | 12.2 | 11.0 | 0.9 | 1.33 | 0.22 |
| Cell viability index | 68.0 | 75.0 | 6.0 | -1.17 | -0.20 |
Formula Used
1. Z score: The standardized distance from the reference mean is calculated with z = (x − μ) / σ.
2. Effect size r from z: For many z-based tests, the effect size can be estimated with r = z / √N.
3. Variance explained: The percentage of explained variation is r² × 100.
4. Cohen d conversion: A useful approximation is d = 2r / √(1 − r²).
5. Fisher transformation: For intervals around r, use 0.5 × ln((1+r)/(1−r)) and then transform back.
6. P values: Tail probabilities are derived from the standard normal distribution using the computed z value.
How to Use This Calculator
- Enter a sample or biomarker label to identify the biological measurement.
- Type the observed value, the reference mean, and the reference standard deviation.
- Use the direct z-statistic field only when you already have a z value.
- Enter the total sample size used for converting z into effect size r.
- Select the alpha level and choose one-tailed or two-tailed testing.
- Pick the number of decimals you want in the output.
- Press Calculate Now to display results above the form.
- Review the metrics, graph, formulas, and export buttons for reporting.
Frequently Asked Questions
1. What does the z score mean in biology?
It shows how far an observed biological value sits from a reference mean in standard deviation units. Positive values are above the mean, and negative values are below it.
2. Why convert z into effect size r?
The r value gives a standardized magnitude that is easier to compare across studies. It helps summarize how meaningful a biological effect may be, not just whether it is statistically significant.
3. Can I enter a z-statistic directly?
Yes. When you already have a z-statistic from software or a paper, place it in the direct z field. That value becomes the source for p values and effect size conversions.
4. What sample size should I use?
Use the total number of observations associated with the z-based test. The conversion to effect size r depends on that total, so consistency with your study design matters.
5. Is a large z score always a large biological effect?
Not always. Very large samples can produce strong statistical evidence for relatively modest biological effects. That is why the calculator reports both z-based significance and effect size magnitude.
6. What does variance explained represent?
It is the square of r expressed as a percentage. This estimate describes how much variation is associated with the observed effect in a compact and interpretable way.
7. When should I use one-tailed instead of two-tailed testing?
Use one-tailed testing only when your biological hypothesis clearly predicts one direction before analysis. Two-tailed testing is more conservative and is appropriate for most routine comparisons.
8. Can this calculator replace full statistical software?
No. It is best for quick interpretation, teaching, and reporting support. Complex modeling, repeated measures, mixed effects, and assumption checks still require dedicated statistical analysis tools.