Does the difference hold up statistically?
The chi-square test checks two groups for a real difference — and Cramér's V tells you how strong it is.
Group A against group B
Check significance
Chi-square test with Yates' correction on a 2×2 table.
How many people in this group gave the answer you are measuring.
p-value
0.0074
SignificantSmall effect
Chi-square with Yates' correction on the 2×2 table. Cramér's V is computed from the uncorrected statistic, the way R and SPSS report it.
Make differences between audiences visible
With empirio.ai you filter results by any characteristic you collected and compare groups directly against each other — without exporting the data first.
- Compare mode for two groups
- Cross-tabulations in one click
- SPSS export for deeper analysis
What is the chi-square test?
The chi-square test checks whether two groups differ on a categorical question — yes/no, bought/did not buy, satisfied/dissatisfied — by more than chance would explain. It compares the frequencies you observed against the ones you would expect if the groups were identical. The larger the gap, the higher the statistic and the smaller the p-value. On small samples Yates' correction keeps the test from calling significance too readily.
How does this differ from the p-value calculator?
Both answer the same question and land in practically the same place on larger samples. The p-value calculator uses the z-test for two proportions; this one uses the chi-square statistic with Yates' correction — which judges a little more cautiously — and adds Cramér's V. So you see not only whether the groups differ, but how clearly.
Reading Cramér's V
Significance alone is not enough. On very large samples even tiny, practically irrelevant differences become significant. Cramér's V measures the strength of the association on a scale from 0 to 1 and does not depend on sample size. Look for results that are both: significant and of a meaningful effect size.
Reading Cramér's V
| Cramér's V | Effect size |
|---|---|
| below 0.10 | Very small — usually irrelevant in practice |
| 0.10 to 0.30 | Small effect |
| 0.30 to 0.50 | Medium effect |
| above 0.50 | Large effect |
Common questions
What does the significance calculator do?
It uses a chi-square test to check whether two groups differ significantly on a yes/no question — suited to group comparisons and A/B tests.
How does it differ from the p-value calculator?
Both give a p-value for two proportions. The significance calculator uses the chi-square statistic with Yates' correction and adds Cramér's V as the effect size — so you see not only whether, but how strongly, the groups differ.
What is Cramér's V?
Cramér's V measures the strength of an association between 0 (no effect) and 1 (perfect association). As a rule of thumb, around 0.1 is a small effect, 0.3 a medium one and 0.5 a large one.
When is a result significant?
The standard is the 95 % level, meaning a significance level of 0.05: if the p-value falls below it, the difference counts as statistically significant. For important decisions, 99 % is worth using.