Calculate the p-value for two groups
Do two groups really differ, or is the gap just chance? The two-sided z-test for proportions answers that.
Group A against group B
Calculate p-value
Two-sided z-test for two independent proportions.
How many people in this group gave the answer you are measuring.
p-value
0.0132
Significantz = (p₂ − p₁) / √(p̄ · (1 − p̄) · (1/n₁ + 1/n₂)), with p read from the standard normal distribution.
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What is the p-value?
The p-value answers one question: how likely would a difference at least this large between two groups be, if in truth there were none at all? When that probability is very small, the result argues against chance and the difference is called statistically significant. The p-value says nothing about how large or how important a difference is in practice.
How to read the result
The usual threshold is 5 %: if the p-value falls below 0.05, the difference counts as significant. For consequential decisions 1 % is often chosen instead. The reverse matters just as much: a p-value above 0.05 does not prove there is no difference — it only means the data are not enough to establish one. Very often the sample is simply too small.
Significance is not relevance
With very large samples almost any difference becomes significant, including a completely trivial one. So always report both: the p-value and the actual size of the difference in percentage points. A significant difference of 0.4 percentage points is statistically real and practically meaningless.
Reading p-values
| p-value | What it means |
|---|---|
| below 0.01 | Very strong evidence against the null hypothesis |
| 0.01 to 0.05 | Significant at the usual 0.05 level |
| 0.05 to 0.10 | Not established — often the sample is simply too small |
| above 0.10 | No difference that the data can support |
Common questions
What does the p-value tell me?
How likely a difference at least this large would be if there were no real difference at all. A small p-value argues against that assumption.
When is a result significant?
The usual level is 5 %: if the p-value falls below 0.05, the difference counts as statistically significant. For sensitive decisions 0.01 is often used.
How is the p-value calculated here?
With a two-sided z-test for two proportions: z = (p₂ − p₁) / √(p̄ · (1 − p̄) · (1/n₁ + 1/n₂)) using the pooled share p̄. The p-value follows from the standard normal distribution.
Does a p-value above 0.05 mean there is no difference?
No. It only means the data are not enough to establish one. Very often the sample is simply too small — more answers bring clarity.