# Determining how much data is needed for statistical significance of a percentage difference between two points?

Imagining the following situation where A/B are independent results:

• A is a 51% result, given N datapoints
• B is a 50% result, given M datapoints

how many data points (ie N and M) do you need to have confidence that the difference between A/B is statistically significant?

There are various sample size calculators you can use online and in various software for a two-sample proportions test.

Here's the calculation using Stata that suggests that you would need N=M=39,240 for a two-sided alternative test at conventional levels:

. power twoproportions .50 .51

Performing iteration ...

Estimated sample sizes for a two-sample proportions test
Pearson's chi-squared test
Ho: p2 = p1  versus  Ha: p2 != p1

Study parameters:

alpha =    0.0500
power =    0.8000
delta =    0.0100  (difference)
p1 =    0.5000
p2 =    0.5100

Estimated sample sizes:

N =    78,480
N per group =    39,240

• @enderland Did this clarify things? – Dimitriy V. Masterov Feb 5 '18 at 22:06