# What statistical test to use on TRUE/FALSE (Boolen) data between groups? [duplicate]

Suppose each group as 1000 people.

How does one tell if there is a significant difference between these independent groups?

---------UPDATE--------

The actual data is: Group 1: 5195 true, 2658 false (n = 7853) Group 2: 5579 true, 2297 false (n = 7876)

I used prop.test and chisq.test to check if there are significant differences between the groups. My R code and outputs are below. I am not sure how to interpret this:

R CODE: prop.test(c(5195,5579),c(7853,7876))

OUTPUT: 2-sample test for equality of proportions with continuity correction

data: c(5195, 5579) out of c(7853, 7876) X-squared = 39.737, df = 1, p-value = 2.906e-10 alternative hypothesis: two.sided 95 percent confidence interval: -0.06145244 -0.03219530 sample estimates: prop 1 prop 2 0.6615306 0.7083545

R CODE: chisq.test(rbind(c(2658,2297),c(5195,5579)))

OUTPUT: Pearson's Chi-squared test with Yates' continuity correction

data: rbind(c(2658, 2297), c(5195, 5579)) X-squared = 39.737, df = 1, p-value = 2.906e-10

• What tests have you been learning? And what is a “significant” difference to you?
– Dave
Nov 10 '21 at 20:11
• In R, you could use prop.test to see if proportions $0.5$ and $0.2$ are significantly different with sample sizes of $n=1000.$ Equivalently, you could use chisq.test with at 2-by-2 table with columns for Gps 1 & 2 and rows for Yes & No. Either test gives P-value very nearly $0.$ Please see if this matches with topics you have covered recently. Post results as an edit to your question, if you have difficulty with interpretation. R code prop.test(c(500,200), c(1000,1000))) or chisq.test(rbind(c(500,200),c(500,800))). Nov 10 '21 at 20:24
• @BruceET That looks a lot like an answer!
– Dave
Nov 10 '21 at 20:31
• stats.stackexchange.com/…
– whuber
Nov 10 '21 at 21:16