For this example, there are 100k people who have purchased a backpack. Out of the 100k that did purchase a backpack, 75% of the backpack buyers are female. 3.9 million people did not purchase the backpack. Out of the 3.9M that did not purchase the backpack, 76% are female.

I am trying to find which test to use to figure out if men are more likely to shop for backpacks.

So in summary: Group A:

  • 75% of buyers are female

  • 100k total buyers of backpacks

Group B:

  • 76% of buyers are female
  • 3.9M non-buyers of backpacks

Is there a significant difference between the 2 groups in terms of if men shop for backpacks more than females?


1 Answer 1


You can use a chi-squared ($\chi^2$) test. I simulate what your data would look like below, but with less N:

# make data frame
dat <- data.frame(
  group = c(rep("A", 100), rep("B", 3900)),
  gender = c(rep("F", 75), rep("M", 25), rep("F",  2964), rep("M", 936))

# randomly re-arrange so top 10 shows variability
dat  <- dat[sample(1:nrow(dat), nrow(dat)), ]

A sample of the data would look like this:

# show example of data

     group gender
2091     B      F
182      B      F
3887     B      M
2217     B      F
758      B      F
2136     B      F

From these data, you can make a frequency table:

# show table
table(dat$group, dat$gender)

And run a chi-squared test:

# run chisq test
chisq.test(dat$group, dat$gender)

Which, in this case, suggests that the 75% female rate is not statistically significantly different from the 76% female rate:

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

data:  dat$group and dat$gender
X-squared = 0.012678, df = 1, p-value = 0.9104

You can also feed in a frequency table from your data:

# frequency table of entire data
freq <- matrix(
  c(100000 * .75, 100000 * .25, 
    3900000 * .76, 3900000 * .24), 
nrow  = 2)

# do chisq test

Which shows a significant difference:

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

data:  freq
X-squared = 53.361, df = 1, p-value = 2.775e-13

It is worth noting that, in such large samples, even very trivially small differences can return a result that is statistically significant. It is up to you on the interpretation end to decide whether or not that 1 point difference is actionable.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.