Let's say I'm trying to compare if two groups of people are significantly different from each other in terms of their access to the internet.

One could code each person's internet access categorically (doesn't have, has), or as a numerical score (0, 1).

I can easily use the Chi-Square test to compare the 2 groups using the categorical values.

My question is, is it also valid to use the t-test to compare the scores (the average score for each group)? The reason I ask is that one of the requirements of the t-test is that the dependent variable be normally distributed. Do 2-level dependent variables (e.g. with values 0 and 1) pass the 'normally distributed' test?

(Bonus question, is data such as male/female considered binomial? If not, what's a good name to describe such 2-level data?)


A $t$-test is indeed inappropriate for binary data (that is, variables with only two values) because binary data can't be normally distributed. The most obvious reason why is that a normal distribution is continuous. It has infinitely many possible outcomes, not just two.

"Binomial" is sometimes used to describe binary data, but it's usually reserved for terms like "binomial distribution", "binomial test", and "binomial coefficient".

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  • $\begingroup$ Ah -- binary is the word I was looking for! That's the best way to describe it I guess. $\endgroup$ – thanks_in_advance Jul 20 '16 at 22:23
  • $\begingroup$ Also known as the 'sign test' I believe $\endgroup$ – HEITZ Jul 20 '16 at 22:27
  • $\begingroup$ @HEITZ I didn't understand, what's known as a 'sign test'? $\endgroup$ – thanks_in_advance Jul 22 '16 at 5:52
  • $\begingroup$ @user1883050: my mistake, sign test is based on binomial distribution but doesn't apply in this case $\endgroup$ – HEITZ Jul 22 '16 at 21:47

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