# Determine if data is IID [duplicate]

I have data usage from Android and Iphones, and I want to check if the Iphone users consume more than the Android ones. I thought about doing a t-test, but I am not sure if the ID - I think we should be ok with the independence - holds. Also, how important is this requisite ?

• If you have multiple measurements for at least some users then your data is not iid. Feb 15, 2019 at 8:42
• May 8, 2021 at 13:19

Based on the comments below, I've removed my first answer and have replaced it with my follow-up comment, which the OP may have found much more useful.

If the two populations are normal and you are testing for a difference in means,so there is a chance that they are not identically distributed, then yes, you can use the t-test of means. If the variances are different, then the Welch t-test adjusts the value of the standard error used in determining the test statistic. It also adjusts the number of degrees of freedom non-trivially See Wikipedia's Welch's t-test page for details.

What IID has do with a) study design (lots!) and/or b) actual raw unconditional data (nothing!) is a question for another post and really should not have part of my answer to this question. Apologies.

• Thanks Peter. So let's suppose my data is normally distributed, but the mean and variance differ so it's not ID. I'd like to test if that difference is significant. Should I be ok doing a t-test? What is the risk there?
– Luis
Feb 15, 2019 at 3:59
• If the two populations are normal and you are testing for a difference in means,so there is a chance that they are not identically distributed, then yes, you can use the t-test of means. If the variances are different, then the Welch t-test adjusts the value of the standard error used in determining the test statistic t. It also adjusts the number of degrees of freedom non-trivially See en.wikipedia.org/wiki/Welch's_t-test for Welch's t-test with different variances. Feb 15, 2019 at 4:23
• Wow! I applaud your enthusiasm, and in good faith welcome you to the site, but I find this answer lousy! Nonparametric tests are not test of means (not without additional extremely rigid assumptions). I am also baffled as to why you consider IID a property of the analytic model, and do not direct attention to the question of whether a data generating process produces IID data, particularly given that there are a host of tests to provide evidence for and against the IID assumption. Finally, you go wide in your answer instead of narrowly honing in on the OP's question. Feb 21, 2019 at 17:39
• @Alexis, thank you for your warm welcome, and I take your criticism to heart, so thank you for that as well. I seem to have upset several people with this answer. I think my key error was trying to read more into the question than the OP intended, and the rebound lay-up -- which was the conventional Welch's T-test answer -- was what the OP was looking for. I should simply ask the question "What does IID have to do with a) study design and b) actual data?" in a separate post. Feb 22, 2019 at 2:22
• No upsets here. Just intellectual criticism. And welcome again, please stay around. Feb 22, 2019 at 4:03