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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 ?

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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.

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  • $\begingroup$ 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? $\endgroup$
    – Luis
    Feb 15, 2019 at 3:59
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    $\begingroup$ 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. $\endgroup$ Feb 15, 2019 at 4:23
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    $\begingroup$ 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. $\endgroup$
    – Alexis
    Feb 21, 2019 at 17:39
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    $\begingroup$ @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. $\endgroup$ Feb 22, 2019 at 2:22
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    $\begingroup$ No upsets here. Just intellectual criticism. And welcome again, please stay around. $\endgroup$
    – Alexis
    Feb 22, 2019 at 4:03

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