A group is normally distributed but the other isn't

MrM

New Member
#1
Hi everyone,
Using Shapiro -Wilk test I found that the assumption of normality for the control group was satisfied but that of the experimental group wasn't. I'm going to compare the means of the two groups. I wonder which appropriate statistical analysis will I use .
Thanks in advance
 
#2
Hi, since the assumption of normality is thus violated you can either apply a Wilcoxon-rank-sum test (U-Test) or a permutation T-test, with a both appropriate
 
#3
I wouldn't necessarily jump to saying the normality assumption is violated and that you need a different test. The formal tests, such as SW, can be highly sensitive to unimportant deviations from normality (in other words, you'll reject Ho, but there's little practical effect).

Can you give us some more information?

What is the variable you're analyzing data for?
How is it measured?
How many cases are in each group?
What is the estimated variance in each group?
 
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hlsmith

Omega Contributor
#4
I will agree with ondanssetron here even though they may be a Transformer. Just kidding, I just saw the tron termination on your name.


Some normality tests will reject the null hypothesis of normally for small departures from the distribution if the sample size is large. So people may call this 'over-powered' test. This doesn't mean you have to throw out parametric tests. More details and exploration is needed.


Which statistical test were you hoping to run?


Also, mmercker's recommendations may be viable options, though not totally necessary.


P.S., Can you make your font any bigger, just kidding. :)
 

MrM

New Member
#5
Thanks
I want to compare the means of two groups : a control group (N=30) and an experimental group (N= 30) before being subjected to an achievement test. I want to run a t test using SPSS for independent samples but I want to check its assumptions . Using Shapiro -Wilk test I found that the assumption of normality for the control group was met but that of the experimental group wasn't.The variable I.m analyzing data for is the dependent variable ( the scores of both the control group and experimental group ). The independent variable is the participants in both groups. The variance in the experimental group is 21.4 and in the control group is 24.4 . The observation in each group is 30 .The mean of the experimental group is 11.5 and for the control group is 10.3. Can I still run a T test for independent samples?
Thanks in advance
 
#6
Thanks
I want to compare the means of two groups : a control group (N=30) and an experimental group (N= 30) before being subjected to an achievement test.
How are these scores measured (is it like an exam score, or is it a score from a likert-type question)?
Is there a range on the scores possible?
Is each individual only assigned to one group (i.e. subject n only receives the one of these two treatments)?
How were the participants assigned to groups?

I want to run a t test using SPSS for independent samples but I want to check its assumptions .
This is always a good idea!

Using Shapiro -Wilk test I found that the assumption of normality for the control group was met but that of the experimental group wasn't.
A few quick things. As mentioned above, formal tests of normality can reject Ho without much practical implications. I would recommend examining normal probability plots (Q-Q) for the dependent variable by group, as well as considering histograms just to get another angle. (You can post these up if you'd like).

Further, failure to reject Ho on "a test for normality" does not mean the data are from a normal distribution. This is true of any hypothesis test: failing to reject the null does not prove or suggest the null, it means you have insufficient evidence of the alternative hypothesis (in this case, you don't have enough evidence to say the data are from a nonnormal distribution in the one group, but this doesn't mean they are from a normally distributed population).

The variable I.m analyzing data for is the dependent variable ( the scores of both the control group and experimental group ). The independent variable is the participants in both groups. The variance in the experimental group is 21.4 and in the control group is 24.4 . The observation in each group is 30.
The groups are balanced groups and the variances appear relatively close (via the eyeball test).If your sample size doesn't quite make it to "large enough" for the CLT, it doesn't appear that the variances are so different to greatly impact the results, although you could test this if you felt uncomfortable relying on the CLT. If you believe the central limit theorem (CLT) can apply to your case, then you only need to fulfill the assumption of independent random sampling (I'm assuming these aren't paired measurements).

Can I still run a T test for independent samples?
Thanks in advance
It's definitely possible, but it depends on some answers to the above questions. Let's see where we go from there.
 

MrM

New Member
#7
Thanks for your patience
Actually, these aren't paired measurements. Also, the scores are not for a likert scale . They are exam scores. Each individual was only assigned to one group .The participants are assigned randomly.
 
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CowboyBear

Super Moderator
#8
Can I still run a T test for independent samples?
Well, what does your pre-registered protocol say you'd do in this situation?

Aside from that, it looks like your DV takes only integer values, so you know ahead of time that it isn't normally distributed. Testing this formally doesn't tell you anything. Looking at the degree to which the distribution is approximated by a normal distribution would be possibly more useful. But on the whole, normality is by far the least important assumption of OLS, so my suggestion would be to focus your efforts elsewhere. It's fine to run an independent samples t-test with the magnitude of skewness and kurtosis you're looking at. There are surely more important threats to the validity of your study to focus on here - e.g., the poor statistical power with n = 30; any potential confounders; issues with error dependency; etc.