Suppose we have two groups and Only Data from first group pass normality test. Then in this case , which tests should i use normal T test or non parametric T test(mann whitney). Also i cant remove outliers to make data normal.
Kindky help
Vinit -
Looking at other distributions has not been a big part of the literature because you often want to look at means, and then the Central Limit Theorem can make approximate normality, or at least the t-distribution, attractive. (You might also consider Chebyshev's Inequality.)
You can probably use the following:
https://online.stat.psu.edu/stat414/node/203/
That is an explanation on the Penn State web pages of a confidence interval around the difference in two means, allowing for different population variances.
I suggest this confidence interval as more practically interpretable than a "test." You'd want to see what confidence levels do or do not include zero. To have a higher confidence level and/or a shorter interval, you'd need a larger sample size (i.e., more evidence).
Of course this only compares means, but you get variance information. It's at least a good start for your study.
Cheers - Jim
Look at histogram of d=x1-x2. If it is symmetric you can use ordinary t-tests.
D. Booth
There are some t-tests that are robust measures, the normality assumption can be violated. Check them. Non-parametric tests are good but weak
Hi Vinit, If your second group is not far from normal distribution, since t-test is robust against normality you can use t-test.
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