Before using any statistical test, the researcher should check the assumption of that particular test. after checking the assumptions, the researcher will decide whether to use the parametric or non parametric test. for example, If a researcher is interested in see the gender difference on optimism. the researcher should check assumptions like, whether the data is normally distributed or not, whether the value of skewness & Kurtosis are within the range or not, what type of sampling technique has been used whether probability or non probability technique.

If the data is normally distributed and there is no violation of assumptions then you can use the parametric test such as t-test. however if the data is not normally distributed you are suppose to use its opposite that is non-parametric test (Mann-Whitney U test).

Thanks for the reply but my question is whether I can assume normality for both groups (male and female) when the total data of both male and female of say optimism (your example) is normal. To complicate things say the total data is normal but groups are not or one group is normal and other is not. Then what? Should I go for non parametric test? More over if I break one dimension into two or three categories based on, say low and highly optimistic or so, then there become cases for parametric and non parametric for a data on single variable optimism. Hope I am making sense with my question.

Don't fret too much about Normality. With such a large sample size, any test you do should be fairly robust against lack of Normality.

Thanks Adrian. I also feel so. That is why I have written the sample size. But can you quote some books regarding this as reference. Andy Field suggest not to care for sample >200. Any Other reference? Further one of my group showing mean of 137 and SD 181 suggesting a skewed data (and in reality it is skewed with outlier I cannot remove. SPSS normality tests also suggest non-normality). Can someone question this if I apply t test without going for the normality test in my paper. I am also going for Spearman’s rho on this basis as against pearson’s  ‘r’.  Or am I overly cautious?

Or to be simply put can I say my sample was fairly large so I don’t need any normality test on any of continuous data !

For the reference search litterature  on "central limit theory" .

For the second question: Unless subgroups were planned for explicitly in the protocol (in terms  of sample size) I would suggest not to "split" the data but rather run an anova/regression (or similar) and look for interaction terms/effect modifiers to study group effect.  Good luck

I believe the reason that Andy Field or any other not suggesting a normality test for a sample size >200 or 500 may not be because that data will be normal in any way but because the test assessing normality will misinform you. Or at least, one should bear in mind this possibility that most normality tests will fail for large data samples even they are (coming from) normal (distributions).

You can try both t test and its nonparametric equivalent and compare the results if you are suspicious although they are not testing the same thing. I believe that t-test will be OK with your situation. As Adrian said, do not stick to normality, I generally do not check for normality before performing a t-test. I attached some links. Heteroscedasticity might be a concern for your case. You could try Welch's t test. I am amazed by the length of discussion in first link.

https://www.researchgate.net/post/Can_I_use_a_t-test_that_assumes_that_my_data_fit_a_normal_distribution_in_this_case_Or_should_I_use_a_non-parametric_test_Mann_Whitney2

http://stats.stackexchange.com/questions/9573/t-test-for-non-normal-when-n50

Thanks Anthony, Mehmet and Karen for your reply. Though still I could not decide on the test to be used. Perhaps I need not to be thinking too much about when the sample is large enough. But again when the SD of the data is too higher than mean, I fear someone will question the authenticity of ‘t’ test in this case?? Is too high SD is the case for any other non-parametric test like Mann-Whitney U?

Higher SD is due to the outliers, which you you cannot remove.

I would agree with Mehmet and Adrian that with such a sample size you should not be worrying about the normality. I remember something similar happened to me and I was indecisive regarding type of the test to be used. I applied both t-test and its non-parametric equivalent and they were telling the same thing. So I went for the t-test. I also had high SD but not higher as yours.

I am sure you must have found a solution by yourself now, as your post is about 02 months old. It would be great if you could share the solution or the path followed by you, so that someone else could be benefited from it.

Thanks. 

Usman yes there are outliers that cannot be removed. Ali, Iam going for t test.

Log transformation didn't work. And for anova also, normality is one of pre-requisite!

Sharma, I forgot o mention about Cohen's d, for examining the effect size of mean difference (if significant). It is quite handy in interpretation of t tests.

Data on both the groups have to be Normal. We remove outliers and then check for Normality to proceed further. 

ok