I have a data sample of 190 but I have a few outliers and my data is not normally distributed. I intend to use paired T-test to evaluate the pre-post treatment over time. What should I do?
In addition, should I test for validity and reliability too? Or there is no need to?
The paired variables are not what's assumed to be normal, but rather the differences. And for the purposes of the exactness of significance level, really only under $H_0$.
The differences won't actually be normal either, even under $H_0$. The assumptions under which the null distribution of the test was derived are in practice never true, and testing for them will in large samples show you that. Discovering this non-normality may be more or less inconsequential, since what matters is how much difference it makes to your significance level (and perhaps to power), which may often be fairly modest.
With a sample size of 190 for the significance level to be much different from the selected value, you'd need the population distribution of the differences to be pretty strongly non-normal, in the case where $H_0$ was true (which is probably not true of the data, so testing it on the data may not be particularly relevant). It's not likely that all of these things are at issue together.
However, if this was a particular concern, you can do things about the fidelity to the significance level for your test but I wouldn't be inclined to worry. This is not to suggest you shouldn't choose a better parametric model if you can - and not just for significance level. When asking for advice like this, it's a good idea to explain what sort of variable you're measuring. In many cases this may hint at potential models.
