Normality test before testing the difference between two groups. Is it necessary? I would like to know, when comparing the means in two groups, one with 15 patients and another with 70, if it is necessary to test for normality.
 A: While it is possible to test for normality, it is often not very useful to do so. Very few datasets come from an exactly normal distribution and many parametric statistical procedures work well even when the distribution is only "kind of normalish". 
(I will note that the unequal sample size may mean that procedures might not be quite so robust to departures from normality as would be the case with equal samples.)
When the sample is small it contains little information about its underlying distribution and so the normal distribution test has low power and you get lots of false negatives. Conversely, when the sample is large and the test has high power, it starts to indicate significant departures in cases where the distribution is close enough to normal that there is no real problem.
Examine your data in a couple of normal distribution plots to get a feel for the shape of the distributions. If there is substantial deviation then you can either transform the data (log transformations are often appropriate) or use non-parametric methods. With sample sizes of 17 and 70 most non-parametric tests will have good power relative to the normal distribution based tests. For example, a permutations test will power equal to that of a Student's t-test.
Really you should provide a lot more information in your question, such as what the measurements are, what sort of tests you wish to perform, whether the research is exploratory or designed, what hypotheses you are interested in, and so on. That way the answers can be more specific and you will gain more assistance.
