If 250 is the size of your sample I will not advocate any test of normality for (at least) 3 reasons
1 - with such a sample size your test will be quite powerful, and as many statistical techniques can accommodate a mild departure from normality, such a power is worst than useless;
2 - be aware that the tails of a "normal" sample (where an outlier could be?) are always problematic and normality test are very sensitive to those tails;
3 - in case of non normality a simple test won't give you any hint on how to correct or what to do -- A QQ-plot instead can give you indication(s) on how your data depart from normality and then how to "correct" to normality. A grossly straight line in the middle of the plot is usually sufficient to admit that normality assumptions are fulfilled.
Ok thank you sir.. can you provide any reference research paper to quote which support that parametric test can be used for a large sample even when data are not normally distributed, though i got one as follows:
Parametric tests generally require the residuals are normally distributed, not the data itself. So you need to check if residuals are normal by a qqplot of residuals.
You can try using Kolmorov-smirnoff test which reflects if the data has significative difference it is not normal data. If you have non differences is normal. And of course you have to explore Kurtosis ( -3.0 to 3.0) and Skewness = (0.8- 0.8).
I would disagree with Jean. The sample size does not affect whether normality matters. It is true that most parametric tests are fairly robust to some non-normality but with today's software it is fairly easy to choose a test which does not require normality.
If you choose to go with a test which requires normality, be very up front about the lack of normality and take it into account in interpretation of findings. Although tests requiring normality are fairly robust, you are introducing error into your findings. Depending on how the results will be used and other sources of error, the error may or may not be a problem.
I did not say that the normality matters or not according to sample size, but that the tests of normality become too powerful when the sample size is above, say, 100 or 200 and that is the reason why, in this case, a graphical check is to be preferred.