Some of my data are not normally distributed with the kolmogorov-smirnov and Shapiro-wilk tests being significant with values of 0.00. Although Kurtosis and skewness were within -2 and +2, normal values were marked as outliers, for example, Apgar scores of 0 and 10. Can the fact that the data is not normally distributed be disregarded, considering samples sizes above 200 in most cases?
It may be recommended to perform the mahalanobis distance to remove the data at typical .000
It is better to go for non parametric test if your data are not normally distributed. For few variables whatever the sample size or whatever the techniques (like transform etc.) applied, it will not satisfy normality condition. One such variable is Apgar scores. In such case it is appropriate to apply non parametric test.
Try for non parametric test if your data are not normally distributed. Your sample size is not big enough too.