In R, I have a sample of 348 measures, and want to know if I can assume it is normally distributed for future tests.
Essentially following another Stack answer, I am looking at the density plot and the QQ plot with:
qqnorm(Clinical$cancer_age);qqline(Clinical$cancer_age, col = 2)
I do not have a strong experience in Statistics, but they look like examples of normal distributions I have seen.
Then I am running the Shapiro-Wilk test:
shapiro.test(Clinical$cancer_age) > Shapiro-Wilk normality test data: Clinical$cancer_age W = 0.98775, p-value = 0.004952
If I interpret it correctly, it tells me it is safe to reject the null hypothesis, which is that the distribution is normal.
However, I have encountered two Stack posts (here, and here), which strongly undermine the usefulness of this test. Looks like if the sample is big (is 348 considered as big?), it will always say that the distribution is not normal.
How should I interpret all that? Should I stick with the QQ plot and assume my distribution is normal?