Testing Normality

[Allabux]

hi

Why we are generally using Anderson- Darling test to test the
Normality?

is there any chance that Anderson-Darling test result is saying the
data is normal and other test are showing the data is not normal?

[sreejith k.s]

Anderson-Darling test is only one of the tools to test the normality
of the sample,

yes you can definitely use other tools like P-P plots to check the
normality,both will give the same result

[Allabux]

testing normality we have three tests (i think based on requirement).

Anderson-Darling test
This test compares the empirical cumulative distribution function of
your sample data with the distribution expected if the data were
normal. If this observed difference is sufficiently large, the test
will reject the null hypothesis of population normality.

Ryan-Joiner normality test
This test assesses normality by calculating the correlation between
your data and the normal scores of your data. If the correlation
coefficient is near 1, the population is likely to be normal. The Ryan-
Joiner statistic assesses the strength of this correlation; if it
falls below the appropriate critical value, you will reject the null
hypothesis of population normality. This test is similar to the
Shapiro-Wilk normality test.

Kolmogorov-Smirnov normality test
This test compares the empirical cumulative distribution function of
your sample data with the distribution expected if the data were
normal. If this observed difference is sufficiently large, the test
will reject the null hypothesis of population normality.

If the p-value of these test is less than your chosen a-level, you can
reject your null hypothesis and conclude that the population is
nonnormal.