The grant size results in a p-value of 3*10^-20 (for the null hypothesis “the grant size follows a normal distribution”).
The logarithm of the grant size results in a p-value of 0.3 (for the null hypothesis “the grant size follows a lognormal distribution”).
So it looks like we can confidently reject the grant size following a normal distribution, but it could well follow a lognormal distribution. This aligns well with my expectations.
Thanks for commenting!
I had not tested it, but your are kind of right! Applying the Shapiro-Wilk normality test to:
The grant size results in a p-value of 3*10^-20 (for the null hypothesis “the grant size follows a normal distribution”).
The logarithm of the grant size results in a p-value of 0.3 (for the null hypothesis “the grant size follows a lognormal distribution”).
So it looks like we can confidently reject the grant size following a normal distribution, but it could well follow a lognormal distribution. This aligns well with my expectations.