As I understand it, tests of normality are not all that useful because: they are underpowered & won’t reject normality at the small samples where you need to know about non-normality because it’ll badly affect your conclusions; and at larger samples [...], because real-world data is rarely exactly normal, they will always reject normality even when it makes not the slightest difference to your results
I agree that normality tests are too insensitive for most small samples, and too sensitive for pretty much any big sample, but I’d presumed there was a sweet spot (when the sample size is a few hundred) where normality tests have decent sensitivity without giving everything a negligible p-value, and that the LW survey is near that sweet spot. If I’d been lazy and used R’s out-of-the-box normality test (Shapiro-Wilk) instead of following goocy’s recommendation (Lilliefors, which R hides in its nortest library) I’d have got an insignificant p of 0.11, so the sample [edit: of non-zero donations] evidently isn’t large enough to guarantee rejection by normality tests in general.
Also, you don’t have to look at only one year’s data; you can look at 3 or 4 by making sure to filter out responses based whether they report answering a previous survey.
Certainly. It might be interesting to investigate whether the log-normal-with-zeroes distribution holds up in earlier years, and if so, whether the distribution’s parameters drift over time. Still, goocy’s complaint was about 2014′s data, so I stuck with that.
I agree that normality tests are too insensitive for most small samples, and too sensitive for pretty much any big sample, but I’d presumed there was a sweet spot (when the sample size is a few hundred) where normality tests have decent sensitivity without giving everything a negligible p-value, and that the LW survey is near that sweet spot. If I’d been lazy and used R’s out-of-the-box normality test (Shapiro-Wilk) instead of following goocy’s recommendation (Lilliefors, which R hides in its
nortestlibrary) I’d have got an insignificant p of 0.11, so the sample [edit: of non-zero donations] evidently isn’t large enough to guarantee rejection by normality tests in general.Certainly. It might be interesting to investigate whether the log-normal-with-zeroes distribution holds up in earlier years, and if so, whether the distribution’s parameters drift over time. Still, goocy’s complaint was about 2014′s data, so I stuck with that.