Help understanding the results of the Lilliefors test I have a set of annual rainfall data for Thailand which is gridded, so I have approximately 30x18 grid squares. I am trying to test whether the gamma distribution is suitable for my data, so I am doing the Lilliefors test on the rainfall data from each grid square. I appear to have implemented this fine in Matlab. The problem I am having is trying to understand my results. Here is an example from one grid square:
Test statistic = 0.0782
Critical value (1% significance level) = 0.0958
Critical value (5% significance level) = 0.0811
Critical value (10% significance level) = 0.0738

So from this, I think I reject the null hypothesis at the 10% level, but not at the 1% & 5% levels (as the null hypothesis is rejected if the test statistic exceeds the critical value).
Thing is, I don't really understand how I can accept something at the 1% and 5% level but not the 10% level. I am really not a statistician, so I do struggle to get my head around this stuff. I do tests for statistical significance in my work, where something can be statistically significant at the 10% level but not at the 5% or 1% level, so I think this is why I can't understand it being the other way around.
What does my result say about the goodness of fit using the gamma distribution for my data?
 A: Regarding the interpretation of the "rejection/not rejection" issue:
The $\alpha$% significance level is "the probability that the test will reject a true null hypothesis".
So  
"Reject at 10% level": we reject the null hypothesis knowing that there is a 10% chance that we are rejecting it wrongly.  
"Not reject at 5% level": we do not reject the null hypothesis remarking that "if we were to reject it, there would be a 5% chance of the rejection being wrong".  
But wait: what is the meaning of this last phrase, it seems nonsensical: why do we care about the probability of a wrong rejection since we do not reject the null in the first place?
We care, because it is the other way around: the reason of no-rejection is exactly the decision from our part to bear a probability of wrong rejection of only 5% (and not higher). In other words, exactly because we are being very "conservative", very "intolerant" towards the prospect of a wrong rejection, we find ourselves unable to reject the null.  
Whether we reject the null hypothesis or not, is not only a matter of the data and the statistical methods we employ: it is as much a matter of a choice we make, a decision we take, about how high a probability of a wrong rejection we want to accept. The "usual" significance levels, 1%, 5%, 10%, do not have any statistical or in general "objective" justification whatsoever (only historical-sociological, and perhaps philosophical such).
