lower bound of true significance - what does this mean?!


New Member
I've been doing tests of normal distribution (Kolmogorov-Smirnoff tests) and next to some of the significances in SPSS it has an asterix and then it says 'this is a lower bound of the true significance'. Can someone tell me what this means?!



Doesn't actually exist
for many statistical tests either because of sample size or lack of convergence of the algorithm or just because there no formal theory to has been forumalted to obtain an exact solution, many p-values are only approximations or, in this case, you an either provide a floor (lower bound) or a ceiling (upper bound) with regards to the range of values the true p-value can be found on. depending on which upper/lower bound you get, your results can be useful or not very informative. for instance, you're doing the K-S test for equality of distributions (in which case SPSS always has the normal as default) and say for, the sake of argument, that you're setting your alpha = .05. if the lower bound is .05 or anything above that then you have somewhat of statistical evidence to claim that your data is normally distributed (failure to reject the null hypothesis)... HOWEVER, if the lower bound is less than .05, you dont really know whether you've rejected the null hypothesis or not because the true p-value could be anywhere between (lower-bound)up to .9999

i've always felt at odds with this "didnt-reject-the-null-hence-i-showed-equality" but almost everybody uses it that way so i guess i'm just gonna have to let it be (for now...)