Levene's p versus the test statistic p
Levene's p versus the test statistic p
When an value is set at .05, any p that is smaller than .05 is producing a statistically significant different result, while any value greater than .05 is producing a statistically similar result.
p≤.05 statistical difference
p>.05 statistical similarity
When do we want one or the other? It depends on the question asked.
For example, when we are looking at two sets of data to see if they are homogenous to one another for the purpose of equal variances, we want p>.05 so there IS statistical similarity. Therefore the Levene’s test demonstrates homogeneity (equal variance) when p>.05. (This generally results in an F≈1.) When Levene’s is statistically similar this is a GOOD thing, because it gives us confidence that data sets have similar distributions (even though their means might be different). In other words, the curves look similar, even though their centers might be at different points on the number line.
On a t test, you are generally trying to show a difference (although not always the case). Therefore the p≤.05. If p≤.05 then we know that tcrit<tstat. If p>.05, then tcrit>tstat.
contributed by Frank LaBanca, EdD
This is a great visual for 'significantly different and similar'.
contributed by John Ryan Drawing by Frank LaBanca, EdD
