Test to determine significance for non normal data with different variance and unequal n?

Question

How can I find out if the differences in length and width of cut marks left in fabric are significantly different between groups (knife types)?

Additional Information

Groups:

KnifeType1 n=15
KnifeType2 n=15
KnifeType3 n=11
KnifeType4 n=15
KnifeType5 n=6
KnifeType6 n=4
KnifeType7 n=4
KnifeType8 n=5

I want to test length and width separately, and all measurements are in mm.

The data is not normally distributed, and the groups have very different variances; do I have to rely on Welch's t test?

I'm trying to determine if the lengths and widths of cut marks would help you determine what type of knife was used-possibly by seeing if the mean lengths and widths are sig different from each other. I'm using SPSS, and have a year of undergraduate stats.

Update I read that Welch's t test was pretty robust agains nonnormality, would it be okay to use that one and state that the normality assumption was violated?

Answer 1

If 2 knife types have the exact same mean, but very different variances then you would still have information useful to classification, if you are seeing a cut that lies far from the mean relative to the small variance, but reasonble from the large variance then it seems much more likely to have come from the knife with the larger variance. So focusing on differences is means when there are other differences is probably not the best approach.

You should look into classification analysis, possibly K nearest neighbors methods, or a Bayesian approach (using either the distribution that you believe fits the data, or a smoothed approximation like a logspline estimate).

Answer 2

If you had equal N's, you might try a 2 way ANOVA with blocks. But you have different numbers of observations for your four variables (i.e., unequal N's). Unequal N's make a 2 way ANOVA problematic since the various possible comparisons are not independent.

One possible approach would be to do 2 one-way ANOVAs, one for length and one for width. One-way ANOVAs are more forgiving with respect to unequal N's.

BTW, a more complete description of your situation might allow for additional and perhaps more relevant suggestions. Also, there are many pitfalls and complexities in doing statistical analyses. You might want to seek in-person assistance.