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

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)?

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?

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Can you say more about your situation? Are your variables your groups? Do you have different numbers of measurements for each study unit? Are length & width 2 different response variables? You may find it helpful to read this blog post in formulating your question. – gung Aug 22 '12 at 17:21
Sorry about that. I thought it was a straightforward thing, but after reading about it... – Kendra Aug 28 '12 at 10:51
After your recent edit you start your post with a question that is considerably different than the one you end up with. Whether a variable differs significantly between different groups is a very from trying to predict the group by your variables. Is the last one where you want to go? – Erik Aug 28 '12 at 14:52
I see what you're saying. I just assumed that significant difference would allow me to tentatively say if one knife type goes with a length or width than the others. My question would probably be predicting groups based on variables, like you said, but that seems like it would be very complex and outside the range of what I can feasibly do on my own. – Kendra Aug 28 '12 at 14:56

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).

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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.

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 I'm doing analysis on fabric trauma. I have four different knifes, and I've measured the dimensions of the tears they leave in fabric, and would like to see if the knives leave overall different length and widths in the fabric. – Kendra Aug 22 '12 at 14:44 If you are just interested in whether the knives leave any tears, you could dichotomize the fabric samples as tear or no-tear and do a chi-square analysis. If you are interested in the total size of the tear, you could add the length and width of the tear and do one ANOVA. If you are interested in the length of both the length and width tears, you might use the approach I described in my answer. The ANOVA has some sensitivity to distribution, so you should see if your data meets the assumptions of ANOVA, at least approximately. Good luck. – Joel W. Aug 22 '12 at 19:20