Hi optomist1

Some thoughts in my usual, verbose style.

1) I am a big fan of visually checking data prior to any analysis.

You state quite clearly that you checked to assess the distribution of each sample. Was this done visually? Did you plot the two distributions on the same graph? I expect that you did, but it's nice to have that confirmed.

The reason for asking is that, if the two distributions do not overlap, there is limited use in doing a formal test. The distributions are clearly different and any useful statistical test will simply tell you what is obvious just by looking at the graphs. No overlap = different. This of course assumes that you have sufficient data.

I assume that you have checked the data visually, and that there is a problematic amount of overlap between the two sets of data, hence the need for a test.

2) How different in shape are the distributions?

You state that one is Normal and one is Weibull. Weibull distributions can take a wide range of shapes from a one sided 'ski jumpl' shape, a highly skewed 'sand dune' shape (not a mathematical description, but I hope you know what I mean!), all the way to a classic bell shaped 'Normal' looking curve.

If your Weibull distribution looks like a Normal curve, but it fits the Weibull distribution a little better, perhaps you don't need to worry about the slight difference in shapes. Many parametric tests are robust to slight departures from Normality. You only have 30 data to define the curve, which is not a huge number. Perhaps if you repeated your comparison experiment, the "Weibull-ness" (!!!) would turn out to be just an artefact of the small sample size.

On the other hand, if you are comparing a bell with a ski jump, I understand only too clearly why you posted your above question.

3) Regarding the requirement for Normal data for t-tests and ANOVA.

Yes, they require Normal data. Both procedures were developed on the assumption of Normal data. The usual get-out-of-jail-free clause has already been stated above. "Many parametric tests are robust to slight departures from Normality." So if your data are only a bit non Normal, you should be ok.

If you need non parametric tests, you have a choice. For an equivalent of the t-test, you have the Wilcoxon (or Mann-Whitney) test. There are also non parametric equivalents for ANOVA. Be aware that non-parametric tests do assume that the underlying distributions are the same, so if you do have wildly different shapes, these tests may not be reliable.

4) When is data not Normal?

Sadly, that is a bit like the oxymoron of "exact uncertainties". There isn't a razor sharp cutoff between Normal and non Normal. All you get is increasingly unreliable statistical tests.

If you can, get more data. If your operator and your crimping machine are repeatable, you can combine the two sets of data to reduce the variance and get a better idea of the shape of the distributions.

4) Irrespective of any formal tests, remember the difference between statistical significance and practical significance.

Is the difference worth any investment in new equipment? This is a financial question, but very important. If you only have a slight difference in the reliability of your final product, is it worth the cost of the new equipment?

Hope this helps

NC