Tests of Comparison in Weibull

[Sheri Randall]

[Originally Posted: 5/2/00-- Transferred by ReliaSoft Moderator]

Does Reliasoft's "Tests of Comparison"in Weibull++ apply only to relatively large data sets? Can it be used with much confidence on small sample sizes (say less than 8 points in each data set)?

[Dr. Dave]

[Originally Posted: 5/23/00-- Transferred by ReliaSoft Moderator]

The test of comparison can be performed in Weibull++ for any sample size that allows you to estimate the parameters. Given the parameters, the results of the comparison test are calculated assuming the estimated values are exactly correct. The probability that one population is better than a second is caculated as a point estimate; there is no confidence level associated with it. We cope with that by using a strong rule of thumb about what probability is strong enough to make a decision.

If you have small sample size(s) and the confidence in the probability one is better is of concern, it is possible to do a small simulation study for your sample sizes to see what the usual variation is when there is no difference between the population, and how hard it may be to find small differences when you have small sample sizes. That must be a custom solution at this point.

-- Dr. Dave

[Sheri Randall]

[Originally Posted: 5/24/00-- Transferred by ReliaSoft Moderator]

Dr. Dave, Thank you so much for answering my question. I didn't think it would take so long for someone to respond. Actually, I was surprised it was you. I really enjoyed your Weibull ++ training class in Dayton (end of March). I'm not sure if you realized who I was. Next time you are in Ohio I will challenge you to a game of darts! I'm not very good at foosball.

Anyway, I remember from your class that as a rule of thumb you want 80-90% probability in order to conclude that one data set is better than the other when using the Tests of Comparison. However, it seems that most of the examples in class dealt with fairly large sample sizes, say 20-30 pieces. I am leery about using the different tools available when having small sample sizes (6-8).

I didn't quite understand your last paragraph about doing a small simulation study.