"Kevin McDonald" <[EMAIL PROTECTED]> wrote in message zmSj8.18887$[EMAIL PROTECTED]">news:zmSj8.18887$[EMAIL PROTECTED]... > I am a graduate student with very little training in statistics. My > supervisor has assigned me a small project in which I must select an > appropriate statistical test. The project involves 20 microlitre pipette > tips. Pipette tips are used to dispense small volume of liquids in > experiments. The tips are sold in lots of 50 and I must assess whether > differences exist between 8 different lots. I performed an experiment in > which I dispensed and weighed ten 20uL samples for each tip in a lot. I > then calculated the mean sample weight dispensed for each tip. This gave > me a total of 50 samples for each of the eight lots(population). I have > decided to perform a one way ANOVA test. > > Questions: > 1. Is this an appropriate test?
No, if you are interested only in these 8 lots consisting of just the 50 tips, which are in each lot. Then only measurement variation is relevant for comparing the lots with respect to mean performance (or with respect to variability within the lots, if you like). Yes, under certain conditions, if the lots are considered to be a random sample from a population of lots and if the tips within lots are considered to be a random sample from a population of tips. In this more general point of view you will be interested in estimating variance components (and testing, if you like, but you may take for sure that all variance components differ from zero). > 2. Does the fact that each of the 50 samples in a lot is a mean itself have > any influence on the statistical test. That is, can means be used to > calculate a mean for the population(lot)? These are two different questions. In the "Yes" case the answer is no and yes respectively. Depending on the design of the experiment, there may be more than the 3 levels of variability considered by you. But, for simplicity, suppose that all measurements have been done in a completely random order. Then all measurement variability is represented in the differences between samples within tips. Besides this, there is the variabilty between tips within lots and the variability between lots. >From your data, assuming that the posed conditions are met, variance components for these 3 levels of variation can be estimated using analysis of variance for a nested design. It is also possible to use this analysis for testing. Depending on the point of view taken, the mean square for differences between lots should be tested against the mean square for samples within tips (the "No" case above) or against the mean square between tips within lots (the "Yes" case above). If the measurements still had to be done I would recommend a two stage setup. In the first stage you should measure only 2 samples with each of 2 or 3 randomly chosen tips from each lot to get an idea of the magnitude of the variance components. In the second stage you could decide on a larger sample for obtaining sufficient precision; probably you would need far less measurements than the 4000 you did. (Given your data, you can simulate this suggestion, eventually!) Jos Jansen . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
