Let's see. That is 10 samples from each tip in a lot of 50: 500 measurements, and we've only looked at 1 lot. 7 more to go! That's a lot of work. Maybe there is some way we can do a little less work, and get information of almost the same precision. Maybe a lot less work.
the process is called 'designing an experiment.' AKA, planning. You are asked if there is a difference in pipette performance, between the 8 lots. We believe that each of the 20 mu liter samples will be slightly different than the others, if only we could measure them precisely enough. So the first consideration is going to be, what is the smallest difference between 2 samples that can possibly be measured, using your methods? If you use a 1 quart measuring cup, you aren't going to find many differences (duh!) Let's assume that you can measure a 20 mu l sample to within 0.05 mu l, most of the time. Now back to that variation between droplets. (side question: how many molecules of H2O is that? - 0.05 mul = 50 nano l) Some of the variation comes from how you do it - trial to trial on a single pipette. Some comes from differences between pipettes, within a single lot. Some comes from differences between the lots (we are assuming that maybe the average pipette from lot 1 is different than an average pipette from lot 4). You have been asked if this last difference is 'statistically significant,' or more correctly, whether this difference is worth discussing. If it is statistically significant, then we can detect this difference, in spite of the clutter from the other sources of variation. In other words, differences between lots will be 'larger' than differences within lots, or within a single pipette. One method for testing to detect this difference is a 2-way AnoVa. You would set up your data in 3 columns, the lot #, the pipette #, and the measurement. Then you would ask some software to crunch the numbers, comparing different lots, and different pipettes. If the software produced a 3-D chart, showing average measurement for each pipette, arrayed in rows by lot #, you might be able to see the results graphically, and select out the odd-balls by eye. Iff the statistics told you there was a real difference in some of them. I don't love your 1 way AnoVa, because it assumes mathematically that you made no variation in your measurements with each pipette. Which you did - you can't avoid it. This variation may be larger than any variation in pipette, too. Your 1 way AoV can't discover this. OK, so we've got to write down each measurement. How many do we have to make? 8 * 500? I think maybe a lot less. If you have some idea of the variation between the different groups, you can make some rational estimates, but without that, and with some trepidation about 4,000 measurements, I'd suggest that you continue to take 10 measurements on each pipette, but only do it with say 20 pipettes in each lot. That will get you down to 8 * 20 * 10 = 1600 measurements. If that is a burden, you might cut that to 7 measurements on each of 12 pipettes, for 8 * 12 * 7 = 672 measurements. Depending on what you know about your measurement error, you might keep the 10 repeats, and go much smaller on the pipettes. How did I get these numbers? Intuition, based on my visualization of the spread in measurements, pipettes, etc. The actual magic number is 18, not 20, but I can't go into that here - too long a story. Now, how to make the measurements. If you do all the measurements on one set of pipettes, then the next set... you will be learning how to do it as you go along, and I bet your individual measurement error will decrease, until you get tired and sloppy. You want to do equally well with all of them, or at least, equally well or poorly with each group, especially each lot. therefore, you should do one pipette from each lot, in sequence. Nah, that still leaves you with a pattern of execution. You should mark all the pipettes, mix them up, then take them out one at a time, and test each pipette in a random order. If you want to get careful, use a list of random numbers to assign order to the pipettes. Don't think you need to randomize the pipettes? Guess again, Kev! How much confounding variation do you want to introduce into your design and analysis? How much can you afford? Information costs money (and time). Here is one point of the trade off. Now, I think, you are ready to run your tests. You will need to practice measuring each droplet. Well, you already did that, 500 times. You will need to work carefully and patiently, avoiding fatigue. You will need to make somewhere between 700 and 4000 measurements. Even Excel (which I don't recommend for the final analysis) can handle 4000 lines of 3 columns, so you should have no problem doing the analysis. Hope you can enter the data automatically. Make sure your results include some graphs, so you can see what you've done. And maybe you _will_ find differences between lots! that are larger than your operator variation. cheers, Jay Kevin McDonald wrote: > > 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? > 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)? > > . > . > ================================================================= > Instructions for joining and leaving this list, remarks about the > problem of INAPPROPRIATE MESSAGES, and archives are available at: > . http://jse.stat.ncsu.edu/ . > ================================================================= -- Jay Warner Principal Scientist Warner Consulting, Inc. 4444 North Green Bay Road Racine, WI 53404-1216 USA Ph: (262) 634-9100 FAX: (262) 681-1133 email: [EMAIL PROTECTED] web: http://www.a2q.com The A2Q Method (tm) -- What do you want to improve today? . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
