If you do a one-way analysis of variance, instead of a mess of t tests, you will pull out a generalized variation in counts, which is to say, a standard deviation (stdev).
If you do it with the 3 samples & 20 repetitions as you suggest below, I _think_ you will wind up with an estimated stdev for the sample counts. And this _assumes_ that the samples were pulled independently from the same flask, and that the 20 count locations were not related to one another in any way.
Then there is the question of the distribution of particle counts. It could be well away from a "Normal' dist, which might throw off your interpretation of what a stdev means. Have you checked?
Let's assume for a moment that the dist. is Normal, and proper independence exists. We still need to know what 'close enough' is.
If you could say "an estimate of mean within 'delta' is close enough" then I would suggest that you use
n ~>= (2*s/delta)^2
where s is the stdev.
I'm sure this estimate can be refined, and should be. No matter what you do, however, you have to say what 'close enough' is.
Cheers,
Jay
Euh wrote:
Hello all,
I'm trying to evaluate the concentration of suspended particles �n a flask. I took 3 differents samples from the flask and, for each sample, I did 20 counts under the microscope (= at 20 different locations on the microscope slide)
I ended up with the data posted below this post.
My question is:
Given this data, what is the minimum number of samples and/or counts required to insure that I get a value close enough to the true value ?
To adress the issue of "how many samples", I was thinking of compairing the mean of each column with the global mean using a t-test (since the variance is unknown). Is this the right approach ? Should I use the paired or unpaired t-test ?
To determine the minimum number of counts, what should I do ?
Thanks for the help
Data (each column is a sample, each row is a count)
98 108 115 123 102 120 88 90 93 65 71 92 95 56 131 68 145 138 114 136 116 82 100 98 87 85 70 109 116 56 134 157 34 102 60 113 130 90 125 53 121 63 124 111 81 114 92 117 118 131 109 76 55 113 97 256 108 79 146 72 . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
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