Introductory Applied Statistics for the Life Sciences
Introductory Applied Statistics for the Life Sciences STAT 371
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Mrs. Triston Collier
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This 4 page Class Notes was uploaded by Mrs. Triston Collier on Thursday September 17, 2015. The Class Notes belongs to STAT 371 at University of Wisconsin - Madison taught by Staff in Fall. Since its upload, it has received 9 views. For similar materials see /class/205079/stat-371-university-of-wisconsin-madison in Statistics at University of Wisconsin - Madison.
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Date Created: 09/17/15
Multiple comparisons When we carry out an ANOVA on k treatments we test Ho m uk versus a H0 is false Assume we reject the null hypothesis ie we have some evidence that not all treatment means are equal Then we could for example be interested in which ones are the same and which ones differ For this we might have to carry out some more hypothesis tests This procedure is referred to as multiple comparisons Key issue We will be conducting say T different tests and we become concerned about the overall error rate sometimes called the familywise error rate Overall error rate Prreject at least one Ho all Ho are true 1 1 Prreject first first H0 is trueT if independent 3 T x Prreject first first H0 is true generally Types of multiple comparisons There are two different types of multiple comparisons procedures Sometimes we already know in advance what questions we want to answer Those comparisons are called planned or a priori comparisons Sometimes we do not know in advance what questions we want to answer and the judgement about which group means will be studied the same depends on the ANOVA outcome Those comparisons are called unplanned or a posteriori comparisons The distinction Planned comparisons adjust for just those tests that are planned Unplanned comparisons adjust for all possible comparisons Former example We previously investigated whether the mean blood coagulation times for animals receiving different diets A B C or D were the same Imagine A is the standard diet and we wish to compare each of diets B C D to diet A gt planned comparisons After inspecting the treatment means we find that A and D look similar and B and C look similar but A and D are quite different from B and C We might want to formally test the hypothesis MAMDMBMC gt unplanned comparisons Another example A plant physiologist recorded the length of pea sections grown in tissue culture with auxin present The purpose of the experiment was to investigate the effects of various sugars on growth Four different treatments were used plus one control no sugar 0 No sugar 0 2 glucose 0 2 fructose o 1 glucose 1 fructose o 2 sucrose