PSLS.PPT.Ch24

# PSLS.PPT.Ch24 - OnewayANOVA: Comparingseveralmeans PSLS...

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One-way ANOVA:  Comparing several means PSLS chapter 24 © 2009 W.H. Freeman and Company

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Objectives (PSLS chapter 24) One-way ANOVA Comparing several means The ANOVA F-test ANOVA assumptions ANOVA calculations Using Table F Interpreting results from an ANOVA
Comparing several means When comparing >2 populations, the question is not only whether each population mean µ i is different from the others, but also whether they are significantly different when taken as a group . We would probably find significance if we specifically compared the two extremes, sample3 and sample5. Population Sample 4 Sample 1 Sample 2 Sample 5 Sample 6 Sample 3

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There should only be one null hypothesis, stating that we have sampled many times from the same population. It would be wrong to test a series of 2-sample null hypotheses or to only test the two most extreme results. If we set α = 5% and run multiple analyses, we can expect to incorrectly reject H 0 (Type I error) about 5% of the time. Population Sample 4 Sample 1 Sample 2 Sample 5 Sample 6 Sample 3
Handling multiple comparisons statistically The first step in examining multiple populations statistically is to test for an overall statistical significance as evidence of any difference among the parameters we want to compare. ANOVA F-test If that overall test showed statistical significance , then a detailed follow-up analysis can examine all pair-wise parameter comparisons to define which parameters differ from which and by how much. more complex methods (see Chapter 26)

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How do we compare several means? We want to know if the observed differences in sample means are likely to have occurred by chance just because of the random sampling. This will likely depend on both the difference between the sample means and how much variability there is within each sample.
Do nematodes affect plant growth? A botanist prepares 16 identical planting pots and adds different numbers of nematodes into the pots. Seedling growth (in mm) is recorded two weeks later. Nematodes and plant growth Nematodes 0 10.8 9.1 13.5 9.2 10.65 1,000 11.1 11.1 8.2 11.3 10.43 5,000 5.4 4.6 7.4 5 5.6 10,000 5.8 5.3 3.2 7.5 5.45 Seedling growth Overall mean 8.03 x i Hypotheses: All μ i are the same ( H 0 ) versus not all i are the same ( H a )

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A factor is a variable that can take one of several levels used to differentiate one group from another. An experiment has a one-way or completely randomized design if several levels of one factor are being studied and the individuals are randomly assigned to its levels. ( There is only one way to group the data. ) 1-way: 4 levels of nematode quantity in seedling growth experiment But 2 seed species and 4 levels of nematodes would be a 2-way design. One-way ANOVA
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## This note was uploaded on 10/07/2011 for the course BSTT 400 taught by Professor Sallyfreels during the Fall '11 term at Ill. Chicago.

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PSLS.PPT.Ch24 - OnewayANOVA: Comparingseveralmeans PSLS...

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