Unformatted text preview: S Total = SSTO = x ij x 2 SS
SS Groups
SS Error DF
k–1
N–k Total groups SSTO MS
MS Groups
MS Error N–1 values Confidence Interval xi t * sp df = N – k ni 174 Under H0, the F statistic follows an F(k – 1, N – k) distribution. F
F Try It! Comparing 3 Drugs We wish to compare three drugs for treating some disease. A quantitative response is measured such that a smaller value indicates a more favorable response. A total of N 19 patients are randomly assigned to one of the three drug (treatment) groups. The data are provided below: independent random samples seems ok Data from Drug 1 7.3 8.2 10.1 6.0 9.5 Data from Drug 2
7.1
10.6
11.2
9.0
8.5
10.9
7.8 Data from Drug 3 5.8 6.5 8.8 4.9 7.9 8.5 5.2 Let’s first look at this data graphically. N = 19
k= 3
n 1 = 5, n 2 = 7, n 3 = 7
Note: the medians seem to
differ with Drug 3 giving the
lower responses overall.
This is what we are testing
about. Tells us we have
some evidence against H0. Recall the assumptions for performing an F‐test and think about how you would check these assumptions. Each sample is a ... random sample (hard to check here) The k random samples are ... independent ok via randomization! For each of population the model for the response is... a normal distribution (via qq plots) The k population variances are .... equal. 1 2 2 2 k2 (sample stdevs + IQRs) The IQRs are similar (lengths of the boxes), there are no outliers, how many qqplots would we need to make? A: 3 one for each group! State the hypotheses to be tested: H0: 1 = 2 = 3 versus Ha: at least one i is different 175 Note: We would use a computer or calculator to work at least the basic summaries in steps 1 and 2, and likely to create the entire ANOVA table for us. Let’s be sure we understand where the values are coming from and how to interpret the final results. Step 1: Calculate the mean and variance for each sample: 7.3 8.22 8.2 8.22 9.5 8.22 2.74
7.3 8.2 10.1 6 9.5
x1 8.22 s12 5 1
5 2
x2 9.30
s 2 2.61
2 2 2 Note: sample...
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This document was uploaded on 02/25/2014 for the course STATS 250 at University of Michigan.
 Summer '10
 Gunderson
 Statistics, Variance

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