Ch 16 - ANOVA

The degrees of freedom used to find the t multiplier

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Unformatted text preview: ____ b. State your conclusions regarding the differences between the mean response for the three drug groups based on the Tukey multiple comparison method. We can conclude that the population mean responses differ for … subjects taking Drug 2 and Drug 3 but do not differ for … subjects taking Drugs 1 and 3 nor Drugs 1 and 2. 178 Individual Confidence Intervals for the Population Means Sometimes it is helpful to examine a confidence interval for the mean for each population. Since in ANOVA we assume the population standard deviations are all equal, the estimate of that common population standard deviation s p MSE is used in forming the individual confidence intervals. The degrees of freedom used to find the t* multiplier will be those associated with the estimated standard deviation, namely N – k. The summary for the individual confidence intervals is provided below. Try It! Comparing 3 Drugs We were comparing k = 3 groups based on a total of N = 19 observations. The pooled standard deviation for the comparison of the three drugs data set is sp = 1.62. The sample means and sample sizes were: Drug 1: Drug 2: Drug 3: Sample mean = 8.22 Sample mean = 9.30 Sample mean = 6.80 Sample size = 5 Sample size = 7 Sample size = 7 The degrees of freedom for the t* multiplier is N – k = __19 – 3 = 16 ___. From the table of t* multipliers (Table A.2) with confidence level = 0.95 and the above degrees of freedom we have t* = __2.12 ____ Drug 3 was descriptively the best. Compute a 95% confidence interval for the population mean response for all subjects taking Drug 3. 6.80 1.30 (5.50, 8.10) 179 Try It! Memory Experiment In a memory experiment, three groups of subjects were given a list of words to try to remember. The length of the list for the first group was 10 words (short), whereas for the second group it was 20 words (median) and for the third group 40 words (long). The percentage...
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