18.12 A psychologist employs a two-factor experiment to study the combined effec

Question

18.12 A psychologist employs a two-factor experiment to study the combined effect of sleep deprivation and alcohol consumption on the performance of automobile drivers. Before the driving test, the subjects go without sleep for various time periods and then drink a glass of orange juice laced with controlled amounts of vodka. Their performance is measured by the num- ber of errors made on a driving simulator. Two subjects are randomly assigned to each cell, that is, each possible combination of sleep depriva tion (either 0, 24, 48, or 72 hours) and alcohol consumption (either 0,1, 2, or 3 ounces), yielding the following results NUMBER OF DRIVING ERRORS SLEEP DEPRIVATION (HOURS) ALCOHOL CONSUMPTION OUNCES 24 4 72 T 29 841 36 1296 53 2809 68 4624 5 5 12 4 4 10 9 6 7 13 15 cm 25 30 64 67 625 900 4096 4489 G= 186 G2-34596 (a) Summarize the results with an ANOVA table (b) If appropriate, conduct additional F tests, estimate effect sizes, and use Tukey's HSD test.

Explanation / Answer

ANOVA table is

By looking at p-values for each factor and interaction, we conclude that:

Both the factors 1 &2 have impact on driving errors whereas their interaction doesn't have any impact. (at 5% level)

Anova: Two-Factor With Replication SUMMARY 0 24 48 72 Total 0 Count 2 2 2 2 8 Sum 3 6 9 11 29 Average 1.5 3 4.5 5.5 3.625 Variance 4.5 2 0.5 0.5 3.696429 1 Count 2 2 2 2 8 Sum 4 6 13 13 36 Average 2 3 6.5 6.5 4.5 Variance 2 0 0.5 4.5 5.714286 2 Count 2 2 2 2 8 Sum 8 7 19 19 53 Average 4 3.5 9.5 9.5 6.625 Variance 2 4.5 4.5 12.5 12.83929 3 Count 2 2 2 2 8 Sum 10 11 23 24 68 Average 5 5.5 11.5 12 8.5 Variance 2 4.5 4.5 18 16.28571 Total Count 8 8 8 8 Sum 25 30 64 67 Average 3.125 3.75 8 8.375 Variance 3.839286 2.785714 9.714286 12.55357 ANOVA Source of Variation SS df MS F P-value F crit Sample 115.125 3 38.375 9.164179 0.000918 3.238872 Columns 182.625 3 60.875 14.53731 7.84E-05 3.238872 Interaction 20.125 9 2.236111 0.533997 0.829228 2.537667 Within 67 16 4.1875 Total 384.875 31

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