The following data were generated from a 2 The following data were generated fro

Question

The following data were generated from a 2 The following data were generated from a 2 times 2 factorial experiment with 3 replicates, where factor A levels represent two different injection procedures of an anesthetic to the occipital nerve (located in the back of the neck), and factor B levels represent two different drugs, which physicians recommend to increase the effectiveness of the injections. Three headache patients were randomly selected for each combination of injection and drug. Test at the 5% significance level to determine if differences exist among means of Factor A levels or among means of Factor B levels and if interaction between factors A and B exists Use the partial output from ANOVA. Which one of the following statements is true? a) Differences do not exist among the levels of factor A, differences exist among the levels of factor B, and there is no interaction between the two factors. b) Differences exist among the levels of factor A, differences exist among the levels of factor B, and there is interaction between the two factors. c) Differences do not exist among the levels of factor A, differences do not exist among the levels of factor B, and there is no interaction between the two factors. d) Differences exist among the levels of factor A, differences exist among the levels of factor B, and there is interaction between the two factors. e) Differences do not exist among the levels of factor A, differences exist among the levels of factor B, and there is interaction between the two factors.

Explanation / Answer

Right choice is a) Difference do not exist among the levels of factor A, differences exizt among the levels of factor B, and there is no interaction between two factors

this 22 factorial with r=3 replication , so total df=22*3-1=11

MS is calcuate using formula MS=SS/df

f is calculate using formula MS/MSE

here at p-value of Factor A is more than alpha=0.05, so this is not significant

p-value of Factor B is less than alpha=0.05, so this is significant

p-value of interaction is more than alpha=0.05, so this is not significant

so we conclude that choice a) is right

Source of Variation SS df MS F critical F(0.05,1,8) P-value Factor A 5.333 1 5.333 1.23068047 5.31765506 0.29950615 Factor B 56.333 1 56.333 12.9997981 5.31765506 0.00692653 Interaction 1.333 1 1.333 0.30761243 5.31765506 0.59431101 Error 34.667 8 4.333375 Total 11

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