Detergent manufacturers frequently make claims about the effectiveness of their

Question

Detergent manufacturers frequently make claims about the effectiveness of their products. A consumer protection service decided to test the five best-selling brands of detergent, where each manufacturer claims that its produce produces the “whitest whites” in all water temperatures. The experiment was conducted in the following way. One hundred fifty white sheets were equally soiled. Thirty sheets were washed in each brand?10 with cold water, 10 with warm water, and 10 with hot water. After washing, the “whiteness” scores for each sheet were measured with laser equipment.

                        Column 1: Water temperature code

                        Column 2: Scores for detergent 1 (first 10 rows = cold water, middle 10 rows =                                    warm, and last 10 rows = hot)

                        Column 3: Scores for detergent 2 (same format of as column 2)

                        Column 4: Scores for detergent 3 (same format of as column 2)

                        Column 5: Scores for detergent 4 (same format of as column 2)

                        Column 6: Scores for detergent 5 (same format of as column 2)

Perform a statistics analysis using a 5% significance statistical evidence to infer that

there are differences in whiteness score between the five detergents,

there are differences in whiteness scores between the three water temperatures,

there are interaction between detergents and temperatures.

For the three tests in (a)?which one should be tested first? If this test is significant, what should we do?

Temperature Detergent1 Detergent2 Detergent3 Detergent4 Detergent5 Cold 66 83 70 44 84 Cold 87 62 75 59 67 Cold 55 61 62 47 99 Cold 41 85 68 60 85 Cold 68 75 72 79 73 Cold 49 78 92 62 74 Cold 52 68 70 73 76 Cold 57 66 71 64 82 Cold 66 93 74 69 79 Cold 64 80 81 79 81 Warm 78 63 71 70 87 Warm 65 47 88 80 100 Warm 68 88 90 78 83 Warm 75 74 85 72 82 Warm 57 71 78 71 93 Warm 48 71 69 75 76 Warm 84 71 60 101 87 Warm 69 68 80 81 76 Warm 55 80 61 87 70 Warm 78 69 88 82 79 Hot 99 82 97 85 84 Hot 87 85 98 83 95 Hot 57 72 79 94 82 Hot 84 71 60 89 74 Hot 93 72 84 77 97 Hot 64 77 58 100 87 Hot 90 73 79 92 80 Hot 85 88 86 102 76 Hot 64 75 91 93 91 Hot 84 77 75 86 96

Explanation / Answer

Two-way ANOVA: Response versus Temperature, Detergent

Source DF SS MS F P
Temperature 2 3915.3 1957.63 17.84 0.000
Detergent 4 2968.9 742.22 6.77 0.000
Interaction 8 2456.2 307.03 2.80 0.007
Error 135 14810.5 109.71
Total 149 24150.8

First we test whether the interaction between detergents and temperatures is present or absent. If interaction effect is present then it is meaningless to test whether the differences in whiteness score between the five detergents is significant or not and the differences in whiteness scores between the three water temperatures is significant or not.

Since p-value corresponding to interaction is 0.007<0.05 so interaction effect is significantly present and so it is not required to test the differences in whiteness score between the five detergents is significant or not and the differences in whiteness scores between the three water temperatures is significant or not separately

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