A researcher wanted to know if individuals have better reaction times depending on when the test is taken -- in the morning or in the afternoon. He randomly assigned 16 participants to take the same reaction time test in either the morning or the afternoon. The following results were obtained, where lower scores indicate faster reaction time. Assume that the parametric test assumptions ARE violated. Conduct an appropriate statistical test using an alpha of .05 and the eight steps of hypothesis testing. Note: more information given in table than is needed Individual Morning (X1) R1 X12 Individual Afternoon (X2) R2 X22 D Ranks D2 + - 1 79 6241 9 91 8281 -12 144 2 88 7744 10 92 8464 -4 16 3 95 9025 11 87 7569 8 64 4 78 6084 12 87 7569 -9 81 5 81 6561 13 94 8836 -13 169 6 83 6889 14 86 7396 -3 9 7 80 6400 15 82 6724 -2 4 8 84 7056 16 93 8649 -9 81 Total 668 56000 712 63488 -44 568 Means 83.5 89 -5.5
A researcher wanted to know if individuals have better reaction times depending on when the test is taken -- in the morning or in the afternoon. He randomly assigned 16 participants to take the same reaction time test in either the morning or the afternoon. The following results were obtained, where lower scores indicate faster reaction time. Assume that the parametric test assumptions ARE violated. Conduct an appropriate statistical test using an alpha of .05 and the eight steps of hypothesis testing.
Note: more information given in table than is needed
|
Individual |
Morning (X1) |
R1 |
X12 |
Individual |
Afternoon (X2) |
R2 |
X22 |
D |
Ranks |
D2 |
+ |
- |
|
1 |
79 |
|
6241 |
9 |
91 |
|
8281 |
-12 |
|
144 |
|
|
|
2 |
88 |
|
7744 |
10 |
92 |
|
8464 |
-4 |
|
16 |
|
|
|
3 |
95 |
|
9025 |
11 |
87 |
|
7569 |
8 |
|
64 |
|
|
|
4 |
78 |
|
6084 |
12 |
87 |
|
7569 |
-9 |
|
81 |
|
|
|
5 |
81 |
|
6561 |
13 |
94 |
|
8836 |
-13 |
|
169 |
|
|
|
6 |
83 |
|
6889 |
14 |
86 |
|
7396 |
-3 |
|
9 |
|
|
|
7 |
80 |
|
6400 |
15 |
82 |
|
6724 |
-2 |
|
4 |
|
|
|
8 |
84 |
|
7056 |
16 |
93 |
|
8649 |
-9 |
|
81 |
|
|
|
Total |
668 |
|
56000 |
|
712 |
|
63488 |
-44 |
|
568 |
|
|
|
Means |
83.5 |
|
|
|
89 |
|
|
-5.5 |
|
|
|
|
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