t-test
example


Problem: Sam Sleepresearcher hypothesizes that people who are allowed to sleep for only four hours will score significantly lower than people who are allowed to sleep for eight hours on a cognitive skills test. He brings sixteen participants into his sleep lab and randomly assigns them to one of two groups. In one group he has participants sleep for eight hours and in the other group he has them sleep for four. The next morning he administers the SCAT (Sam's Cognitive Ability Test) to all participants. (Scores on the SCAT range from 1-9 with high scores representing better performance).

SCAT scores
8 hours sleep group (X) 5 7 5 3 5 3 3 9
4 hours sleep group (Y) 8 1 4 6 6 4 1 2

 
x (x-Mx)2 y (y - My)2
5 0 8 16
7 4 1 9
5 0 4 0
3 4 6 4
5 0 6 4
3 4 4 0
3 4 1 9
9 16 2 4
Sx=40 S(x-Mx)2=32 Sy=32 S(y-My)2=46
Mx=5
My=4
   

*(according to the t sig/probability table with df = 14, t must be at least 2.145 to reach p < .05, so this difference is not statistically significant)

Interpretation: Sam's hypothesis was not confirmed. He did not find a significant difference between those who slept for four hours versus those who slept for eight hours on cognitive test performance.


Practice by creating your own data and then check your work with the Virtual Statistician t-test Calculator
(Only works with n = 8)



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