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MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Step 1

let X denote the scores due to  brightness discrimination,

& Y denote the scores due to pattern discrimination.

sample size, n = 10

Assuming that the scores are normally distributed. To test whether both the tasks were easier to learn or one easier than the other a paired t-test would be used. The hypothesis of no difference is

    H0: μx=μyH1: μx≠μy

Under the null hypothesis, the test statistic is

       t=d¯S/n~tn-1

where d¯=1n∑idi       ;di=xi-yi,  i = 1, 2, ..., n

 &     S=1n-1∑i(di-d¯)2

Calculations for the test statistic

S.No. X Y d=X-Y  (d - d¯)2
1 22 14 8 0.36
2 16 8 8 0.36
3 10 5 5 5.76
4 15 7 8 0.36
5 25 13 12 21.16
6 33 15 18 112.36
7 8 10 -2 88.36
8 26 15 11 12.96
9 18 11 7 0.16
10 13 14 -1 70.56
Total 186 112 74 312.4

    d¯=1n∑idi=110×74=7.4

  S=1n-1∑i(di-d¯)2    = 19×312.4  = 5.89

     

 

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