Testing the Hypothesis
To test the null hypothesis, we compare the observed and the expected frequencies. If the actual and the expected values are nearly equal to each other we accept the null hypothesis and if there is a large difference between the two values we reject the null hypothesis. This is what we do as far as observation of the data is concerned and then reaching a conclusion. But mathematically, we employ the chi square statistic given by
where,
f_{o} is the observed frequency
f_{e} is the expected frequency.
If this value happens to be smaller, then we conclude that there is a little difference between the actual and the expected frequencies and if the difference is larger, then we conclude that the actual and the expected values are not equal. This is identical to the conclusion where we reach by observing the data. Further this value is compared with the value obtained from the table. We look at how the value is obtained from the table.
f_{o}
f_{e}
f_{o} - f_{e}
(f_{o} - f_{e})^{2}
(f_{o} - f_{e})^{2}/(f_{e})
400
475
-75
5625
11.84
550
75
450
-25
625
1.32
500
25
600
525
10.71
1.19
Total
50.12
The value of the Chi Square Statistic is = 50.12.