Test whether the contingency table has independent row and column variables. The critical value is with one degree of freedom is X2r = 7.879.
Test whether the
| 392 | 13 |
| 564 | 57 |
Here, use chi square test for independence of two categorical variables.
The hypothesis will be as follows:
Null hypothesis: H0: Two categorical variables are independent.
Alternative hypothesis: Ha: Two categorical variables are dependent.
Assume level of significance = = 0.005
Test statistic formula is given as below:
Chi square =
Where, O is observed frequencies and E is expected frequencies.
Given here,
Number of rows = r = 2
Number of columns = c = 2
Degrees of freedom =
α = 0.005
Critical value = 7.879439
(by using Chi square table)
Calculation tables for test statistic are given as below:
|
Observed Frequencies |
|
|||||
|
Column variable |
Calculations |
|
||||
|
Row variable |
C1 |
C2 |
Total |
(O - E) |
|
|
|
R1 |
392 |
13 |
405 |
14.63158 |
-14.6316 |
|
|
R2 |
564 |
57 |
621 |
-14.6316 |
14.63158 |
|
|
Total |
956 |
70 |
1026 |
|||
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