Chapters10-11: Chi-Square Test of Independence
From William E. Becker, Statistics for Business and Economics Using Microsoft Excel 97, S.R.B. Publishing, 1997, p. 375-376. Reproduced with permission of S.R.B. Publishing.
Exercise 11.3 (p. 375-376) Absenteeism among assembly line workers is of concern. In particular, there may be a relationship between the day of the week on which absences occur and the type of job performed by the worker. Workers are classified as skilled, semiskilled, and laborer. A random sample of days absent was selected from records kept over the past several years; workers were never included more than once in the following results:
Days Absent Among Assembly Line Workers
Type of Worker
|
Days |
Skilled |
Semiskilled |
Laborer |
|
Mondays |
18 |
23 |
21 |
|
Tuesdays |
10 |
16 |
17 |
|
Wednesdays |
12 |
11 |
9 |
|
Thursdays |
17 |
16 |
16 |
|
Fridays |
22 |
26 |
20 |
Are days and type of worker independent?
Answer: We are testing the following hypothesis:
H0: Days and type of worker are independent.
HA: Days and type of worker are not independent.
To test this hypothesis, we can construct the following expected frequency table:
|
|
Skilled |
Semiskilled |
Laborer |
Total |
|
Monday |
19.28 |
22.46 |
20.26 |
62 |
|
Tuesday |
13.37 |
15.57 |
14.05 |
43 |
|
Wednesday |
9.95 |
11.59 |
10.46 |
32 |
|
Thursday |
15.24 |
17.75 |
16.01 |
49 |
|
Friday |
21.15 |
24.63 |
22.22 |
68 |
|
Total |
79 |
92 |
83 |
254 |
The x2 test statistic is calculated to be
This calculated x2 value is smaller than the typical critical values. For example, the critical x2(0.05, df=8) = 15.5073, at a 0.05 a level. Thus, we cannot reject H0 at a = 0.05. Alternatively, we can look at the p-value, which is determined in EXCEL as 0.936282917 =CHIDIST(2.96908,8). The calculated Chi-square is small and the p-value is large; thus, we conclude that days and type of worker are independent.
Go to:
Examples of EXCEL Use
Statistics for Business and Economics WWW Page