Homework SourseNote Though two of the 15 cells will not show expected frequ
Note: Though two of the 15 cells will not show expected frequency at least 5, the approximation of the test statistic by a chi-square distribution could be considered good enough. So you can use chi-square test. This question could be answered either by manually or preparing a SAS data set and using SAS.
Solution
Null Hypothesis: There is no association between physician specialty and recommended treatment.
Alternate Hypothesis: There is a association between physician specialty and recommended treatment
Chi-Square Test
Observed Frequencies
Column variable
Calculations
R
CR
C
Total
fo-fe
Int
6
22
42
70
0.75
4.5
-5.25
sur
23
61
127
211
7.175
8.25
-15.425
Rad
2
3
54
59
-2.425
-11.75
14.175
onc
1
12
43
56
-3.2
-2
5.2
Gyn
1
12
31
44
-2.3
1
1.3
Total
33
110
297
440
Expected Frequencies
Column variable
R
CR
C
Total
(fo-fe)^2/fe
Int
5.25
17.5
47.25
70
0.1071
1.1571
0.5833
sur
15.825
52.75
142.425
211
3.2531
1.2903
1.6706
Rad
4.425
14.75
39.825
59
1.3290
9.3602
5.0453
onc
4.2
14
37.8
56
2.4381
0.2857
0.7153
Gyn
3.3
11
29.7
44
1.6030
0.0909
0.0569
Total
33
110
297
440
Data
Level of Significance
0.05
Number of Rows
5
Number of Columns
3
Degrees of Freedom
8
Results
Critical Value
15.507
Chi-Square Test Statistic
28.9860
p-Value
0.0003
Reject the null hypothesis
Calculated chi square =28.986
Table value of chi square =15.507
Calculated chi square 28.986 > 15.507, table value
The null hypothesis is rejected.
We conclude that there is association between physician specialty and recommended treatment.
| Chi-Square Test | ||||||||
| Observed Frequencies | ||||||||
| Column variable | Calculations | |||||||
| R | CR | C | Total | fo-fe | ||||
| Int | 6 | 22 | 42 | 70 | 0.75 | 4.5 | -5.25 | |
| sur | 23 | 61 | 127 | 211 | 7.175 | 8.25 | -15.425 | |
| Rad | 2 | 3 | 54 | 59 | -2.425 | -11.75 | 14.175 | |
| onc | 1 | 12 | 43 | 56 | -3.2 | -2 | 5.2 | |
| Gyn | 1 | 12 | 31 | 44 | -2.3 | 1 | 1.3 | |
| Total | 33 | 110 | 297 | 440 | ||||
| Expected Frequencies | ||||||||
| Column variable | ||||||||
| R | CR | C | Total | (fo-fe)^2/fe | ||||
| Int | 5.25 | 17.5 | 47.25 | 70 | 0.1071 | 1.1571 | 0.5833 | |
| sur | 15.825 | 52.75 | 142.425 | 211 | 3.2531 | 1.2903 | 1.6706 | |
| Rad | 4.425 | 14.75 | 39.825 | 59 | 1.3290 | 9.3602 | 5.0453 | |
| onc | 4.2 | 14 | 37.8 | 56 | 2.4381 | 0.2857 | 0.7153 | |
| Gyn | 3.3 | 11 | 29.7 | 44 | 1.6030 | 0.0909 | 0.0569 | |
| Total | 33 | 110 | 297 | 440 | ||||
| Data | ||||||||
| Level of Significance | 0.05 | |||||||
| Number of Rows | 5 | |||||||
| Number of Columns | 3 | |||||||
| Degrees of Freedom | 8 | |||||||
| Results | ||||||||
| Critical Value | 15.507 | |||||||
| Chi-Square Test Statistic | 28.9860 | |||||||
| p-Value | 0.0003 | |||||||
| Reject the null hypothesis |
