I have run a chi squared test on this data. 4 of the expected frequencies are be
ID: 3252283 • Letter: I
Question
I have run a chi squared test on this data. 4 of the expected frequencies are below 5, so I need to collapse columns. Which columns are best to collapse so that the test works but without changing the story.
Table 1: Relationship between general health and BMI (row percentages General Health BAD Excellent Very good Good Fair Poor N N(%) N N N Underweight 3 (23) 5 (39) 3 (23) 1 (8) 10 (4) Healthy weight 61 (22) 110 (39) 78 (28) 24 (90 Overweight 27 (80 128 (38) 134 (400 36 (11) 13 (4) 11 (4) 75 (25) 146 (48) 60 (20) 11 (4) Obese Total 100 (9) 316 (34) 363 (42) 123 (13) 35 (4) Total N 13 (1000 283 (1000 338 (1000 303 (1000 (100)Explanation / Answer
Answer:
a).
I have run a chi squared test on this data. 4 of the expected frequencies are below 5, so I need to collapse columns. Which columns are best to collapse so that the test works but without changing the story.
Collapse the columns Excellent and very good to one column.
Collapse the columns fair and poor to one column.
Chi-square Contingency Table Test for Independence
c1
c2
c3
Total
r1
Observed
4
5
4
13
Expected
5.77
5.04
2.19
13.00
r2
Observed
171
78
34
283
Expected
125.64
109.64
47.72
283.00
r3
Observed
155
134
49
338
Expected
150.06
130.94
56.99
338.00
r4
Observed
86
146
71
303
Expected
134.52
117.38
51.09
303.00
Total
Observed
416
363
158
937
Expected
416.00
363.00
158.00
937.00
65.07
chi-square
6
df
4.17E-12
p-value
Still we get 1 expected frequency is below 5. But this may not violate the assumption.
Chi-square Contingency Table Test for Independence
c1
c2
c3
Total
r1
Observed
4
5
4
13
Expected
5.77
5.04
2.19
13.00
r2
Observed
171
78
34
283
Expected
125.64
109.64
47.72
283.00
r3
Observed
155
134
49
338
Expected
150.06
130.94
56.99
338.00
r4
Observed
86
146
71
303
Expected
134.52
117.38
51.09
303.00
Total
Observed
416
363
158
937
Expected
416.00
363.00
158.00
937.00
65.07
chi-square
6
df
4.17E-12
p-value