In a study of eating disorders
In a study of eating disorders among adolescent girls, aresearcher asked each of the subjects whether they would prefer togain weight, lose weight, or maintain their present weight. ForWhite girls: 34 want to reduce weight, 66 would like to maintainweight, and 31 want to gain weight; For African- American girls: 23want to reduce weight, 44 would like to maintain weight, 68 want togain weight.
You are asked to examine whether race influences adolescentgirls’ attitude towards their weight, i.e. Perform thefollowing:
a. State the hypotheses (4pts)b. Set up the contingency table, along with the marginal row andmarginal column (10pts)c. Use the 6-steps hypothesis test to determine whether raceinfluences attitude towards weight(26pts)
Answer:
Chi-square test of independence
Solution:
Part a
Here, we have to use chi square test for independence of twocategorical variables.
Null hypothesis: H0: Race does not influence attitudetowards weight.
Alternative hypothesis: Ha: Race influences attitudetowards weight.
Part b
Calculation tables for test statistic are given as below:
|
Observed Frequencies |
||||
|
|
Column variable |
|
||
|
Row variable |
Reduce weight |
maintain weight |
Gain weight |
Total |
|
White Girls |
34 |
66 |
31 |
131 |
|
African American Girls |
23 |
44 |
68 |
135 |
|
Total |
57 |
110 |
99 |
266 |
Part c
We assume level of significance = α = 0.05
Test statistic formula is given as below:
Chi square = ∑[(O – E)^2/E]
Where, O is observed frequencies and E is expectedfrequencies.
E = row total * column total / Grand total
We are given
Number of rows = r = 2
Number of columns = c = 3
Degrees of freedom = df = (r – 1)*(c – 1) = 1*2 = 2
α = 0.05
Critical value = 5.991464547
(by using Chi square table or excel)
Calculation tables for test statistic are given as below:
|
Observed Frequencies |
||||
|
|
Column variable |
|
||
|
Row variable |
Reduce weight |
maintain weight |
Gain weight |
Total |
|
White Girls |
34 |
66 |
31 |
131 |
|
African American Girls |
23 |
44 |
68 |
135 |
|
Total |
57 |
110 |
99 |
266 |
|
Expected Frequencies |
||||
|
|
Column variable |
|
||
|
Row variable |
Reduce weight |
maintain weight |
Gain weight |
Total |
|
White Girls |
28.07142857 |
54.17293233 |
48.7556391 |
131 |
|
African American Girls |
28.92857143 |
55.82706767 |
50.2443609 |
135 |
|
Total |
57 |
110 |
99 |
266 |
|
Calculations |
||
|
(O – E) |
||
|
5.928571 |
11.82707 |
-17.7556 |
|
-5.92857 |
-11.8271 |
17.75564 |
|
(O – E)^2/E |
||
|
1.25209 |
2.582093 |
6.46618 |
|
1.214991 |
2.505586 |
6.274589 |
Chi square = ∑[(O – E)^2/E] = 20.29552888
P-value = 0.0000392
(By using Chi square table or excel)
P-value < α = 0.05
So, we reject the null hypothesis
There is sufficient evidence to conclude that Race influencesattitude towards weight.
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