Chi-Square Test of Association and T-Test for Breastfeeding Duration

Epidemiology for Health and Medical Sciences II
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Answer 1:
a) A 2x2 contingency table for assessing relationship between treatment group and primary
outcome. The following table output has been created in STATA. Treatment group
variables are row in rows (control and intervention), and outcome variables (any formula
and exclusive) are in columns. The observed frequencies, expected frequencies, and chi-
square test statistic with the p-value have been evaluated (Park, 2011).
STATA OUTPUT FOR CHI-SQUARE TEST OF ASSOCIATION
b) Null hypothesis: There is no association between treatment group and primary outcome
(breast feeding outcome) after 6 months, implying that there no difference in outcome of
breastfeeding duration between control and intervention groups.
Alternate hypothesis: There is a statistically significant association between treatment
group and primary outcome (breast feeding outcome) after 6 months, implying that there
is significant difference in outcome of breastfeeding duration between control and
intervention groups.
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c) First, the row total and column total of the observed frequencies were evaluated. The
expected frequency value for a cell has been calculated by dividing the product of row
total and column total (corresponding to that particular cell) by grand total of observed
frequency. The detail calculation has been done in excel, and concerned formula with
worksheet has been provided below (McHugh, 2013).
Hand Calculations:
For example, column total for “any formula” is 233 and row total for “control” treatment
group is 178. The grand total is evaluated as 340. Hence, expected frequency for
“control” group on “any formula” will be = 233 * 178 / 340 = 121.98.
Control and Any formula has Observed frequency = 128
Expected frequency = 233 * 178 / 340 = 121.98.
Control and Exclusive has Observed frequency = 50
Expected frequency = 107 * 178 / 340 = 56.02.
Intervention and Any formula has Observed frequency = 105
Expected frequency = 233 * 162 / 340 = 111.02.
Intervention and Exclusive has Observed frequency = 57
Expected frequency = 107 * 162 / 340 = 50.98.
EXCEL OUTPUT FOR METHOD OF OBSERVED AND EXPECTED FREQUENCY
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EXCEL OUTPUT FOR OBSERVED AND EXPECTED FREQUENCY
Observed
Frequency Breast feeding outcome at 6 months
Treatment Groups Any formula Exclusive Total
Control 128 50 178
Intervention 105 57 162
Total 233 107 340
Expected
Frequency Breast feeding outcome at 6 months
Treatment Groups Any formula Exclusive Total
Control 121.98 56.02 178
Intervention 111.02 50.98 162
Total 233 107 340
d) 𝜒 2 statistic (degrees of freedom = (r -1) * (c – 1)) is evaluated using the below formula:
𝜒 2 = ∑ (observed frequency – expected frequency) ^ 2 / (expected frequency).
The detailed calculation procedure has been performed in MS Excel. The following excel
table explains the detailed calculations.
Chi-Square test statistics Calculation for each cell:
Control and Any formula = (128 – 121.98) ^2 / 121.98 = 0.30
Control and Exclusive = (50 – 56.02) ^2 / 56.02 = 0.65
Intervention and Any formula = (105 – 111.02) ^2 / 111.02 = 0.3
Intervention and Exclusive = (57 – 50.98) ^2 / 50.98 = 0.71
The row total of Chi-square test statistic is the sum of the chi square values in the
particular row. The column total of Chi-square test statistic is the sum of the chi square
values in the particular column. The final Chi-Square test statistic is evaluated by taking
either the row total or the column total of Chi-Square table (Howell, 2011).
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