Interpret results from a chi-squared test. Background Information: A large study
ID: 3222531 • Letter: I
Question
Interpret results from a chi-squared test.
Background Information:
A large study was carried out to test the hypothesis that development of breast cancer is associated with the birth of a woman’s first child when she is 30 years or older. This is a case-control study; 3,220 women with breast cancer and 10,245 controls were selected. The controls were sampled so that the distribution of their ages matched the distribution of the women with breast cancer, but the cases were not individually matched. (This is an unmatched case-control study.)
The women in the study all had at least one child. (The children born to women with breast cancer were born at least a year before their mothers’ cancers were diagnosed.) The women’s age at the birth of their first child was categorized as less than 30 years or 30 years of age or older.
age at birth of first child
30 years 29 years
breast cancer 683 2537 3220
control 1498 8747 10245
STATA Outputs:
. prtesti 3220 683 10245 1498, count
Two-sample test of proportions x: Number of obs = 3220
y: Number of obs = 10245
------------------------------------------------------------------------------
Variable | Mean Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
x | .2121118 .0072042 .1979918 .2262318
y | .1462177 .0034907 .1393759 .1530594
-------------+----------------------------------------------------------------
diff | .0658941 .0080054 .0502039 .0815844
| under Ho: .0074434 8.85 0.000
------------------------------------------------------------------------------
diff = prop(x) - prop(y) z = 8.8527
Ho: diff = 0
Ha: diff < 0 Ha: diff != 0 Ha: diff > 0
Pr(Z < z) = 1.0000 Pr(|Z| > |z|) = 0.0000 Pr(Z > z) = 0.0000
. tabi 683 2537 1498 8747, row exp chi2
+--------------------+
| Key |
|--------------------|
| frequency |
| expected frequency |
| row percentage |
+--------------------+
| col
row | 1 2 | Total
-----------+----------------------+----------
1 | 683 2,537 | 3,220
| 521.6 2,698.4 | 3,220.0
| 21.21 78.79 | 100.00
-----------+----------------------+----------
2 | 1,498 8,747 | 10,245
| 1,659.4 8,585.6 | 10,245.0
| 14.62 85.38 | 100.00
-----------+----------------------+----------
Total | 2,181 11,284 | 13,465
| 2,181.0 11,284.0 | 13,465.0
| 16.20 83.80 | 100.00
Pearson chi2(1) = 78.3698 Pr = 0.000
Question: Interpret the results from the chi-squared test in words.
Explanation / Answer
Here the level of significance is 0.05. Also P-value is 0.0000. Since P-value is less than the level of significance, we reject the null hypothesis and we conclude that the development of breast cancer is associated with the birth of woman's first child when she is 30 years or older.
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