Question

A study was conducted to investigate potential risk factors for ectopic pregnancy. Of the 279 women who had experienced ectopic pregnancy, 28 had suffered from pelvic inflammatory disease. Of the 279 women who had not experienced ectopic pregnancy, 6 had suffered from pelvic inflammatory disease.

1. Construct a 2x2 contingency table for these data.
2. Estimate the relative odds of suffering ectopic pregnancy for women who have had pelvic inflammatory disease versus women who have not. Interpret your result.
3. Construct a 95% confidence interval for the population odds ratio.
4. Test the null hypothesis that there is no association between pelvic inflammatory disease and ectopic pregnancy at the 0.05 level of significance.

Answer 1

A study was conducted to investigate potential risk factors for ectopic pregnancy. Of the 279 women who had experienced ectopic pregnancy, 28 had suffered from pelvic inflammatory disease. Of the 279 women who had not experienced ectopic pregnancy, 6 had suffered from pelvic inflammatory disease.

1. Construct a 2x2 contingency table for these data.

	ectopic pregnancy	No ectopic pregnancy
disease	28	6	34
No disease	251	273	524
	279	279	558

2. Estimate the relative odds of suffering ectopic pregnancy for women who have had pelvic inflammatory disease versus women who have not. Interpret your result.

Odds of disease with ectopic pregnancy = 28/251

Odds of disease with no ectopic pregnancy = 6/273

Odds ratio = (28/251)/( 6/273)

=5.0757

3. Construct a 95% confidence interval for the population odds ratio.

95 % CI: = 2.0672 to 12.4623

4. Test the null hypothesis that there is no association between pelvic inflammatory disease and ectopic pregnancy at the 0.05 level of significance.

Ho: there is no association between pelvic inflammatory disease and ectopic pregnancy

H1: there is a association between pelvic inflammatory disease and ectopic pregnancy

Chi-Square Test
Observed Frequencies
	Column variable				Calculations
	ectopic pregnancy	No ectopic pregnancy	Total		fo-fe
disease	28	6	34		11	-11
No disease	251	273	524		-11	11
Total	279	279	558
Expected Frequencies
	Column variable
	ectopic pregnancy	No ectopic pregnancy	Total		(fo-fe)^2/fe
disease	17	17	34		7.1176	7.1176
No disease	262	262	524		0.4618	0.4618
Total	279	279	558
Data
Level of Significance	0.05
Number of Rows	2
Number of Columns	2
Degrees of Freedom	1
Results
Critical Value	3.8415
Chi-Square Test Statistic	15.1590
p-Value	0.0001
Reject the null hypothesis

Calculated chi square = 15.159 > critical chi square 3.841 at 0.05 level. Ho is rejected.

We conclude that there is an association between pelvic inflammatory disease and ectopic pregnancy at the 0.05 level of significance.