Question

Background: Despite their antimicrobial potential, vaginal lactobacilli often fail to retain dominance, resulting in overgrowth of the vgna by other bacteria, as observed with bacterial vaginosis. It remains elusive however to what extent interindividual differences in vaginal Lactobacillus community composition determine the stability of this microflora. In a prospective cohort of pregnant women we studied the stability of the normal vaginal microflora (VMF) (assessed on Gram stain) as a function of the presence of the vaginal Lactobacillus index species (determined through culture and molecular analysis with tRFLP).

Results: From 100 consecutive Caucasian women vaginal swabs were obtained at mean gestational ages of 8.6 (SD 1.4), 21.2 (SD 1.3), and 32.4 (SD 1.7) weeks, respectively. Based on Gram stain, 77 women had normal or Lactobacillus-dominated vaginal microflora (VMF) during the first trimester of which 56 remained normail in the third trimester. Th3 remaining 23 women tested abnormal in the first trimester and 13 of them converted in the second or third trimester.

Test the null hypothesis that having an abnormal result in the first trimester is related to having an abnormal result in the third trimester (Hint: What type of chi-square test is this?). (5 pts).

Answer 1

Since we have to check the dependence between the results of the first trimester to the third one, we will use chi square test of independence to get statistical significance of this statement. Our null hypothesis would be that these two trimester results are independent and the alternate hypothesis would be that they are dependent. To do this test, we need to create the joint frequency table and the expected joint frequency table, which are as follows:

Joint Frequency Table

Result in first Trimester	Result in third Trimester
	Normal	Abnormal	Total
Normal	56	21	77
Abnormal	13	10	23
Total	69	31	100

Expected Joint Frequency distribution

Result in first Trimester	Result in third Trimester
	Normal	Abnormal	Total
Normal	53	24	77
Abnormal	16	7	23
Total	69	31	100

The test statistic used here is

IN this case, the obtained value of the test statistic is 2.393 and the corresponding p-value is

As the p-value is less than 5%, hence at 5% confidence level, we can reject the null hypothesis and say that the abnormal result in the first semester is related to having an abnormal result in the third semester.