Question

A study was done to investigate whether a relationship existed between HPV (human papillomavirus) status and HIV infection status. HPV status and HIV infection status were obtained for 97 women.

Table of hpv by hiv
hpv	hiv
Frequency Expected Row Pct	Seropositive/Symptomatic	Seropositive/Asymptomatic	Seronegative	Total
Positive	23 12.928 60.53	5 7.4433 13.16	10 17.629 26.32	38
Negative	10 20.072 16.95	14 11.557 23.73	35 27.371 59.32	59
Total	33	19	45	97

Statistic	DF	Value	Prob
Chi-Square	2	19.6478	<.0001
Likelihood Ratio Chi-Square	2	19.8286	<.0001
Mantel-Haenszel Chi-Square	1	17.0081	<.0001
Phi Coefficient		0.4501
Contingency Coefficient		0.4104
Cramer's V		0.4501

Fisher's Exact Test
Table Probability (P)	<.0001
Pr <= P	<.0001

Question 1

Which test is appropriate for these data, chi-square or Fisher's Exact test?

a)	Chi-square, because this is a test of homogeneity.

b)	Chi-square, because all of the expected frequencies are > 5.

c)	Fisher's Exact, because one of the observed frequencies is ≤ 5

Question 2

What are the test statistic, degrees of freedom, and p-value for the test you chose (chi-square or Fisher's Exact test)?

a)	Fisher's Exact Test: no test statistic, no d.f., p<0.0001

b)	Chi-Square: 19.6478, 2, p<0.0001

c)	Chi-Square: 19.6478, p<0.0001

d)	Chi-Square: 17.0081, 1, p<0.0001

Question 3

How would you present your conclusion to a "layperson" (i.e., someone who has no knowledge of statistics)?

a)	Since p>0.05, we fail to reject the null hypothesis and conclude that there is insufficient evidence to show the HPV and HIV status are associated.

b)	Since p<0.05, we reject the null hypothesis and conclude that there is a significant association between HPV and HIV status. Those who were positive for HPV were more likely to be HIV seropositive/symptomatic than those who were negative for HPV.

c)	Conclude that there is a significant association between HPV and HIV status. Those who were positive for HPV were more likely to be HIV seropositive/symptomatic than those who were negative for HPV .

d)	Conclude that there is a significant association between HPV and HIV status. Those who were positive for HPV were less likely to be HIV seropositive/symptomatic than those who were negative for HPV.

Question 4

What is the correct calculation of the degrees of freedom (d.f. = 2) for this contingency table?

a)	d.f. = 2 because there are two rows

b)	d.f. = 2 because the number of columns minus 1 equals 2.

c)	The d.f. are given by (r-1)(c-1).

d)	The d.f. are given by r + c.

Answer 1

1) Here we will use chi-square test as here we want to test homogeneity also the variables here are categorical.

Option (a) is correct.

Q2)

From the table test statistics is 19.6478

degrees of freedom is 2

and p value <0.0001

So, Option (C) is correct.

Q3)

Since, our p-value<0.0001<0.05. So, we reject the null hypothesis and conclude that there is significant association between the HPV and HIV status.

Option (B) is correct.

Q4)

In Chi-square test degrees of freedom is given as

(r-1)*(c-1) = (2-1)(3-1) = 1*2

= 2

Option (C) is correct.