Question

# A study was done to investigate whether a relationship existed between HPV (human papillomavirus) status and...

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.

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.

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