Non-Parametric test – Assignment March 2009 MUSPH Page 1 of 2

In attempting to determine whether a new anti-leprosy vaccine was effective or not against leprosy, villages were “paired” to receive the new anti-leprosy vaccine and no intervention(i.e., by taking one village from a given parish and giving the residents in it the anti-leprosy vaccine and taking another village from the same parish and allocating it to no intervention. Thus, within each community (parish) one village serves as the intervention village and a second paired village serves as a control village. (Note that it would have also been possible to design this study by looking at the baseline leprosy prevalence rates in the same village BEFORE intervention & the leprosy rates AFTER intervention in the same village. Hopefully, the attempt to take a village from the same parish achieves the same result). After several months the age-standardized leprosy prevalence rates were compared in 10 such paired “intervention” and “control” villages and are presented in Table 1 below.

Could you perform the appropriate non-parametric test (based on the lecture presentation) to help determine if the new anti-leprosy vaccine is effective in decreasing leprosy prevalence.

Table 1: Leprosy prevalence rates in ten pairs of villages

Village Pair (Parish) no. / Prevalence of leprosy (per thousand) / Difference
(di) / Ignoring sign / Ranks / Signed Ranks
Intervention / No Intervention
1 / 6 / 10
2 / 9 / 13
3 / 3 / 6
4 / 12 / 11
5 / 10 / 10
6 / 4 / 7
7 / 7 / 8
8 / 5 / 8
9 / 7 / 5
10 / 5 / 9

*Recall that any group of tied ranks is allotted the mid rank of the group.

a) Complete the column marked Difference (d) in Table 1 above.

b) Complete the column marked Rank in Table 1 above.

c) T+ = Sum of ranks of positive differences = (fill in)

d) T- = Sum of ranks of negative differences = (fill in)

e) Which of T+ and T- is smaller? (fill in)

f) What is n (i.e. how many non-zero differences are there)? (fill in)

g) Based on this n what is the critical value from Table 2 that you will use to compare with the smaller of if T+ or T-? Critical value (W) from Table 2 (Use critical value for Wilcoxon Signed Rank test from table 2 ) is: __ (fill in)

[NOTE: I AM ATTACHING AN EASIER TO USE WILCOXON SIGNED RANK TEST TABLE (TABLE 2). YOU CAN USE THIS INSTEAD OF TABLE 3 THAT I ORIGINALLY PROVIDED – IF YOU HAVE ALREADY DONE THIS USING TAB LE 3 THAT IS OK AS WELL THE FINAL ANSWER IS NOT AFFECTED)

h) Use the smaller of T+ or T- to compare with the appropriate critical value from Table 2 that you selected above. Is the smaller of T+ or T- less than or greater than this critical value? Smaller than Critical value ___ (indicate your choice by underlining the correct response)

i) If the smaller of T+ or T- is smaller than the critical value (W) then you conclude that that difference between the intervention is significant at the 5% significance level. Based on this non-parametric test is the prevalence of leprosy significantly lower in the intervention villages? Yes it is ____ No it is Not__ (indicate your choice by underlining the correct response)

Two tailed test and the Critical value for Wilcoxon Signed Rank test table. (NEXT PAGE)

Table 2

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DANSTAN BAGENDA (Tel: 070-BAGENDA)