A clinical trial is run to investigate the effectiveness of an experimental drug

Question

A clinical trial is run to investigate the effectiveness of an experimental drug in reducing preterm delivery to a drug considered standard care and to placebo. Pregnant women are enrolled and randomly assigned to receive either the experimental drug, the standard drug or placebo. Women are followed through delivery and classified as delivering preterm (< 37 weeks) or not. The data are shown below.

Is there a statistically significant difference in the proportions of women delivering preterm among the three treatment groups? Run the test at a 5% level of significance. Give null and alternative hypotheses, test statistic, and conclusion

Preterm Experimental Drug Standard drug Placebo Yes 17 23 35 No 83 77 65

Explanation / Answer

we will apply chi square test of homogenity on above:

null hypothesis: proportions of women delivering preterm among the three treatment groups are same.

alternate hypothesis: proportions of women delivering preterm among the three treatment groups are different.

for 2 degree oif freedom and 0.05 level of significance ; critical value =5.991

from above chi stat 8.96 is higher then critical value hence we reject null hypothesis and conclude that  proportions of women delivering preterm among the three treatment groups are different.

Observed O experimental standard drug Placebo Total Yes 17 23 35 75 No 83 77 65 225 Total 100 100 100 300 Expected E=rowtotal*column total/grand total experimental standard drug Placebo Total Yes 25.000 25.000 25.000 75 No 75.000 75.000 75.000 225 Total 100 100 100 300 chi square =(O-E)^2/E experimental standard drug Placebo Total Yes 2.560 0.1600 4.0000 6.720 No 0.853 0.053 1.333 2.240 Total 3.413 0.213 5.333 8.9600

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