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Analyzing the Effectiveness of Vaccines and Understanding Statistical Significance in Research

Discusses vaccines and statistical significance.

Daniel Kim
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Analyzing the Effectiveness of Vaccines and Understanding StatisticalSignificance in Research1.A group of researchers conducted an experiment to determine which vaccine is more effective forpreventing getting the flu. They tested two differenttypes of vaccines: a shot and a nasal spray. To testthe effectiveness, 1000 participants were randomly selected with 500 people getting the shot and 500the nasal spray. Of the 500 people were treated with the shot, 80 developed the flu and 420 did not. Ofthe people who were treated with the nasal spray, 120 people developed the flu and 380 did not. Thelevel of significance was set at .05. The proportion of people who were treated with the shot whodeveloped the flu = .16, and the proportion of the people who were treated with the nasal spray was .24.The calculated p value = .0008.We have to research Is there any significant difference between two typres of vaccine i.e, a shot andnasal spray used for preventing nasal spray?To examine the difference of effect we conduct test based on given observation i.e.,n1= 500 , n2= 500 ,p1= 0.16 , p2= 0.24 , alpha = 0.05Our Hypothesis is defined asNullHypothesis : shot spray is equaleffective thannasal sprayVsAlternativeHypothesis : shot spray is moreeffective thannasal spraySince sample sie are large enough ( >30)To conduct this testing we useZ test with pas pooled estimate of proportion = 0.20Z= (p1–p2) / sqrt(p*1-p *(1/n1+ 1/n2)=-0.08 /0.025=-3.2P(Z<-3.2) =0.0008P value = 0.0008 < 0.05(significance level)

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Statistics

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