Relative Risk

1. In a study to judge the effectiveness of inoculation in preventing a virus infection,the following results were obtained :

A. Estimate the relative risk of infection.
B. By how much does inoculation reduce the risk of infection?
C. Estimate the odds ratio.Interpret your estimate.
D. State the appropriate null and alternative hypotheses for this problem.
E. Is inoculation effective in preventing the virus infection? Justify your answer.

Ans.R-software
> epi.2by2(tab1,method = "cohort.count",conf.level = 0.95)

Point estimates and 95 % CIs:

X2 test statistic: 7.669 p-value: 0.006
Wald confidence limits
* Outcomes per 100 population units

A) Relative risk of infection = 0.22
B) Inoculation Reduces Risk of infection by( 1 - 0.22 )= 0.78 = .78 times
C) Odds Ratio = 0.20
The odds of Inoculation getting infected are 0.20 times the odds of a not inoculated getting infected
D) Null Hypothesis: Their is no difference between Inoculated and Not Inoculated across Infected and Not infected
Aternative Hypothesis: Their is a significant difference between Inoculated and Not Inoculated across Infected and Not infected
E) Yes, Inoculation is effective in preventing the virus infection as the p-value of the chi-square test is 0.006 which is less then 0.05. Hence,We reject null hypothesis an conclude that inoculation is effective.

2. After a customer service course, 30customers were asked whether or not they were completely stisfied with their service. A year later same experiment is conducted to see whether or not the effects of the customer service course have waned. the results are :

A. Have the effects of the course waned ?
B. State clearly the null and alternative hypotheses tested in part (a).
C. Analyze the residuals and interpret your results.

Ans.> tab2

Point estimates and 95 % CIs:

X2 test statistic: 4.32 p-value: 0.038
Wald confidence limits
* Outcomes per 100 population units

A) Yes, The effects of the course waned by 0.21 times. from (1 - ( 1/1.27)) = 0.21
B) Null Hypothesis: Their is no difference between 1st sample and 2nd_sample accross Response
Alternative Hypothesis: Their is significant difference between 1st sample and 2nd_sample accross Response
C) Since the Computed P-value is 0.038, which is less than 0.05, we reject null hypotheisis and conclude that their is a significant difference between 1st and 2nd sample accross Response.