Standard Error of Proportion & Two Proportions

Standard Error of Proportion

1. Standard Error of a) Proportion b) Difference between proportions Jagdish D. Powar Statistician cum Tutor Community Medicine SMBT, IMSRC, Nashik

2. Competency & Learning objectives Competency SLOs(Core) CM6.3, Describe, discuss and demonstrate the application of elementary statistical methods including test of significance in various study designs   The student should be able to Write a Null hypothesis and alternative hypothesis for z test for proportion Calculate confidence interval for proportion Perform z test for proportion and draw a conclusion from it Perform z test for two proportions 2

3. Standard error of proportion is given by SE(P)= q=100-p Applications:- To find the confidence interval for population proportion from sample. To test whether the sample is drawn from population with proportion P .   Standard error of proportion 3

4. Confidence Interval for Population Proportion. 95% confidence interval for population proportion ( p -1.96*SE(p), p +1.96*SE(p)) 99% confidence interval for population proportion (p -2.58*SE(p), p +2.58*SE(p)) Z- test for proportion: H : The sample is drawn from population having population proportion(P) H 1: The sample is not drawn from population having population proportion(P ) Z= , SE(P)= If Z < 1.96 then accept the null hypothesis otherwise reject NH .   4

5. 1) In a sample of 1000 people, 400 were males and 600 females. What is the estimate of proportion of females in the town with 95 %, 99% confidence interval? Ans- Here n=1000, p= Proportion of females= 600*100/1000 =60%, q=100-p =40% Standard error of proportion is given by SE(P)= = = 1.55 a) 95 % confidence interval for population proportion (p -1.96*SE(p), p +1.96*SE(p )) (60-1.96*1.55,60+1.96*1.55) =(56.96%, 63.04%) b) 99 % confidence interval for population proportion ( p -2.58*SE(p), p +2.58*SE(p )) (60-2.58*1.55,60+2.58*1.55) = (56.00%, 63.99%)   5

6. 2) The proportion of blood group A among Indians is 30%. In a batch of 100 individuals if it is observed as 25%, what is your conclusion about the group? Ans- Given values n= 100, p= proportion of blood group A in sample =25%, q=100-p= 75% P= proportion of blood group A in Indian population =30% H : The sample is drawn from Indian population with population proportion of blood group A, P = 30% H 1 : The sample is not drawn from Indian population with population proportion of blood group A, P ≠ 30% Z-test for proportion :- Z= , SE(P )= = = =4.58 Z= Here Cal Z < 1.96 hence accept the null hypothesis, The sample is drawn from Indian population.   6

7. Z-test for difference between two proportions H o :- There is no significant difference between two population proportion P1 = P2 H 1 :- There is significant difference between two population proportion P1 ≠ P2 Z= observed difference between proportion SE p1-p2 Z = SE(p1-p2 )= If Z < 1.96 then accept Ho otherwise reject Ho .   Standard error of difference between two proportions 7

8. 1) A survey of 400 children in age group 0-5 years showed prevalence rate of protein calorie malnutrition to be 15%. Another study showed prevalence of 5% in a sample of 300 of same age group. Can we say that there is statistical significance in difference between the two prevalence rates? Ans- Given values n1= 4 00, p1= 15%, q1= 100-15 =85% n2 =300, p2=5%, q2= 100-5=95% Z-test for difference between two proportions Ho:- There is no significant difference between two population (prevalence) proportion P1= P2 H1:- There is significant difference between two population proportion P1≠ P2 Z = SE(p1-p2 )= = = 2.18 Z = = =4.59 >1.96 Here Cal Z > 1.96 hence reject Ho, there is significant difference in prevalence of protein calorie malnutrition   8

9. 9 Thank You