Chapter 22 Comparing Two Proportions

Comparing 2 Proportions How do the two groups differ? Did a treatment work better than the placebo control? Are this years results better than last years?

Remember!!! Var(X – Y) = Var(X) + Var(Y) SD(X – Y) = √[(Var(X) + Var(Y)] – only when X and Y are independent

Standard Deviation Of The Difference Between Two Proportions *proportions observed in independent random samples are independent* *be sure to use notation to differ between variables*

*We don’t always know what the true p is. When you don’t find the SE (Standard Error)*

Assumptions and Conditions Within each group the data should be based on results for independent individuals. Check: – Randomization condition: each data set should be selected at random – 10% condition: if sampled without replacement, then the sample should be less than 10% of the population – Independent Groups Assumption: The two groups need to be independent of each other

And… Success/Failure Condition: BOTH groups have at least 10 successes and 10 failures

the sampling distribution model for a difference between two independent proportions Provided that the sampled values are independent, the samples are independent, and the sample sizes are large enough, the sampling distribution of is modeled by a Normal model with mean = standard deviation =

A two-proportion z-interval When the conditions are met, we are ready to find the confidence interval for the difference of two proportions, p 1 – p 2. The confidence interval is where we find the standard error of the difference, from the observed proportions The critical value z * depends on the particular confidence level, C, that you specify