# Standard Error Of Proportion Difference

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## Confidence Interval For Difference In Proportions Calculator

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## The Confidence Interval For The Difference Between Two Independent Proportions

for the difference between two sample proportions, p1 - p2. Estimation Requirements The approach described in this lesson is valid whenever the following conditions are met: Both samples are simple random samples. The samples are independent. Each 2 proportion z interval conditions sample includes at least 10 successes and 10 failures. The Variability of the Difference Between Proportions To construct a confidence interval for the difference between two sample proportions, we need to know about the sampling distribution of the difference. Specifically, we need to know how to compute the standard deviation or standard error of the sampling distribution. The standard deviation of the sampling distribution is the "average" deviation between all possible sample differences (p1 - 2 proportion z interval example p2) and the true population difference, (P1 - P2). The standard deviation of the difference between sample proportions σp1 - p2 is: σp1 - p2 = sqrt{ [P1 * (1 - P1) / n1] * [(N1 - n1) / (N1 - 1)] + [P2 * (1 - P2) / n2] * [(N2 - n2) / (N2 - 1)] } where P1 is the population proportion for sample 1, P2 is the population proportion for sample 2, n1 is the sample size from population 1, n2 is the sample size from population 2, N1 is the number of observations in population 1, and N2 is the number of observations in population 2. When each sample is small (less than 5% of its population), the standard deviation can be approximated by: σp1 - p2 = sqrt{ [P1 * (1 - P1) / n1] + [P2 * (1 - P2) / n2] } When the population parameters (P1 and P2) are not known, the standard deviation of the sampling distribution cannot be calculated. Under these circumstances, use the standard error. The standard error (SE) can be calculated from the equation below. SEp1 - p2 = sqrt{ [p1 * (1 - p1) / n1] * [(N1 - n1) / (N1 - 1)] + [p2 * (1 - p2) / n2] * [(N2 - n2) /

200 entering students in 1989 showed 74% were still

## Confidence Interval For Two Population Proportions Calculator

enrolled 3 years later. Another random sample of 200 confidence interval difference in proportions ti-84 entering students in 1999 showed that 66% were still enrolled 3 years later. This

## Margin Of Error For Two Proportions Calculator

constitutes an 8% change in 3-year retention rate. However, the 8% difference is based on random sampling, and is only an estimate http://stattrek.com/estimation/difference-in-proportions.aspx?Tutorial=AP of the true difference. What is the likely size of the error of estimation? The calculation of the standard error for the difference in proportions parallels the calculation for a difference in means. (7.5) where and are the SE's of and , respectively. http://www.stat.wmich.edu/s216/book/node85.html For the retention rates, let with standard error and with standard error . Then the difference .74-.66=.08 will have standard error We now state a confidence interval for the difference between two proportions. The SE for the .08 change in retention rates is .045, so the .08 estimate is likely to be off by some amount close to .045. However, the 95% margin of error is approximately 2 SE's, or .090. A 95% confidence interval for the difference in proportions p1-p2 is or . Coverting to percentages, the difference between retention rates for 1989 and 1999 is 8% with a 95% margin of error of 9%. A 95% confidence interval for the true difference is . Next: Overview of Confidence Intervals Up: Confidence Intervals Previous: Sample Size for Estimating 2003-09-08

0 otherwise. The standard deviation of any variable involves the confidence interval expression . Let's suppose there are m 1s (and n-m 0s) among the n subjects. Then, and is equal to (1-m/n) for m observations and 0-m/n confidence interval for for (n-m) observations. When these results are combined, the final result is and the sample variance (square of the SD) of the 0/1 observations is The sample proportion is the mean of n of these observations, so the standard error of the proportion is calculated like the standard error of the mean, that is, the SD of one of them divided by the square root of the sample size or Copyright © 1998 Gerard E. Dallal

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