Difference Of Proportions Standard Error
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a sample survey produces a proportion or a mean as a response, we can use the methods in section 10.2 and 10.3 standard error difference in proportions calculator to find a confidence interval for the true population values. standard error of difference between two proportions In this section we discuss confidence intervals for comparative studies. How do we assess the difference between standard error for proportions formula two proportions or means when they come from a comparative observational study or experiment? To address this question, we first need a new rule. Standard standard deviation proportions Error of a DifferenceWhen two samples are independent of each other,Standard Error for a Difference between two sample summaries =\[\sqrt{(\text{standard error in first sample})^{2} + (\text{standard error in second sample})^{2}}\] Example 10.6.A medical researcher conjectures that smoking can result in wrinkled skin around the eyes. The researcher recruited150 smokersand250 nonsmokersto take part in an
Confidence Interval Proportions
observational study and found that 95of thesmokersand105of thenonsmokerswere seen to have prominent wrinkles around the eyes (based on a standardized wrinkle score administered by a person who did not know if the subject smoked or not). Some results from the study are found inTable 10.2. Table 10.2. Results of the Smoking and wrinkles study (example 10.6) SmokersNonsmokersSample Size150250Sample Proportion with Prominent Wrinkles95/150 = 0.63105/250 = 0.42Standard Error for Proportion\(\sqrt{\frac{0.63(0.37)}{150}} = 0.0394\)\(\sqrt{\frac{0.42(0.58)}{250}} = 0.0312\)How do the smokers compare to the non-smokers? The difference between the two sample proportions is 0.63 - 0.42 = 0.21. We would like to make a CI for the true difference that would exist between these two groups in the population. So we compute\[\text{Standard Error for Difference} = \sqrt{0.0394^{2}+0.0312^{2}} ≈ 0.05\]If we think about all possible ways to draw a sample of 150 smokers and 250 non-smokers then the differences we'd see between sample proportions would approximately follow the normal curve. Thus, a 95% Confidence Interval f
200 entering students in 1989 showed 74% were still
Variance Proportions
enrolled 3 years later. Another random sample of 200 t test proportions entering students in 1999 showed that 66% were still enrolled 3 years later. This central limit theorem proportions constitutes an 8% change in 3-year retention rate. However, the 8% difference is based on random sampling, and is only an estimate https://onlinecourses.science.psu.edu/stat100/node/57 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
4. Significance of the Difference between the Results for CandidateX and CandidateY in a SinglePoll Calculator 1: Estimated Population Percentage and Margin of Error This http://faculty.vassar.edu/lowry/polls/calcs.html calculator can be used for analyzing the results of a poll of your own (inwhich case, keep in mind the requirement of a representative sample) or for checking the preciseness of the results of polls reported in the news media. Enter the respective percentages of respondents within the sample who favor CandidateX and CandidateY into the top two cells; enter the standard error size of the sample into the third cell; and then click the "Calculate" button. This calculator will also work if the sample percentage for only one of the candidates is entered. Note: For polls reported in the news media, the margins of error tend to be rounded to the nearest integer. They also often appear to be based on the percentage for difference of proportions the candidate who has the majority or plurality within the sample. Candidate X Y Percentage in sample favoring: % % Sample size: Estimated Percentage in population favoring: % % 95% Confidence Interval: lower limit: % % upper limit: % % margin of error: ±% ±% The 'margin of error' reported here is calculated as one-half the distance between the upper limit and the lower limit. Note that these upper and lower limits are precisely equidistant from the estimated population percentage only when that percentage is close to 50. Calculator 2: Estimating Sample Size when the Report of a Poll Fails to Provide that Essential Bit of Information It occasionally happens that the press report of a poll will give no indication of the size of the sample on which the poll is based. In cases if this sort, Calculator2 will estimate the size of the sample on the basis of two items of information that probably will be given in the report: the margin of error and the largest of the candidate percentages. Ifthe reported margin of error is entered as an integer