Calculating Standard Error Of Percentage
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and answer site for people interested in statistics, machine learning, data analysis, data mining, and data visualization. Join them; it only takes a minute: Sign up Here's how it works: Anybody can ask calculating standard error of estimate a question Anybody can answer The best answers are voted up and rise to the top Calculating Standard deviation of percentages? up vote 0 down vote favorite 1 I have the following data X 1 2 3 4 5… Y 10 12 13 14 15… X/Y 10% 16% 23% etc. How do I find the standard deviation of percentage (last line)? Can I treat the ratio as a calculating standard error of measurement normal distribution and apply regular SD formula? standard-deviation share|improve this question asked Nov 6 '13 at 22:36 Nox 1111 This looks like a standard textbook problem. Please review the tag wiki info of the self-study tag and add it if at all applicable. –Glen_b♦ Nov 6 '13 at 23:06 add a comment| 2 Answers 2 active oldest votes up vote 2 down vote You should clarify your question to be clear whether you want the sample standard deviation of the collection of percentages or the estimated standard deviation of each percentage. I'll discuss the second case. You should also clarify the question enough that I can remove some of the 'if's below. If the Y's are total counts of objects of which the X's are counts of some particular subset (such as X='number of people with red hair in a classroom', and Y='number of people in the classroom'), and if you can assume independence of occurrence of the characteristic being counted in X and if you can assume constant probability of occurrence of that characteristic, ... then conditional on Y, you're in a binomial sampling situation and the estimated s.d. of the fraction X/Y is $\sqrt{\frac{1}{Y} \frac{X}{Y}(1-\frac{X}{Y})}$, w
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us Cross Validated Questions Tags Users Badges Unanswered Ask Question _ Cross Validated is a question and answer site for people interested in statistics, machine learning, data analysis, http://stats.stackexchange.com/questions/74797/calculating-standard-deviation-of-percentages data mining, and data visualization. Join them; it only takes a minute: Sign up Here's how it works: Anybody can ask a question Anybody can answer The best answers are voted up and rise to the top Calculating standard deviation associated with percentage change [duplicate] up vote 0 down vote favorite This question already has an http://stats.stackexchange.com/questions/64652/calculating-standard-deviation-associated-with-percentage-change answer here: Standard deviation of a ratio (percentage change) 1 answer I have two data sets. The first data set, let's call it $X$ has an average value of $\bar{x}_{X}$ and standard deviation of $s_{X}$, the second data set $Y$ has an average value of $\bar{x}_{Y}$ and standard deviation of $s_{Y}$.I want to find out the standard error or standard deviation of a percentage change of data set 2 compared to 1. So I have: $$ \frac{\bar{x}_{Y}-\bar{x}_{X}}{\bar{x}_{X}}\cdot100 $$ Now my question is, how to take into account the standard deviations for this percentage value? standard-deviation share|improve this question edited Jul 17 '13 at 22:40 COOLSerdash 10.6k63254 asked Jul 17 '13 at 21:13 Chris Harrod 111 marked as duplicate by COOLSerdash, gung, Peter Flom♦, Scortchi♦, Gala Jul 18 '13 at 12:28 This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question. 3 Hi Chris and welcome to the site! I have a quest
repeatedly randomly drawn from a population, and the proportion of successes in each https://onlinecourses.science.psu.edu/stat200/node/43 sample is recorded (\(\widehat{p}\)),the distribution of the sample proportions (i.e., the sampling distirbution) can be approximated by a normal distribution given that both http://www.jerrydallal.com/lhsp/psd.htm \(n \times p \geq 10\) and \(n \times (1-p) \geq 10\). This is known as theRule of Sample Proportions. Note that some textbooks standard error use a minimum of 15 instead of 10.The mean of the distribution of sample proportions is equal to the population proportion (\(p\)). The standard deviation of the distribution of sample proportions is symbolized by \(SE(\widehat{p})\) and equals \( \sqrt{\frac {p(1-p)}{n}}\); this is known as thestandard error of calculating standard error \(\widehat{p}\). The symbol \(\sigma _{\widehat p}\) is also used to signify the standard deviation of the distirbution of sample proportions. Standard Error of the Sample Proportion\[ SE(\widehat{p})= \sqrt{\frac {p(1-p)}{n}}\]If \(p\) is unknown, estimate \(p\) using \(\widehat{p}\)The box below summarizes the rule of sample proportions: Characteristics of the Distribution of Sample ProportionsGiven both \(n \times p \geq 10\) and \(n \times (1-p) \geq 10\), the distribution of sample proportions will be approximately normally distributed with a mean of \(\mu_{\widehat{p}}\) and standard deviation of \(SE(\widehat{p})\)Mean \(\mu_{\widehat{p}}=p\)Standard Deviation ("Standard Error")\(SE(\widehat{p})= \sqrt{\frac {p(1-p)}{n}}\) 6.2.1 - Marijuana Example 6.2.2 - Video: Pennsylvania Residency Example 6.2.3 - Military Example ‹ 6.1.2 - Video: Two-Tailed Example, StatKey up 6.2.1 - Marijuana Example › Printer-friendly version Navigation Start Here! Welcome to STAT 200! Search Course Materials Faculty login (PSU Access Account) Lessons Lesson 0: Statistics: The “Bi
0 otherwise. The standard deviation of any variable involves the 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 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