Does Standard Error Decreases When Sample Size Increases
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How Is Standard Error Affected By Sample Size
Sample Size Affects Standard Error Statistics Essentials For Dummies Statistics For Dummies, 2nd Edition SPSS Statistics for does standard deviation increase with sample size Dummies, 3rd Edition Statistics II for Dummies Load more EducationMathStatisticsHow Sample Size Affects Standard Error How Sample Size Affects Standard Error Related Book Statistics For Dummies, 2nd Edition By how does standard deviation change with sample size Deborah J. Rumsey The size (n) of a statistical sample affects the standard error for that sample. Because n is in the denominator of the standard error formula, the standard error decreases as n increases. It makes sense that having more data gives less variation (and more precision) in your results.
Distributions of times for 1 worker,How Does Sample Size Effect Standard Deviation
10 workers, and 50 workers. Suppose X is the time it takes for a clerical worker to type and send one letter of recommendation, and say X has a normal distribution with mean 10.5 minutes and standard deviation 3 minutes. The bottom curve in the preceding figure shows the distribution of X, the individual times for all clerical workers in the population. According to the Empirical Rule, almost all of the values are within 3 standard deviations of the mean (10.5) -- between 1.5 and 19.5. Now take a random sample of 10 clerical workers, measure their times, and find the average, each time. Repeat this process over and over, and graph all the possible results for all possible samples. The middle curve in the figure shows the picture of the sampling distribution of Notice that it's still centered at 10.5 (which you expected) but its variability is smaller; the standard error in this case is (quite a bit less than 3 minutes, the standard deviation of the individual times). Looking at
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Standard Deviation Sample Size Relationship
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 Why does increasing the sample size http://www.dummies.com/education/math/statistics/how-sample-size-affects-standard-error/ lower the variance? up vote 14 down vote favorite 4 Big picture: I'm trying to understand how increasing the sample size increases the power of an experiment. My lecturer's slides explain this with a picture of 2 normal distributions, one for the null-hypothesis and one for the alternative-hypothesis and a decision threshold c between them. They argue that increasing sample size will lower variance and thereby cause a higher kurtosis, reducing the shared area under the curves and so http://stats.stackexchange.com/questions/129885/why-does-increasing-the-sample-size-lower-the-variance the probability of a type II error. Small picture: I don't understand how a bigger sample size will lower the variance. I assume you just calculate the sample variance and use it as a parameter in a normal distribution. I tried: googling, but most accepted answers have 0 upvotes or are merely examples thinking: By the law of big numbers every value should eventually stabilize around its probable value according to the normal distribution we assume. And the variance should therefore converge to the variance of our assumed normal distribution. But what is the variance of that normal distribution and is it a minimum value i.e. can we be sure our sample variance decreases to that value? variance sampling power share|improve this question asked Dec 21 '14 at 0:01 user2740 3391213 Your thought experiment concerned normally distributed data but it also applies to data drawn from many other distributions (as noted by @Aksakal, not all! The Cauchy is a commonly cited example of such bad behaviour). For binomial data there is good discussion of how power and standard error vary with sample size at stats.stackexchange.com/q/87730/22228 –Silverfish Dec 21 '14 at 2:26 1 As you are new to CrossValidated, allow me to point out that if you received what you consider a satisfactory answer, you should consider marking it as "accepted" by clicking a green tick to the left of i
the following questions in one or two well-constructed sentences. a. What happens to the standard error of a sampling distribution as the size of http://www.algebra.com/algebra/homework/Probability-and-statistics/Probability-and-statistics.faq.question.648031.html the sample increases? b. Log On Ad: Mathway solves algebra homework problems with step-by-step help! Algebra: Probability and statisticsSection SolversSolvers LessonsLessons Answers archiveAnswers Click here to see ALL problems on Probability-and-statistics Question 648031: Answer the following questions in one or two well-constructed sentences. a. What happens to the standard error of a sampling distribution as the size sample size of the sample increases? b. What happens to the distribution of the sample means if the sample size in increased? c. When using the distribution of sample means to estimate the population mean, what is the benefit of using larger sample sizes? Answer by Theo(7050) (Show Source): You can put this solution on YOUR website! as the size of sample size increases the sample increases, the standard error decreases. standard error equals standard deviation of population divided by square root of sample size. bigger sample size means bigger denominator resulting in smaller standard error. if the sample size increases, the distribution of sample means becomes more normal. this is the main idea of the central limit theorem. even if the population distribution is not normal, the distribution of sample means becomes more normal the larger the sample size. the benefit of larger sample sizes is that the mean of the sample will be closer to the actual population mean and the standard error will be less. the sample mean will be closer to the population mean because the sample size is larger. this also results in a smaller standard error. this also results in a more normal distribution which increases the accuracy of using the z-tables when determing deviations from the population mean. note that the z-tables assume a normal distribution. note that, even if the underlying population is not normal, the distribution of sam