Effect Of Sample Size On Standard Error Of The Mean
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Sample Size And Standard Error Relationship
For Dummies Statistics For Dummies, 2nd Edition SPSS Statistics for Dummies, 3rd Edition Statistics II for Dummies Load more sample size margin of error EducationMathStatisticsHow Sample Size Affects Standard Error How Sample Size Affects Standard Error Related Book Statistics For Dummies, 2nd Edition By Deborah J. Rumsey The size (n) of a statistical sample affects the
Equation For Standard Error Of The Mean
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, 10 workers, and 50 workers. Suppose X is the time it takes for a clerical worker to type does standard deviation increase with sample size 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 the figure, the average times for samples of 10 clerical workers are closer to the mean (10.5) than the individual times are. That's because average times don't vary as much from sample to sample as inthis involves comparing samples between one regime and another (which may be a control). Sample size is important because Larger samples increase
Sample Size Confidence Interval
the chance of finding a significant difference, but Larger samples cost more
Sample Size Variance
money. Why does a larger sample size help? The sample size is chosen to maximise the chance of uncovering sample size t test a specific mean difference, which is also statistically significant. Please note that specific difference and statistically significant are two quite different ideas. The specific difference is chosen by the researcher http://www.dummies.com/education/math/statistics/how-sample-size-affects-standard-error/ in terms of the outcome measure of the experiment. For instance, 3kg mean weight change in a diet experiment, 10% mean improvement in a teaching method experiment. Statistical significance is a probability statement telling us how likely it is that the observed difference was due to chance only. The reason larger samples increase your chance of significance is because they more reliably http://www.conceptstew.co.uk/pages/nsamplesize.html reflect the population mean. Imagine we are doing a trial on whether a particular diet regime helps with weight loss. A random sample of people are chosen and each person is weighed before and after the diet, giving us their weight changes. Finally we work out the mean weight change of the entire sample. To get a statistically significant result we want a result which is unlikely to have happened if the diet makes no difference (the null hypothesis). Imagine a scenario where one researcher has a sample size of 20, and another one, 40, both drawn from the same population, and both happen to get a mean weight change of 3kg. How likely is it that a 3kg weight change will be statistically significant in these two scenarios? To help us here we'll show a distribution curve from each scenario. What you see above are two distributions of possible sample means (see below) for 20 people (n=20) and 40 people (n=40), both drawn from the same population. On each we have superimposed a sample mean weight change of 3kg. The curves are both
Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta http://stats.stackexchange.com/questions/89456/why-does-the-standard-deviation-not-decrease-when-i-do-more-measurements Discuss the workings and policies of this site About Us Learn more about Stack Overflow the company Business Learn more about hiring developers or posting ads with 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, data mining, and sample size 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 Why does the standard deviation not decrease when I do more measurements? [duplicate] up vote 11 down vote favorite 6 This question already has an effect of sample answer here: Difference between standard error and standard deviation 4 answers I made 100 measurements of a certain quantity, calculated mean and standard deviation (with MySQL), and got mean=0.58, SD=0.34. The std seemed too high relative to the mean, so I made 1000 measurements. This time I got mean=0.572, SD=0.33. I got frustrated by the high standard deviation, so I made 10,000 measurements. I got mean=0.5711, SD=0.34. I thought maybe this was a bug in MySQL, so I tried to use the Excel functions, but got the same results. Why does the standard deviation remain high even though I do so many measurements? standard-deviation experiment-design share|improve this question edited Mar 11 '14 at 5:14 Jeromy Anglim 27.6k1393195 asked Mar 10 '14 at 14:03 Erel Segal-Halevi 4041313 marked as duplicate by Nick Cox, Glen_b♦, whuber♦ Mar 11 '14 at 12:00 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. add a comment| 3 Answers 3 active oldest vot