Does Error Rate Decrease Sample Size Increases
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Relationship Between Type 2 Error And Sample Size
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How Does Sample Size Effect Standard Deviation
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How To Decrease Type 2 Error
different sample size - hypothesis testing? [duplicate] up vote 8 down vote favorite This question already has an answer here: Why are the number of false positives independent of sample size, if we use p-values to compare two independent datasets? 2 answers I don't understand why the probability of getting a type I error when performing a hypothesis test, isn't affected. Increasing $n$ $\Rightarrow$ decreases standard deviation $\Rightarrow$ make the normal distribution spike more at the true $µ$, and effect of sample size on power the area for the critical boundary should be decreased, but why isn't that the case? (Cross posted on Math Stack Exchange.) hypothesis-testing sample-size likelihood type-i-errors share|improve this question edited Dec 31 '14 at 3:45 gung 73.8k19160309 asked Dec 29 '14 at 12:37 Stats 535 marked as duplicate by gung, Glen_b♦, whuber♦ Dec 31 '14 at 6:47 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. You choose $\alpha$, so in principle it can do what you like as sample size changes... and really, if you're minimizing the total cost of making the two types of error, it ought to go down as $n$ gets large. It makes no sense for people to keep using $\alpha=0.05$ (or whatever) while $\beta$ drops to ever more vanishingly small numbers when they get gigantic sample sizes. –Glen_b♦ Dec 29 '14 at 14:06 1 I feel like I am missing some common point which you other guys has already understood. As far as I understand from the reponses is my theory correct, but the probability is kept eventhougt that isn't the case.. ??? –Stats Dec 29 '14 at 14:22 Limiting distribution of test statistic is unaffected by the sample size, I see no reason why one should decrease $\alpha$. Choice of $\alpha$ can be arbitrary. One can choose $\alpha=0.1$
WorkSocial MediaSoftwareProgrammingWeb Design & DevelopmentBusinessCareersComputers Online Courses B2B Solutions Shop for Books San Francisco, CA Brr, it´s cold outside Search Submit Learn more with dummies Enter your email to join our mailing list for FREE content right to your inbox. Easy! Your email Submit RELATED ARTICLES How Sample Size Affects the Margin of how to reduce type 1 error Error Statistics Essentials For Dummies Statistics For Dummies, 2nd Edition SPSS Statistics for Dummies, 3rd causes of type 1 error Edition Statistics II for Dummies Load more EducationMathStatisticsHow Sample Size Affects the Margin of Error How Sample Size Affects the Margin of Error large sample size advantages Related Book Statistics For Dummies, 2nd Edition By Deborah J. Rumsey In statistics, the two most important ideas regarding sample size and margin of error are, first, sample size and margin of error have an inverse relationship; http://stats.stackexchange.com/questions/130604/why-is-type-i-error-not-affected-by-different-sample-size-hypothesis-testing and second, after a point, increasing the sample size beyond what you already have gives you a diminished return because the increased accuracy will be negligible. The relationship between margin of error and sample size is simple: As the sample size increases, the margin of error decreases. This relationship is called an inverse because the two move in opposite directions. If you think about it, it makes sense that the more information you have, the more http://www.dummies.com/education/math/statistics/how-sample-size-affects-the-margin-of-error/ accurate your results are going to be (in other words, the smaller your margin of error will get). (That assumes, of course, that the data were collected and handled properly.) Suppose that the Gallup Organization's latest poll sampled 1,000 people from the United States, and the results show that 520 people (52%) think the president is doing a good job, compared to 48% who don't think so. First, assume you want a 95% level of confidence, so you find z* using the following table. z*-Values for Selected (Percentage) Confidence Levels Percentage Confidence z*-Value 80 1.28 90 1.645 95 1.96 98 2.33 99 2.58 From the table, you find that z* = 1.96. The number of Americans in the sample who said they approve of the president was found to be 520. This means that the sample proportion, is 520 / 1,000 = 0.52. (The sample size, n, was 1,000.) The margin of error for this polling question is calculated in the following way: According to this data, you conclude with 95% confidence that 52% of all Americans approve of the president, plus or minus 3.1%. Using the same formula, you can look at how the margin of error changes dramatically for samples of different sizes. Suppose in the presidential approval poll that n was 500 instead of 1,000. Now the margin of error for 95% confidence
must be considered before we go on to advanced statistical procedures such as analysis of variance/covariance and regression analysis. One can select a power and https://www.andrews.edu/~calkins/math/edrm611/edrm11.htm determine an appropriate sample size beforehand or do power analysis afterwards. However, power analysis is beyond the scope of this course and predetermining sample size is best. Sample Size Importance An appropriate sample size is crucial to any well-planned research investigation. Although crucial, the simple question of sample size has no definite answer due to the many factors involved. We expect large samples to give sample size more reliable results and small samples to often leave the null hypothesis unchallenged. Large samples may be justified and appropriate when the difference sought is small and the population variance large. Established statistical procedures help ensure appropriate sample sizes so that we reject the null hypothesis not only because of statistical significance, but also because of practical importance. These procedures must consider the size of type 2 error the type I and type II errors as well as the population variance and the size of the effect. The probability of committing a type I error is the same as our level of significance, commonly, 0.05 or 0.01, called alpha, and represents our willingness of rejecting a true null hypothesis. This might also be termed a false negativea negative pregnancy test when a woman is in fact pregnant. The probability of committing a type II error or beta (ß) represents not rejecting a false null hypothesis or false positivea positive pregnancy test when a woman is not pregnant. Ideally both types of error are minimized. The power of any test is 1 - ß, since rejecting the false null hypothesis is our goal. Power of a Statistical Test The power of any statistical test is 1 - ß. Unfortunately, the process for determining 1 - ß or power is not as straightforward as that for calculating alpha. Specifically, we need a specific value for both the alternative hypothesis and the null hypothesis since there is a different value of ß for each different value of the alternative hypothesis. Fortunately, if we minimize ß