Does Increasing Sample Size Reduce Type 1 Error
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How To Reduce Type 1 Error In Statistics
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Power And Type 1 Error
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, https://www.researchgate.net/post/Is_there_a_relationship_between_type_I_error_and_sample_size_in_statistic 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 Why is type I error not affected by different sample size - hypothesis testing? [duplicate] up vote 8 down vote favorite This question http://stats.stackexchange.com/questions/130604/why-is-type-i-error-not-affected-by-different-sample-size-hypothesis-testing 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 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
must be considered before we go on to advanced statistical procedures such as analysis of variance/covariance https://www.andrews.edu/~calkins/math/edrm611/edrm11.htm and regression analysis. One can select a power and determine an https://www.ma.utexas.edu/users/mks/statmistakes/errortypes.html 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 sample size has no definite answer due to the many factors involved. We expect large samples to give 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 type 1 error 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 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 negative—a 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 positive—a 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
when it is in fact true is called a Type I error. Many people decide, before doing a hypothesis test, on a maximum p-value for which they will reject the null hypothesis. This value is often denoted α (alpha) and is also called the significance level. When a hypothesis test results in a p-value that is less than the significance level, the result of the hypothesis test is called statistically significant. Common mistake: Confusing statistical significance and practical significance. Example: A large clinical trial is carried out to compare a new medical treatment with a standard one. The statistical analysis shows a statistically significant difference in lifespan when using the new treatment compared to the old one. But the increase in lifespan is at most three days, with average increase less than 24 hours, and with poor quality of life during the period of extended life. Most people would not consider the improvement practically significant. Caution: The larger the sample size, the more likely a hypothesis test will detect a small difference. Thus it is especially important to consider practical significance when sample size is large. Connection between Type I error and significance level: A significance level α corresponds to a certain value of the test statistic, say tα, represented by the orange line in the picture of a sampling distribution below (the picture illustrates a hypothesis test with alternate hypothesis "µ > 0") Since the shaded area indicated by the arrow is the p-value corresponding to tα, that p-value (shaded area) is α. To have p-value less thanα , a t-value for this test must be to the right oftα. So the probability of rejecting the null hypothesis when it is true is the probability that t > tα, which we saw above is α. In other words, the probability of Type I error is α.1 Rephrasing using the definition of Type I error: The significance level αis the probability of making the wrong decision when the null hypothesis is