Lecture 14S

# Lecture 14S - Lecture 14 page 1 page 1 Statistics 371-001,...

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Statistics 371-001, Sp 09 Lecture #142 103 Mar 09 Chapter 7. Comparison of Two Independent Samples (continued) 7. 5 Further Discussion of the t Test 1. Relationship between confidence interval and t test. Use the same three values to calculate both: The confidence interval means that the probability is _________ (the α -level) that this confidence interval contains the mean. The t-test means that, if H 0 is true, the probability is _________ (the α -level) that a t s more (or less) extreme that a certain t -value would be obtained. Both are saying the same thing: The confidence interval is for μ 1 μ 2 . If the confidence interval contains 0, then it is likely that = 0; likewise, if the confidence interval does not contain 0, then it is likely that 0. If the t -statistic is not extreme, then it is likely that = 0; if the t -statistic is extreme, then it is likely that 0 They are different ways of presenting results: Confidence interval indicates the magnitude of . Testing provides information about the strength of the evidence that μ 1 and μ 2 are really different. Described by the p-value. The α -level is arbitrarily selected before the study is done. The p-value is determined by the data. 2. Type I and Type II Error

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Type I error – Erroneous rejection of H 0 when it is true. Eg, Conclude a treatment has an effect when it has no effect. (very bad if treatment has bad side effects for example) Similar to getting 10 heads with a fair coin. To minimize probability of Type I error: Require extreme evidence to reject. Alpha – level of significance Type II error – Erroneous failure to reject H 0 when it is false. Eg, Fail to detect an effective treatment. Would be like getting 5 heads with a biased coin. Beta (ß) – depends on a variety of factors. Can’t minimize both. Look for balance; trade-off. Lecture 14 page 22 page 2
3. Power of a statistical test. The chance of rejecting H 0 when it is false is called the power of a statistical test or 1 – ß. How well can this test (or study) detect an effect if it is there.

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## This note was uploaded on 04/07/2009 for the course STAT 371 taught by Professor Koscik during the Spring '08 term at Wisconsin.

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Lecture 14S - Lecture 14 page 1 page 1 Statistics 371-001,...

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