This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: I. Comparison of Two Independent Populations Confidence Intervals : A 100( 1 ) % confidence interval for ( 1  2 ) when the population standard deviations are unknown is: If 1 and 2 are unknown but 1 = 2 , then a pooled estimate of the common variance is: Using this estimate, a 100(1 )% c.i. for ( 1  2 ) is: Example: Exercise 7.19, page 233. Hypothesis Testing Null and alternative hypotheses, type I and type II errors, test statistics To test H o : 1 = 2 compute t and reject H o in favor of H A of H A : 1 < 2 if t <  t H A : 1 > 2 if t > t H A : 1 2 if t <  t /2 or t > t /2 Example: Exercise 7.33, page 246 If 1 and 2 are unknown but 1 = 2 , then use the pooled Procedure . Sample size Calculation and Power A popular formula for computing the sample size for comparing two means (onesided alternative) is: n 1 = ( 1 2 + 2 2 / k) (z + z ) 2 / ( 1  2 ) 2 n 2 = k n 1 The WilcoxonMannWhitney Test Nonparametric methods are used when: 1 1. The populations are not normal. 2 2. Data are qualitative. 3 3. Data are ranked. To compare two populations, suppose we have a sample of size n 1 from the first population and a sample of size n 2 from the second population (n 1 n 2 ). For each observation in sample 1, count the number of observations in sample 2 that are smaller in value. Let K 1 be the sum of these counts. Similarly, for each observation in sample 2, count the number of observations in sample 1 that are smaller in value. Let K 2 be the sum of these counts. The WilcoxonMannWhitney test statistic U s is the larger of K 1 and K 2 . We use Table 6 to find the critical values II. Comparison of Paired Samples Paired ttest and Confidence Interval In the matched pair designs we apply the onesample tprocedure. Paired designs are used to free the comparisons from the effects of extraneous variables. Example: Problem #4 The Sign Test In many applications we may be interested in comparing matched pairs , when we have ranked or quantitative data....
View
Full
Document
 Winter '07
 AZARI
 Statistics, Standard Deviation

Click to edit the document details