Dr. Michael R. Hyman, NMSU Differences Between Group Means

2 Differences between Groups when Comparing Means Interval or ratio scaled variables t-test –When groups are small –When population standard deviation is unknown z-test –When groups are large

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4 Null Hypothesis about Mean Differences between Groups

5 X 1 = mean for Group 1 X 2 = mean for Group 2 S X 1 -X 2 = the pooled or combined standard error of difference between means t-Test for Difference of Means

6 Pooled Estimate of the Standard Error t-test for the Difference of Means S 1 2 = the variance of Group 1 S 2 2 = the variance of Group 2 n 1 = the sample size of Group 1 n 2 = the sample size of Group 2

7 t-Test for Difference of Means Example

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10 Comparing Two Groups when Comparing Proportions Percentage Comparisons Sample Proportion - P Population Proportion -

11 Differences between Two Groups when Comparing Proportions The hypothesis is: H o :  1   may be restated as: H o :  1   

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13 Z-Test for Differences of Proportions p1 = sample portion of successes in Group 1 p2 = sample portion of successes in Group 2 (p1 - p1) = hypothesized population proportion 1 minus hypothesized population proportion 1 minus Sp1-p2 = pooled estimate of the standard errors of difference of proportions

14 Z-Test for Differences of Proportions: Standard Deviation p = pooled estimate of proportion of success in a sample of both groups p =(1- p) or a pooled estimate of proportion of failures in a sample of both groups n 1 = sample size for group 1 n 2 = sample size for group 2

15 Z-Test for Differences of Proportions: Example

16 Z-Test for Differences of Proportions

17 Z-Test for Differences of Proportions: Example

18 Hypothesis Test of a Proportion  is the population proportion p is the sample proportion  is estimated with p

19 5. :H 5. :H 1 0   Hypothesis Test of a Proportion

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S p  S p  S p  1200 )8)(.2(. S p  n pq S p  20.p  200,1n  Hypothesis Test of a Proportion: Another Example

23 Indeed.001 the beyond t significant is it level..05 the at rejected be should hypothesis null the so 1.96, exceeds value Z The 348.4Z Z Z S p Z p       Hypothesis Test of a Proportion: Another Example

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