CHLH 244 Lecture 10 Pt. II

CHLH 244 Lecture 10 Pt. II - ANOVA Lecture 2 One Way ANOVA...

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ANOVA Lecture 2
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One Way ANOVA table Source of Variation Mean Squares F Ratio P value Between SS b F k-1, N-k Computer generated Within SS w N-k Total SS t N-1 k=# of groups Test statistic If we are given these, k and N, We can do a problem
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Example Source of Variation Sum of Squares df Mean Squares (s 2 ) F Ratio Critical F P value Between 93.75 3 31.25 7.35 3.24 Within 68.00 16 4.25 Total 19 Does the F Ratio exceed the critical value? Yes: So we reject the null hypothesis and say that the group means are not equal at the alpha=0.05 level.
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Post Hoc Test Multiple comparison tests helps to find out where the difference(s) between means are test the hypothesis that all possible pairs of means are equal pairs whose differences exceed the HSD are considered to be significantly different
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Tukey’s HSD (Honestly Significant Difference) 73 . 3 ) 922 (. 05 . 4 5 25 . 4 05 . 4 = = = HSD ( 29 n MS q HSD w k N k - = , , α
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Pair Mean Difference Critical Value A-B 7-1= 6* 3.73 A-C 5-1= 4* 3.73 A-D 4-1= 3 3.73 B-C 7-5= 2 3.73 B-D 7-4= 3 3.73 C-D 5-4=1 3.73 Mean Difference and Critical value for weight gains of all possible pairs
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Calculate the means of groups 1 5 / 5 = = = A A A n X X 7 5 / 35 = = B X 5 5 / 25 = = C X 4 5 / 20 = = D X
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Pair Mean Difference Critical Value A-B 7-1= 6* 3.73 A-C 5-1= 4* 3.73 A-D 4-1= 3 3.73 B-C 7-5= 2 3.73 B-D 7-4= 3 3.73 C-D 5-4=1 3.73 Mean Difference and Critical value for weight gain of each pair There is a significant difference in weight gain between A-B and A-C.
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Example 1 Again, we are interested in finding out about differences in health care service in Illinois elementary schools We have information from four counties : 5 schools for each county We are told at each school how many days a licensed medical professional is on site.
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Example 1: Scenario County A 1 0 1 2 0 County B 3 3 4 5 1 County C 1 2 1 2 1 County D 3 3 1 1 1 Number of days there is a licensed health care provider at 5 schools in four different counties
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Example 1: Question Is there a significant difference in the number of days between the four counties at the α =0.05 level? How do we solve this? ANOVA? Yes…More than two groups and looking for a difference
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Example 1: Hypotheses in ANOVA The null depends on how many groups. For n groups, H 0 : μ 1 = μ 2 = μ 3 = …= μ k So for 4 groups, H 0 : μ 1 = μ 2 = μ 3 = μ 4 The alternative is H 1 : One or more of the means are different from the others
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Example 1: Fill in the table Source of Variation Sum of Squares Df Mean Squares (s 2 ) F Ratio Critical F Between Within Total
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Preparation for calculating SS (sum of squares) A X 2 B X 2 C X 2 D X 2 Total 1 1 3 9 1 1 3 9 0 0 3 9 2 4 3 9 1 1 4 16 1 1 1 1 2 4 5 25 2 4 1 1 0 0 1 1 1 1 1 1 Sum x 4 16 7 9 36 6 60 11 21 98
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Calculate SS between and SS within SS Within = SS
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CHLH 244 Lecture 10 Pt. II - ANOVA Lecture 2 One Way ANOVA...

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