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Class 6 - ANOVA_w_simulation

# Class 6 - ANOVA_w_simulation - Consider four groups labeled...

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Unformatted text preview: Consider four groups labeled 1, 2, 3 & 4. We want to see if the mean is the same for all four Treatm Treatment Group 1 2 3 4 Mean Standard Deviation Independent Sample Sizes The statistics from these four samples will be used to decide if the means are all the same or if at l Mean Standard Deviation Variance between sample means measures closeness of means values to each other. Small versus Large is best determined when comparing to a standard. The pooled variance of data Within groups is a good standard. Variance Between Sample Means = Mean Square Be Variance of Sample Data with Within Groups Mean Squ μ 1 μ 2 μ 3 μ 4 σ 1 σ 2 σ 3 σ 4 n 1 n 2 n 3 n 4 N = n 1 + n 2 + n 3 + n 4 s 1 s 2 s 3 s 4 H : μ 1 = μ 2 = μ 3 = μ 4 H is supported if all sample mean values are close to ea H A : At least one mean is different equivalent H A : Not all are equal H is supported if the variance between sample means is small H a is supported if the variance between sample means is large H : σ 2 Between Groups = σ 2 Within Groups H : σ 2 Between Groups / σ 2 Within Groups = 1 H A : σ 2 Between Groups > σ 2 Within Groups H A : σ 2 Between Groups / σ 2 Within Groups > 1 Test Statistic = Phenomenon Parameters Sample Statistics H A is supported if all sample mean values are NOT clos (i.e. There is a difference between sample means and the larger than anticipated.) The null and alternate hypotheses above for variances are equivalent to the null and alternate hypotheses above for the four means . 1 y 2 y 3 y 4 y ent groups or if at least one is different Will Test on this stuff least one is different. Will Test on this stuff Instead of looking at difference between means, we are looking at diff. between etween Treatment Groups uare Within Groups ach other. se to each other. e variability between means is The Alternate hypothesis of at least one mean being different is supported only when the variance Between means is Greater than the variance Within the groups. This a 1-tail upper-tail test. n variances Analysis results are presented in what is known as an ANOVA table Excel Presentation 1 Factor ANOVA Source of Variation SS df MS Between Groups Within Groups SSE Total Text Presentation One-Way ANOVA Source of Variation df SS MS SSE Total For k treatments and N total observatio Assumptions used for the theoretical development of this analsis procedure: ANOVA is robust to the above assumption if the sample sizes are approximately the sam Note: The analysis procedure tends to work well as long as the sample sizes are approx Note: The analysis procedure tends to work well for distributions departing from norma SS Treatment df Treatment MS Treatment = SS Treatment / df Treatment df Error MSE = SSE / df Error SS Total df Total Treatment (Between) df Treatment SS Treatment MS Treatment = SS Treatment / df Treatment Error (Within) df Error MSE = SSE / df Error df Total SS Total df Treatment = k-1 df Total = N-1 df Error = N-k Independence of data between groups and within each group. of data between groups and within each group....
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Class 6 - ANOVA_w_simulation - Consider four groups labeled...

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