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Lecture 6

06 Lecture 6 (KIN 1G03).pdf

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Dr R Balasubramaniam

KIN 1G03 Lecture 6 Dr R Balasubramaniam SimpleANOV A:Comparing the Means ofThree or More Groups ANOVAT erminology •  The purpose anANOVA (analysis of variance) is to compare the effects of a variable with multiple factors (training intensity:low,med,high) on a single variable (VO 2. •  The independent variable Intensity ofraining is called a FACTOR. •  The FACTOR in this example has 3 LEVELS (low, med,high) •  The dependent variable in this experiment isVO 2 •  ANOVA allows for multiple comparisons while still keeping alpha at 0.05. Familywise Error Rate:Why doANOVA? Now let us consider comparing the effects of NUMBER OF DAYSTRAINING PERWEEK (1,2,3,4,5,6) on STRENGTH. The number of days training is a factor with 6 levels. We could use multiple t-tests to compare (1 v 2,1 v 3,1 v 4,1 v 5,1 v 6;2 v 3,2 v 4,2 v 5,2 v 6;3 v 4,3 v 5,3 v 6;4 v 5,4 v 6;5 v 6). That would require 15 t-tests. This would cause alpha to inflate from 0.05 to 0.26 greatly increasing the probability of making aType I ERROR. ANOVA fixes this problem by doing only one test. Example data set Significance of results plot Assumptions ofANOVA Example data set Sources ofVariance Between Groups variance is the deviation of the group means from the Grand MEAN. Within Groups variance is the deviation of individual scores from their Group Means. Within Groups Deviations Sum of SquaredWithin Deviations SS w 7.40 + 16.86 + 4.00 + 13.40 + 5.71 = 47.37 Between Groups Deviations SS B 7.26 X 7 = 50.82 Mean Square and F Ratio Degrees of freedom •  Dfw= N – k (35 -5) =30 (total number of data points – total number of groups) •  Df = k -1 = 4 (total number of groups – 1) b •  Mean Sum of squares within MS w SS /wf =w47.37/30 = 1.58 Mean Sum of squares between MS = SS /df = 50.82/4 = 12.71 b b b F = MS /MS (referred to as Fisher’s F value). b w F Statistic is a Ratio ofVariances 50.74 =12.69 Each Sum of Squares is divided by its df 4 47.43 to produce a Mean Square. =1.58 30 F ratio is the ratio of variances 12.69 =8.03 1.58 F = MS /bMS e CriticalValues of F Statistic R (also called eta ) and ω " 2 R or eta are rough estimates the size of the effect. 2 ▯ is a more exact test of the Effect. Chapters from the text •  Correlation and •  Chapter 7 Bivariate Regression •  Multiple Regression •  Chapter 7 •  Chapter 8 •  t test/means comparisons (only one- tailed test) •  Chapter 9 •  simpleANOVA •  Nonparametrics •  Chapter 13 Notes re:final exam •  Several short multiple choice and fill-in-the-blank questions •  Problem sets on each of the major exercises that we have done Pearson correlation,bivariate regression,ANOVA,t-test,chi-squared,Spearman correlation and some questions from pre-mid term including frequency analyses. Multiple Regression (MR) •  Predicting one DV from a set
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