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19_anova2

# 19_anova2 - Your schedule of coming weeks Today One-way...

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One-way ANOVA, II 9.07 4/22/2004 Your schedule of coming weeks Two-way ANOVA, parts I and II. No class on Tuesday, 5/4 Thursday class: TA’s talk about statistical learning Today: One-way ANOVA, part II Next week: One-way ANOVA HW due Thursday Week of May 4 Teacher out of town all week and other uses for statistics outside of the scope of this course, and do a bit of a review. Two-way ANOVA HW due Thursday (last HW!) Review from last time p-value P df tot SS tot Total MS wn df wn SS wn F obt MS bn df bn SS bn Between F Mean square df Sum of squares Source Review from last time MS = SS/df F obt = MS bn / MS wn obt to F crit bn , df wn ) ( ) df , ) ( 2 2 = = tot tot tot tot N x x SS df , ) ( 1 2 2 2 = = = = i i i i i bn N M M m n SS df , ) ( 1 1 2 = = = ∑∑ = = i i n j i ij bn tot wn m x SS SS SS Create ANOVA table Within Compare F , df = (df 1 - N 1 - k condits # m n k - N condits # 1

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Relationship to proportion of variance accounted for bn / MS tot = proportion of variance accounted for by the systematic effect wn / MS tot = proportion of variance not accounted for obt is: for proportion = obt F •MS So, another way of looking at F for accounted not variance of proportion accounted variance of significant effect of x-values on y-values Relationship to correlation analysis Similarly, in ANOVA we are not asking whether there is a difference between a particular pair of conditions (“x-values”) Instead, we are testing whether there is a Relationship to correlation analysis • In correlation analysis, we weren’t interested in whether there was a difference in y-values between a particular pair of x-values 0 1 2 3 4 5 6 7 8 9 012345 Glasses of orange juice per day Doctor's visits per year Relationship to correlation analysis • Instead, we were interested in whether there was a significant relationship between the x-values and y-values 0 1 2 3 4 5 6 7 8 9 Glasses of orange juice per day
there may not be a natural ordering to the conditions (x-values) relationship is linear (as in correlation • ANOVA: 0 1 2 3 4 5 6 7 8 9 1 2 3 4 5 Relationship to correlation analysis The main difference between correlation analysis and ANOVA is that in ANOVA So, one shouldn’t expect that the analysis), since it’s not clear what this would mean ANOVA vs. correlation analysis Condition # Response Relationship between ANOVA and pair of x-values, we look for an overall effect of the x-values on the y-values by its y-value The tests for ANOVA and • ANOVA: for proportion = obt F ) 1 ( ) 2 ( 2 2 2 r N r t obt = not accounted for correlation analysis In both cases, since we’re not interested in the difference in mean between a particular looking at how much knowing the x-value of a data point reduces your uncertainty in correlation analysis are very similar In fact, some people treat correlation analysis as a form of ANOVA Correlation: for accounted not variance of proportion accounted variance of Proportion of variance accounted for Proportion of variance 3

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Post-hoc comparisons
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19_anova2 - Your schedule of coming weeks Today One-way...

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