Psyc 60 ANOVA

# Psyc 60 ANOVA - ANOVA Analysis of Variance From t to F. In...

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ANOVA Analysis of Variance

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From  t  to  F In the independent samples  t  test, you  learned how to use the   distribution to  test the hypothesis of no difference  between  two  population means. Suppose, however, that we wish to  know about the relative effect of  three or  more  different “treatments”?
From  t  to  F We could use the  t  test to make comparisons among  each possible combination of two means. However, this method is inadequate in several ways. It is tedious to compare all possible combinations of groups. Any statistic that is based on only part of the evidence (as is  the case when any two groups are compared) is less stable  than one based on all of the evidence. There are so many comparisons that some will be significant  by chance.

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From  t  to  F What we need is some kind of survey test  that will tell us whether there is any significant  difference  anywhere  in an array of categories. If it tells us no, there will be no point in  searching further. Such an overall test of significance is the  test, or the analysis of variance, or ANOVA.
The logic of ANOVA Hypothesis testing in ANOVA is about  whether the means of the samples differ more  than you would expect if the null hypothesis  were true. This question about  means  is answered by  analyzing  variances . Among other reasons, you focus on variances  because when you want to know how several  means differ, you are asking about the variances  among those means.

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Two Sources of Variability In ANOVA, an estimate of  variability between groups  is  compared with  variability within groups . Between-group variation is the variation among the means of the  different treatment conditions due to chance (random sampling  error) and treatment effects, if any exist. Within-group variation is the variation due to chance (random  sampling error) among individuals given the same treatment. A N O V A W i t h i n - G r o u p s V a r i a t i o n V a r i a t i o n d u e t o c h a n c e . B e t w e e n - G r o u p s V a r i a t i o n V a r i a t i o n d u e t o c h a n c e a n d t r e a t m e n t e f f e c t ( i f a n y e x i s t i s ) . T o t a l V a r i a t i o n A m o n g S c o r e s
Variability Between Groups There is a lot of variability from one mean to the next.

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## This note was uploaded on 01/30/2009 for the course PSYC 60 taught by Professor Ard during the Spring '08 term at UCSD.

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Psyc 60 ANOVA - ANOVA Analysis of Variance From t to F. In...

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