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Lecture 6

# PSYC 305 Lecture Notes - Lecture 6: Direct Comparison Test, Variance, Analysis Of Variance

by OC13018

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One-Way ANOVA:

•Purpose:

•To test whether the means of k ( 2) populations significantly differ≧

•Ho : µ1 = µ2 … = µk

•H1 : Not all µ’s are the same (at least one of the means is different)

One-Way ANOVA: Steps

•ANOVA = Analysis of Variance

•Divides the variance observed in data into different parts resulting from different sources;

•Assesses the relative magnitude of the different parts of variance; and

•Examines whether a particular part of the variance is greater than expectation under the null hy-

pothesis

•All means are equal

One-Way ANOVA: Computations

•We can assess the relative magnitude of the two different parts of variance:

•This is called the F statistic (or F ratio)

•One way ANOVA needs the calculation of the two sample variances VB and Vw

•Note, the sample variance is obtained by dividing the Sum of the Squares (SS) of the deviations of

values from the mean by its degrees of freedom (df)

Partitioning Total Variation (SS):

•Total SS (= variation) can be divided into two parts:

•SS(T) = SS(B) + SS(W)

•SS(T) = Total variation

•SS(B) = Between-group variation

•SS(W) = Within-group variation

Total SS:

•SS(T) = the aggregate variation/dispersion of individual observations across groups

•SS(B) = variation between the sample means

•SS(W) = variation that exists among the observations within a particular group

Calculating Sample Variances:

•VT, VB, VW are often called the total, between-group, and within-group Mean Squares, abbreviated

by MS(T), MS(B), and MS(W), respectively

One-Way ANOVA: Computations

•Once VB and VW are obtained, calculate the F statistic value for your samples

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