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Lecture 6

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

Department
Psychology
Course Code
PSYC 305
Professor
Heungsun Hwang
Lecture
6

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PSYC305 Lecture 6 - Jan. 25
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