PSYC 333 Lecture Notes - Lecture 6: Analysis Of Variance, Total Variation, Studentized Range
7 May 2018
School
Department
Course
Professor
PSYC 305 – STATISTICS FOR EXPER DESIGN, WINTER 2018
Lecture 6: Two-Way ANOVA II
Two-Way ANOVA
Statistically examines
Main effects of two factors (IVs) on the dependent variable
Interaction effect between these factors
Hypotheses for main effects:
Row main effect:
H0R: μR1 = μR2 = · · ·= μRr (equal row marginal means)
H1R: Not all μRj are the same
Column main effect:
H0C:μC1 =μC2 =···=μCc(equalcolumn marginal means)
H1C: Not all μCt are the same
For testing these 3 effects, we can settle the hypotheses
hor and hoc = all are the same
Hypotheses for an interaction effect:
H0RC: The interaction between R and C is equal to zero (e.g., RC
= 0)
H1RC: The interaction between R and C is not zero (e.g., RC ≠ 0)
Interaction: RC , so RC=0 = 0 interaction
1. divide entire variance into subvariances
find more resources at oneclass.com
find more resources at oneclass.com
PSYC 305 – STATISTICS FOR EXPER DESIGN, WINTER 2018
2. compare ratios
ANOVA = ANalysis Of VAriance
1. divides the variance/variation observed in experimental data into
different parts resulting from different sources;
2. assesses the relative magnitudes of the different parts of variance; and
3. examines whether a particular part of the variance is greater than
expectation under the null hypothesis.
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
find more resources at oneclass.com
find more resources at oneclass.com
PSYC 305 – STATISTICS FOR EXPER DESIGN, WINTER 2018
Partitioning Variation
Column
SS(B) is partitioned into:
We need to compute the SS terms, and then if u divide by corresponding degrees of
freedom, get MS (mean square)
find more resources at oneclass.com
find more resources at oneclass.com
Document Summary
Main effects of two factors (ivs) on the dependent variable. 0r: r1 = r2 = = rr (equal row marginal means) For testing these 3 effects, we can settle the hypotheses hor and hoc = all are the same. : the interaction between r and c is equal to zero (e. g. , rc. : the interaction between r and c is not zero (e. g. , rc = 0) Interaction: rc , so rc=0 = 0 interaction: divide entire variance into subvariances. Psyc 305 statistics for exper design, winter 2018: compare ratios. Total ss (= variation) can be divided into two parts: We need to compute the ss terms, and then if u divide by corresponding degrees of freedom, get ms (mean square) Ms = variance of r (row) c(column) rc(interaction) She was also interested in difference in reaction time between male and female subjects (factor a).
