PSYC 2020 Lecture Notes - Lecture 16: Complement Factor B
10 Apr 2018
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Two factor ANOVA
● Underlying logic
● Notation and formulas
● Hypothesis test examples
● Interpreting results
Underlying logic
● We wanted to know if room temp effected people on the test - one factor design - we just
have one independant variable, one thing we are manipulating ot form our group, and
we have 1 factor we are manipulating and we have 3 groups
● 2 factor design - 2 things that are changing
○ Temp and then we added humidity
■ 2 x 3 design
■ Diff people in each - one variable is repeated and another is diff
● We are talkign about diff factors adn diff subjects in each groups
● When people add another factor, the anaylsysi would be more complciated and now we
would need more subjects
○ We don't do this for no reason
○ Reason: they have some theoritical reason for why they think the two factors
would influnce what they are mentioning
■ To find out do these two things interact
3 questions that will be answered:
● If we have a 2 factor, there will be 2 main effects:
○ F(A)One f ration - which will answer the question, did th epeople in the low
humidty condition behave diff than the high humidity
■ Looking at the variance cbetween the rows (treatment effect) and divide
that by the variance we expect by chance/ error
○ F(B)Look at the variabilty between the columns, (the main effect temperature),
and dividie by the variance we eecpect by chance (f ratio)
○ F(AxB)
○ - F(A)
○ - F(B)
Interaction between the two factors:
● Does one factor affect or depend upon the other / one level effect the other
find more resources at oneclass.com
find more resources at oneclass.com
○ Paralell lines - no interaction
■ The second one shows that there is an interaction
● Variance in the date that is not explained by the main effect - the left ober treatment
variance and we would divide that be the varaince of chance
find more resources at oneclass.com
find more resources at oneclass.com
● If we have a two factor experiment, and we want to find out the 3 F’s.. we take all the
numbers from the expirment, and we get the total variability
○ SS/df
● Between treatments variabilty - the variabilty between the treatments - due to the
treatments - Variaibilty due to all the treamtments -
○ Factor A - MS(A)/ MS (within)
○ Factor B - MA(B)/Ms (within)
○ Factor AB - MS(AB)/ MS (within)
● Withing treatmnets variabilty - no meausring treatment effect - that’s the variabilty due to
chance/individual different, anything but the treatment
○ If we were doing a one factor indepenant measures design - this would be done.
○ MS(within) - demonaotor in all our chance
● How to summarize the data
○ Two things we are looking at, and we have 2 levels of factors (wieght and how
full someone is)
■ We have 4 uniquee treatment conditions
○ Comletley independant measures design
○ New:
○ Summaraize what happens accross the rows - using the row totals when trying to
come up with a variavbilty number to come up with the effect
■ Same thign with coluns
find more resources at oneclass.com
find more resources at oneclass.com
Document Summary
2 factor design - 2 things that are changing. Diff people in each - one variable is repeated and another is diff. We are talkign about diff factors adn diff subjects in each groups. When people add another factor, the anaylsysi would be more complciated and now we would need more subjects. We don"t do this for no reason. Reason: they have some theoritical reason for why they think the two factors would influnce what they are mentioning. To find out do these two things interact. If we have a 2 factor, there will be 2 main effects: F(a)one f ration - which will answer the question, did th epeople in the low humidty condition behave diff than the high humidity. Looking at the variance cbetween the rows (treatment effect) and divide that by the variance we expect by chance/ error.
