lecture16 - Lecture 16 Two-Factor Between-Subjects Between...

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Lecture 16 wo actor Between ubjects Two-Factor Between-Subjects Design and Analysis of Variance
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Factorial designs Factorial designs are research designs in which two or more independent variables are imultaneously varied simultaneously varied Simplest factorial design: two independent variables are varied and each independent variable contains two levels
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Factorial designs (example) Choline acetyltransferase and Alzheimer patients. cientific hypothesis is that reduced levels of choline Scientific hypothesis is that reduced levels of choline acetyltranferase leads to decreased levels of acetylcholine and is partially responsible for Alzheimers. Choline acetyltransferase could just naturally change as yj y g age. Two factors (A) affection status – Alzheimer or Not (B) Age at death <80 or >=80. Outcome choline acetyltransferase conc. from brain biopsies. 6 individuals per group.
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Graphical Depictions
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Graphical Depictions
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Our Hypotheses We want to know three things. Is there a difference in choline acetyltransferase vels between patients and controls (Factor A)? levels between patients and controls (Factor A)? Is there a difference in choline acetyltransferase levels between older and younger individuals actor B)? (Factor B)? Is there an interaction? Do we see a difference when we compare the enzyme levels for younger ontrols to the levels for older controls than when controls to the levels for older controls than when we compare the enzyme levels of younger patients to the levels of older patients?
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Factorial designs (continued) This design often is called a 2 2 (“two-by- two”) design he first 2 of the 2 indicates that there are two The first 2 of the 2 2 indicates that there are two levels of the first independent variable, identified as factor A he second 2 indicates the number of levels of The second 2 indicates the number of levels of the second independent variable, identified as factor B ach ell r eatment condition presents a Each cell or treatment condition represents a combination formed from one level of each independent variable
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Factorial designs (continued) A score for a subject is represented by X ijk , where the subscripts provide the following formation information i = number identifying the subject within a treatment condition j = level of the A variable that the subject receives k = level of the B variable that the subject receives
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Cell means Cell means Symbolized by Symbolized in general by 1 1 1 2 2 1 2 2 , , , and AB XXX X AB X The means of the n AB scores for a treatment combination Indicates the typical performance of all yp p subjects given one treatment combination in a factorial design
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Main effect means The mean of all subjects given one level of an independent variable, ignoring the classification y the other independent variable in a factorial by the other independent variable in a factorial There are two sets of main effect means ain effect means for factor
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This note was uploaded on 03/15/2010 for the course PSYCHOLOGY 100B taught by Professor Firstenberg,i. during the Winter '10 term at UCLA.

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lecture16 - Lecture 16 Two-Factor Between-Subjects Between...

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