lecture16note - 11/29/2009 Factorial designs Factorial...

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11/29/2009 1 Lecture 16 Two-Factor Between-Subjects Design and Analysis of Variance Factorial designs Factorial designs are research designs in which two or more independent variables are simultaneously varied Simplest factorial design: two independent Simplest factorial design: two independent variables are varied and each independent variable contains two levels Factorial designs (example) Choline acetyltransferase and Alzheimer patients. 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 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. Graphical Depictions Graphical Depictions Our Hypotheses We want to know three things. Is there a difference in choline acetyltransferase levels between patients and controls (Factor A)? Is there a difference in choline acetyltransferase levels between older and younger individuals (Factor B)? Is there an interaction? Do we see a difference when we compare the enzyme levels for younger 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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11/29/2009 2 Factorial designs (continued) This design often is called a 2 2 (“two-by- two”) design The first 2 of the 2 2 indicates that there are two levels of the first independent variable, identified as factor A The second 2 indicates the number of levels of the second independent variable, identified as factor B Each cell or treatment condition represents a combination formed from one level of each independent variable Factorial designs (continued) A score for a subject is represented by X ijk , where the subscripts provide the following information i = number identifying the subject within a 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 Cell means Cell means Symbolized by 1 1 2 2 1 2 , , and AB XXX X The means of the n AB scores for a treatment combination Indicates the typical performance of all subjects given one treatment combination in a factorial design AB X Main effect means The mean of all subjects given one level of an independent variable, ignoring the classification by the other independent variable in a factorial There are two sets of main effect means Main effect means for factor A Symbolized by The difference is the main effect of factor A 2 and A A XX 2 A A Main effect means (continued) Collapse the data over levels of factor B to obtain main effect means for factor A If factor A has an effect on the dependent and will differ from will become larger 2 A A 2 A X 1 A X
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11/29/2009 3
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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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lecture16note - 11/29/2009 Factorial designs Factorial...

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