# Lecture 6 - Factorial Design and Analysis Flashcards

What are factorial designs?

designs which include multiple independent variables - eg an experiment looking at the effect of both gender and time of day on exam score would be a factorial design

What is a one way desgin

a design with only one IV

what is a two way design

a design with 2 IVs

what is a three way design

a design with 3 IVs

How do we name a multifactorial design

we say ‘an x way, (y x z) ……… design E.g. a two-way (2x4) repeated measures design) or a three-way (2x3x5) between groups design In the brackets is how many levels each of the IV’s has)

define a mixed/split plot design

a design where one or more of the IV’s is between groups, and one or more of the IV’s is repeated measures

define main effect

the effect of a single IV

what is an interaction

the effect of 2 variables, when considered together

how many f-ratios would be calculated in a two-way ANOVA? what would they be?

three 1-main effect of IV 1 2-main effect of IV 2 3- interaction between IV 1 and IV 2 The deviations and sum of squares are also calculated for each of these three things.

how many hypothesis are there in a two-way ANOVA and what would they be?

there are 3 1 - means of different levels of IV 1 will be the same 2 - means of levels of IV 2 will be the same 3 - the differences between the means of the different levels of the interaction (IV 1 and IV 2) will be the same

How many mean squares are calculated in a two-way ANOVA? what are they?

1 - main effect of IV 1 2 - main effect of IV 2 3 - interaction (AB) 4 - the error term

what is another way of talking about the interaction

AB (a is variable 1, B is variable 2)

How do we write the results for an IV?

There was a significant main effect of (……). (F_{1,16}=37.604, MSe=11.500, p<0.001). (if non significant then we give the actual f value instead of p)

Then we say

The students who attended lectures, on average, scored higher (mean = 22.100) than those students who did not attend lectures (mean = 12.800)

IF we have this information

We also go on to say that an ANOVA can only tell us that there are differences, not what those differences are, for that, we need to perform further tests.

How do interpret a main effect analysis?

1 - write significant or non-significant next to each of the f-values on the table

Then we state something like the following for each row (which is a pair of comparisons)

There was a significant difference between those students who did attend lectures (mean =25.00) or did not attend lectures (mean = 9.60) when they did not complete worksheets. (F_{1,11}=57.313, MSe=11.500, p<0.001)