psychology statistics
fadi
FactorialInteractions.pdf
Research Methods
Factorial Designs Lab: Interactions
Background information: Ordinal vs. Disordinal Interactions
Ordinal interaction: reflects the fact that an independent variable seems to have more
of an effect under one level of a second independent variable than under another level.
If you graph an ordinal interaction, the lines will not be parallel, but they will not cross.
It is called an ordinal interaction because the interaction may be due to having ordinal
data. That is, despite the existence of an interaction at the statistical level, the
independent variable may have the same psychological effect under all levels of the
second independent variable. Ordinal interactions may result from ceiling or floor
effects.
Disordinal (crossover) interaction: when an independent variable has one kind of effect
in the presence of one level of a second independent variable, but a different kind of
effect in the presence of a different level of the second independent variable. Examples:
Getting closer to someone may increase their attraction to you if you have just
complimented them, but may decrease their attraction to you if you have just insulted
them. It’s called a crossover interaction because the lines in a graph will cross. It’s called
a disordinal interaction because it cannot be explained as an artifact of having ordinal,
rather than interval, data.
Below are 6 possible data outcomes for a hypothetical study of the effects of Age
(young vs. old) and Education (high school vs. college) on Income (in thousands of
dollars). For each data outcome, list and describe all possible Main Effects and
Interaction Effects.
A.
High
School
College Overall
Young 40 40
Old 40 60
Overall
B.
High
School
College Overall
Young 60 40
Old 40 60
Overall
C.
High
School College Overall
Young 20 60
Old 40 80
Overall
D.
High
School College Overall
Young 20 20
Old 120 120
Overall
E.
High
School
College Overall
Young 40 60
Old 40 80
Overall
F.
High
School
College Overall
Young 30 45
Old 35 60
Overall
Additional information:
Based on 1997-1999 statistics from the U.S. Census Bureau, the actual situation is closest to Result F (Day
& Newburger, 2002). People with a college education earn more than those with only a high school
education in both age groups, but the difference is somewhat greater for the older group. Over the
course of a typical working life, people in the United States with a college degree earn an average on 1.8
times more than those with only a high school education.
Day, J.C., & Newburger, E.C. (2002). The big payoff: Educational attainment and synthetic estimates of
work-life earnings. Curent Population Report, Special Studies, p. 23-210. Washington, DC: U.S.
Department of Commerce, Economics and Statistics Administration, U.S. Census Bureau.
