Within-person (or within-subject) effects represent the variability of a particular value for individuals in a sample. You see this commonly examined in repeated measures analysis (such as repeated measures ANOVA, repeated measures ANCOVA, repeated measures MANOVA or MANCOVA…etc). In these instances, a within person effect is a measure of how much an individual in your sample tends to change (or vary) over time. In other words, it is the mean of the change for the average individual case in your sample.
Imagine we collected a score from every person in your town that measured how much they wanted ice cream at the particular moment of data collection (let's say scores could range from 1 to 100, with 100 meaning REALLY WANT ice cream). Further, let's pretend we did this once a day for 5 days. Our within-subject effect would be a measure of how much individuals in our sample tended to change on their wanting of ice cream over the five days.
Between-persons (or between-subjects) effects, by contrast, examine differences between individuals. This can be between groups of cases when the independent variable (IV) is categorical or between individuals when the (IV) is continuous. These type of effects can be observed in either the univariate context or the multivariate context (including repeated measures). Either way, between-subjects effects determine if respondents differ on the dependent variable (DV), depending on their group (males vs. females, young vs. old…etc) or depending on their score on a particular continuous IV.
For example, let's return to our ice cream anecdote. If we want to test whether respondents are more likely to want ice cream if they score highly on an IQ test, we are testing for between-subjects effects. In this example, we are seeing if differences between persons with different IQs also have correspondingly different scores for "wanting ice cream". If course, the correct answer here is obviously yes.
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