Within-Subject and Between-Subject Effects: Wanting Ice Cream Today, Tomorrow, and The Next Day…

The conceptual difference between within-subject and between-subject effects is something I am asked about quite often. So often in fact, I thought a blog posting was warranted! As a quick disclaimer, I know this is a complex issue and the description of what each type of effect actual is varies greatly based on the kind of analysis one is conducting. However, what follows is an attempt to provide a basic conceptual foundation to understand the differences.

Within-person (or within-subject) effects represent the variability of a particular score for individuals in your sample. You will commonly see this being examined in repeated measures analysis (such as repeated measures ANOVA, repeated measures ANCOVA, repeated measures MANOVA or MANCOVA…etc). In this instance, 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 average of the average change of scores for an individual in your sample.

For example, 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.

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Between-persons (or between-subjects) effects, by contrast, don't examine scores of individuals, but instead 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 ask the question: do respondents differ on their score for the 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". For more information, such as how to test for these types of effects, feel free to submit a question to our Stats Question or post to our discussion forum. If demand is great, it may even be a topic for a future video tutorial.

Editorial Note: Stats Make Me Cry is owned and operated by Jeremy J. Taylor. The site offers many free statistical resources (e.g. a blog, SPSS video tutorials, R video tutorials, and a discussion forum), as well as fee-based statistical consulting and dissertation consulting services to individuals from a variety of disciplines all over the world.

Comments

[Charlotte]

Thanks for this information. found it really useful. I am working on my dissertation and this blog gave some relief to the normally boring stastics. thanks x

[Jeremy Taylor]

I'm glad I could be helpful, Charlotte. Please let me know if I can be helpful in any other way. Thanks.

[brittany]

How do the post hoc analyses of interactions differ between completely-randomized and within-subject or mixed models?

[Jeremy Taylor]

Hi Brittany,

Thanks for your question. However, I'm not sure I completely understand what you mean by "completely-randomized" model. Do you mind elaborating on your question a bit?

[Slappy]

Completely-randomized for all intents and purposes is the same at between-subjects.

[J]

I think slappy means if you just treat everyone as one big sample, without any stratification or further identification. In this case, yes, you'd be measuring between-subjects

[Jeremy Taylor]

J,
It is possible for an IV and a moderator to be significantly correlated with each other, but if it is HIGHLY correlated, it is less likely to find significant moderation.

Think of it this way: a moderator predicts the magnitude of association between two other variables (IV and DV). HOWEVER, if a moderator and IV are too highly correlated, then the strength of the association between the IV and DV would essentially vary as a function of the IV itself (in which case there likely is not a true linear association to moderate). Does that make sense?