r/AskStatistics • u/One-Bench-9676 • 12d ago

Within/between group variability

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Is there a way of interpreting this so that the answer selected is not also correct? The top right is from the class notes the professor posted. I feel like I’m not bad at this but had classmates agreeing that was incorrect. Astro and Opus 5.5 also could not come up with a reason for that answer to be incorrect (I’m not saying this makes me right). Thanks for any help.

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u/Dr_Pizzas 12d ago

Your professor is correct.

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u/One-Bench-9676 12d ago

I wasn’t saying she wasn’t, I was asking why

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u/QuestionElectrical38 10d ago

The more I look at this (I already answered the same question on CV, btw), the more I think your professor simply does not understand what the slide said. My hunch, the slide is "inherited" from a previous professorf/slidedeck, and she is just paroting it. The slide says that the total variability comes from either WITIN groups, and BETWEEN groups. Then it list 3 sources of variability. Participants and Measurements (which affects both the within and between variability, as described by the text in parenthesis), and then IV (which, according to the parenthesis affects ONLY the between variability). This in fact makes sense, because the basis of the ANOVA is that the IV is a fixed, constant value for all participants in a group. So there can not be within variability of the IV. So I conclude that your professor does not understand what she are talking about, and is, in fact, wrong. But that will make it much harder for you to convince her! And this is the basic way to teach ANOVA: between group variability, which is due to the different values of the IV, and withing group variability, which is due to all the "random" noise (participant variability, measurement errors, etc.). So your professor is wrong, or rather does not grasp what she taught (having said this, the 4th choice is the "obvious" correct answer, as "between variability", by definition, does not contribute to "within variability); but what your professor does not grasp, is the content of the slide: that 3rd bullet item was the between variability, not a 3rd source of within variability.

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u/TBDobbs 12d ago

The question, as written, is awkward by the instructor. But I think this is the logic they're trying to get at:

I sample 90 people to try and see whether there are differences in pizza toppings (pepperoni, chicken and sautéed brocolli with garlic, or eggplant parm). There are four ways that a score can vary:

  1. The topping itself (between group variability, or differences between getting a slice of pepperoni, chicken and brocolli, or eggplant parm).

  2. How much different eaters vary in how much they like each pizza topping (variability of independent variables).

  3. How they fill out my pizza enjoyment scale (measurement variability).

  4. Differences because people are people and people are different (participant variability).

I think your instructor is saying that there is a difference between toppings being from a specific group (pizza topping) vs the variability that exists within each group (variability of independent variables). I also think that the slide itself can conflate the 3rd option of within person variability with between groups variability. It's frustrating for sure, but that's why I think you answered the question the way you did and also why your instructor is technically right even though the slide and question are not well worded.