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I have a dataset that comprises 200 males and 250 females and I am testing their responses on the relationship between X and Y.

X and Y are continuous and X1 (gender) is categorical.

I am using the general linear model in SPSS to test for main effects and interaction.

As I understand it, this is an 'unbalanced' design because the size of the two groups (males and females) are not the same.

Questions

  1. Is using Sum of Squares (Type III) appropriate in this case?
  2. What alternatives do I have to analyse this data?
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  1. Regression models allow you to borrow information explicitly across groups defined by your predictors. Having balanced design only means that all such groups have effects estimated with equal precision (under regression assumptions: correct mean model, homoskedasticity). This is rarely, if ever, necessary for justifying a statistical model. Traditionally, balanced design is considered for two reasons: to assess whether randomization was truly random in clinical trials and to demonstrate differences between certain study designs and simple random samples. In fact, it's frequently the case that unbalanced designs are more valid and more efficient, provided researchers have adhered to their sampling protocol. To clarify on the SSIII point, this is basically the F-test for the main effects which is a sensible test.

  2. Assuming you're using the linear link in your GLM for continuous outcomes, there are alternatives. However, I feel your current methods seems solid, barring any egregious difficulties in the data of which I'm not aware. A sort of traditional consideration with continuous data is whether a transformation is necessary, such as a logarithmic transform. This would be a choice if you're interested in estimating a "ratio" of Y differences for a unit difference in X (i.e. subjects had 2x the 'Y' among those differing by 1 'X') using a base-2 log transform. There are also rank statistics which I find difficult to interpret, but could be a sensitivity analysis for data which is heavily skewed.

An aside: If you're presenting this data in a "Table 1" I would advise against displaying p-values for balance. It's likely to mislead reviewers and/or readers who think your design depends on such characteristics. You need only be explicit about your sampling methodology, and this model otherwise sounds like a valid approach.

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The normal GLM methods work just fine on unbalanced designs (provided you aren't using expressions that are simplified for the balanced case --- decent software will work right). Unbalanced designs just have less power than balanced designs, but 250 vs 200 isn't going to have that much of an effect.

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    $\begingroup$ I don't believe unbalanced designs have less power, especially since the poster is interested in interaction. Suppose the effect is much stronger in one group which is naturally "over expressed" in the population. By oversampling the under-represented group who have a smaller effect size, the test of association has less power. Take muscle mass before and after enlistment in the army, stratified by gender, as an example. $\endgroup$ – AdamO Dec 28 '11 at 18:23
  • $\begingroup$ You're right. I was implicitly assuming that he was dealing with homoskedastic data, which was unfounded of me. However, the standard GLM techniques will still be fine. $\endgroup$ – user873 Dec 29 '11 at 2:20

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