I am conducting a TPB based study, 1st model is using all the 3 constructs while the hierarchical regression for model 2 will include some demographic factors. From literature, a benchmark sample size of 80 would be acceptable to account for generalizability (Francis et al., 2004). Another literature suggests this formula: N > 50 + 8 m (where m represents the number of independent variables). If m= 3, therefore sample size will be 50 + (8x3)= 74 as the sample size (Tabachnick & Fiddell, 2013, p. 159).
Most of the literatures on multiple regression and TPB only takes the 3 constructs into consideration except when using an extended TPB model.
Does anyone know how I should account for this in my sample size? There are about 8 demographic factors being considered.
These rules of thumb are not suitable for sample size planning in most cases. They are based on assumptions that rarely hold in practice - about the size of effect and probably more importantly absence of collinearity between predictors. As you add in predictors you'd expect multicollinearity to increase and the effective sample size to detect effects of individual predictors to decrease and hence power to drop dramatically.
I"m not familiar with the Francis et al paper but a benchmark n of 80 just seems implausible for most regression studies in most domains.
I think you should consider doing a more detailed power analysis not relying on rules of thumb. Alternatively based the sample size justification on the actual constraints of the situation. If you have say resources to sample 100 people then in my view it's wrong to claim that you planned your sample size using a power calculation. You can still assess what effect sizes you could detect with that n.
Thank you Thom Baguley and Valérie Lederer
for your responses.Alex Thiangichu
, your response is not relevant, kindly re-direct.
Valérie Lederer
I'd disagree with this advice. These rules of thumb are not sensible in general or in this case.First, the rule of thumb is from Green (1991) not T&F (though they do cite him). This is important because Green proposes several variants and he says "Some support was obtained for a rule-of-thumb that of [ 50 + 8 m for the multiple correlation and 104 + m for the partial correlation ]."
Second these rules are predicated on a medium effect size for all predictors. This will almost never happen in practice - he does provide rules for other effect sizes but it makes more sense to do an actual power calculation in my view.
Three, the medium effect size for the partial correlation coefficient (i.e., the semi-partial regression coefficient) assumes implicitly zero collinearity. This is next to impossible and particularly as you add variables including demographics. Even if the simple correlation is "medium" in size once you partial out the contribution of other predictors it will be smaller - often much smaller.
Green, S. B. (1991). How many subjects does it take to do a regression analysis? Multivariate Behavioral Research, 26, 499‐510.
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