When conducting a simple linear regression analysis with one categorical predictor variable and power projected at .80, G*Power suggests a minimum sample size of n = 55. Now, assume that the predictor has three categories, and that I obtain 55 necessary responses. What does it mean for the regression analysis if the number of observations in each category is distributed as something like 5, 10, and 40? That is, 5 observations in category #1, 10 in cat #2 and 40 in cat #3. Or consider a binary predictor variable with 5 in cat #1 and 50 in cat #2?
I have achieved the minimum sample size projection, but do I have enuf data across the categories? Is there a minimum number per category that I should be looking for?
Thanx!
hb
It depends on the variance of the error term. The higher the variance the more cases are needed. Generally, some books say you need to have 4*n cases, where n - the number of IVs. But, as said above, it depends.
You can answer if it's enuf or not enuf only by conducting a small Monte-Carlo experiment. Try generating some datasets that resemble your cases and then apply the linear regression and it will show you how diffuse the estimates are.
It depends on the variance of the error term. The higher the variance the more cases are needed. Generally, some books say you need to have 4*n cases, where n - the number of IVs. But, as said above, it depends.
You can answer if it's enuf or not enuf only by conducting a small Monte-Carlo experiment. Try generating some datasets that resemble your cases and then apply the linear regression and it will show you how diffuse the estimates are.
Dear Howard,
Please note that the fact that your single predictor variable is not continuous makes a simple linear regression model inappropriate to use. By virtue of the term "linear", the condition/assumption of linearity needs to be satisfied in testing the relationship between the dependent and predictor variables - as per the following key assumptions of classical linear regression (CLR)-:
(a). Linearity in parameters - the relationship between the independent variable(s) and the mean of the explained variable must be linear.
(b). Homoscedasticity - the variance of the residual is the same for any value of the independent variable.
(c). Independence of observations – sample observations are independent of each other.
(d). Normality - for any fixed value of a given independent variable, the dependent variable should be normally distributed.
Howard - Is the measurement level of your dependent variable continous?
I assume you are wanting to do a model like
y_i = B_0 + B_1 D1_i + B_2 D2_i + e_i,
where the Ds are dummy variables for two of the groups and you minimize the sum of e_i^2, so an ANOVA. The issue here is that the assumption is that the allocation to groups is fixed. So like with an experiment. It sounds like in your case both the number of people in the different groups and your outcome variable are not. Is this true?
If the measurement level of your independent variable is continuous, with a categorical independent variable having at least three (3) mutually exclusive groups, then the nature of such can best be analysed by testing for mean differences of the dependent variable across groups. The suitable statistical method in that regard is the Analysis of Variance (ANOVA) – a parametric test which compares means of three or more independent groups to assess whether there is statistical evidence that population means are significantly different. Application of ANOVA requires fulfillment of the following assumptions:
(a). Dependent variable must br continuous (interval or ratio level).
(b). Independent variable must divide cases into three or more mutually exclusive groups.
(c). Independent samples or groups (independence of observations)
(d). There is no relationship between the subjects in each sample.
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