The Analysis Factor
Statistical Consulting, Resources, and Statistics Workshops for Researchers
Effect size statistics are required by most journals and committees these days — for good reason.
They communicate just how big the effects are in your statistical results — something p-values can’t do.
But they’re only useful if you can choose the most appropriate one and if you can interpret it.
This can be hard in even simple statistical tests. But once you get into complicated models, it’s a whole new story. [Read more…] about Member Training: Interpretation of Effect Size Statistics
Statistics is, to a large extent, a science of comparison. You are trying to test whether one group is bigger, faster, or smarter than another.[Read more…] about Member Training: Equivalence Tests and Non-Inferiority
by Annette Gerritsen, Ph.D.
In an earlier article I discussed how to do a cross-tabulation in SPSS. But what if you do not have a data set with the values of the two variables of interest?
For example, if you do a critical appraisal of a published study and only have proportions and denominators.
In this article it will be demonstrated how SPSS can come up with a cross table and do a Chi-square test in both situations. And you will see that the results are exactly the same.
If you want to test if there is an association between two nominal variables, you do a Chi-square test.
In SPSS you just indicate that one variable (the independent one) should come in the row, [Read more…] about How to do a Chi-square test when you only have proportions and denominators
When your dependent variable is not continuous, unbounded, and measured on 
an interval or ratio scale, your model will not meet the assumptions of linear models.
Today I’m going to go into more detail about 6 common types of dependent variables that are not continuous, unbounded, and measured on an interval or ratio scale and the tests that work instead.
Side note: the usual advice is to use nonparametric tests when normality [Read more…] about When Dependent Variables Are Not Fit for Linear Models, Now What?
The assumptions of normality and constant variance in a linear model (both OLS regression and ANOVA) are quite robust to departures. That means that even if the assumptions aren’t met perfectly, the resulting p-values will still be reasonable estimates.
But you need to check the assumptions anyway, because some departures are so far that the p-value become inaccurate. And in many cases there are remedial measures you can take to turn non-normal residuals into normal ones.
But sometimes you can’t.
Sometimes it’s because the dependent variable just isn’t appropriate for a linear model. The [Read more…] about 6 Types of Dependent Variables that will Never Meet the Linear Model Normality Assumption
When the dependent variable in a regression model is a proportion or a percentage, it can be tricky to decide on the appropriate way to model it.
The big problem with ordinary linear regression is that the model can predict values that aren’t possible–values below 0 or above 1. But the other problem is that the relationship isn’t linear–it’s sigmoidal. A sigmoidal curve looks like a flattened S–linear in the middle, but flattened on the ends. So now what?
The simplest approach is to do a linear regression anyway. This approach can be justified only in a few situations.
1. All your data fall in the middle, linear section of the curve. This generally translates to all your data being between .2 and .8 (although I’ve heard that between .3-.7 is better). If this holds, you don’t have to worry about the two objections. You do have a linear relationship, and you won’t get predicted values much beyond those values–certainly not beyond 0 or 1.
2. It is a really complicated model that would be much harder to model another way. If you can assume a linear model, it will be much easier to do, say, a complicated mixed model or a structural equation model. If it’s just a single multiple regression, however, you should look into one of the other methods.
A second approach is to treat the proportion as a binary response then run a logistic or probit regression. This will only work if the proportion can be thought of and you have the data for the number of successes and the total number of trials. For example, the proportion of land area covered with a certain species of plant would be hard to think of this way, but the proportion of correct answers on a 20-answer assessment would.
The third approach is to treat it the proportion as a censored continuous variable. The censoring means that you don’t have information below 0 or above 1. For example, perhaps the plant would spread even more if it hadn’t run out of land. If you take this approach, you would run the model as a two-limit tobit model (Long, 1997). This approach works best if there isn’t an excessive amount of censoring (values of 0 and 1).
Reference: Long, J.S. (1997). Regression Models for Categorical and Limited Dependent Variables. Sage Publishing.