Proportion and percentage data are tricky to analyze.
Much like count data, they look like they should work in a linear model.
They’re numerical. They’re often continuous.
And sometimes they do work. Some proportion data do look normally distributed so estimates and p-values are reasonable.
But more often they don’t. So estimates and p-values are a mess. Luckily, there are other options. (more…)
Like the chicken and the egg, there’s a question about which comes first: run a model or test assumptions? Unlike the chickens’, the model’s question has an easy answer.
There are two types of assumptions in a statistical model. Some are distributional assumptions about the residuals. Examples include independence, normality, and constant variance in a linear model.
Others are about the form of the model. They include linearity and (more…)
One common reason for running Principal Component Analysis (PCA) or Factor Analysis (FA) is variable reduction.
In other words, you may start with a 10-item scale meant to measure something like Anxiety, which is difficult to accurately measure with a single question.
You could use all 10 items as individual variables in an analysis–perhaps as predictors in a regression model.
But you’d end up with a mess.
Not only would you have trouble interpreting all those coefficients, but you’re likely to have multicollinearity problems.
And most importantly, you’re not interested in the effect of each of those individual 10 items on your (more…)
Not too long ago, I was in Syracuse for a family trip to the zoo. Syracuse is about 60 miles from where I live and it has a very nice little zoo.
This year was particularly exciting because a Trader Joe’s just opened in Syracuse. We don’t have one where we live (sadly!) so we always stock up on our favorite specialty groceries when we’re near a Trader Joe’s.
On this particular trip, though, we had an unwelcome surprise. My credit card card company believed my Trader Joe’s spree was fraudulent and declined the transaction. I got a notice on my phone and was able to fix it right away, so it wasn’t the big inconvenience it could have been.
But this led us to wonder what it was about the transaction that led the bank to believe it was fraudulent. Do credit card thieves often skip town and go grocery shopping?
The bank was clearly betting so. It must have a model for aspects of a transaction that are likely enough to be fraudulent that it shuts it down. (more…)
Effect size statistics are expected by many journal editors these days.
If you’re running an ANOVA, t-test, or linear regression model, it’s pretty straightforward which ones to report.
Things get trickier, though, once you venture into other types of models.
One of the big assumptions of linear models is that the residuals are normally distributed. This doesn’t mean that Y, the response variable, has to also be normally distributed, but it does have to be continuous, unbounded and measured on an interval or ratio scale.
Unfortunately, categorical response variables are none of these.