The linear model normality assumption, along with constant variance assumption, is quite robust to departures. That means that even if the 
assumptions aren’t met perfectly, the resulting p-values and confidence intervals will still be reasonable estimates.
This is great because it gives you a bit of leeway to run linear models, which are intuitive and (relatively) straightforward. This is true for both linear regression and ANOVA.
You do need to check the assumptions anyway, though. You can’t just claim robustness and not check. Why? Because some departures are so far off that the p-values and confidence intervals 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 (more…)
When your dependent variable is not continuous, unbounded, and measured on 
an interval or ratio scale, linear models don’t fit. The data just will not meet the assumptions of linear models. But there’s good news, other models exist for many types of dependent variables.
Today I’m going to go into more detail about 6 common types of dependent variables that are either discrete, bounded, or measured on a nominal or ordinal scale and the tests that work for them instead. Some are all of these.
(more…)
You probably learned about the four levels of measurement in your very first statistics class: nominal, ordinal, interval, and ratio.
Knowing the level of measurement of a variable is crucial when working out how to analyze the variable. Failing to correctly match the statistical method to a variable’s level of measurement leads either to nonsense or to misleading results.
But the simple framework of the four levels is too simplistic in most real-world data analysis situations.
(more…)
Principal Component Analysis is really, really useful.
You use it to create a single index variable from a set of correlated variables.
In fact, the very first step in Principal Component Analysis is to create a correlation matrix (a.k.a., a table of bivariate correlations). The rest of the analysis is based on this correlation matrix.
You don’t usually see this step — it happens behind the scenes in your software.
Most PCA procedures calculate that first step using only one type of correlations: Pearson.
And that can be a problem. Pearson correlations assume all variables are normally distributed. That means they have to be truly (more…)
There are not a lot of statistical methods designed just for ordinal variables.
But that doesn’t mean that you’re stuck with few options. There are more than you’d think. (more…)
There are many types and examples of ordinal variables: percentiles, ranks, likert scale items, to name a few.
These are especially hard to know how to analyze–some people treat them as numerical, others emphatically say not to. Everyone agrees nonparametric tests work, but these are limited to testing only simple hypotheses and designs. So what do you do if you want to test something more elaborate?
In this webinar we’re going to lay out all the options and when each is (more…)
assumptions aren’t met perfectly, the resulting p-values and confidence intervals will still be reasonable estimates.