The first real data set I ever analyzed was from my senior honors thesis as an undergraduate psychology major. I had taken both intro stats and an ANOVA class, and I applied all my new skills with gusto, analyzing every which way.
It wasn’t too many years into graduate school that I realized that these data analyses were a bit haphazard and not at all well thought out. 20 years of data analysis experience later and I realized that’s just a symptom of being an inexperienced data analyst.
But even experienced data analysts can get off track, especially with large data sets with many variables. It’s just so easy to try one thing, then another, and pretty soon you’ve spent weeks getting nowhere.
I recently had this question in consulting:
I’ve got 12 out of 645 cases with Mahalanobis’s Distances above the critical value, so I removed them and reran the analysis, only to find that another 10 cases were now outside the value. I removed these, and another 10 appeared, and so on until I have removed over 100 cases from my analysis! Surely this can’t be right!?! Do you know any way around this? It is really slowing down my analysis and I have no idea how to sort this out!!
And this was my response:
I wrote an article about dropping outliers. As you’ll see, you can’t just drop outliers without a REALLY good reason. Being influential is not in itself a good enough reason to drop data.
Should you drop outliers? Outliers are one of those statistical issues that everyone knows about, but most people aren’t sure how to deal with. Most parametric statistics, like means, standard deviations, and correlations, and every statistic based on these, are highly sensitive to outliers.
And since the assumptions of common statistical procedures, like linear regression and ANOVA, are also based on these statistics, outliers can really mess up your analysis.
Despite all this, as much as you’d like to, it is NOT acceptable to drop an observation just because it is an outlier. They can be legitimate observations and are sometimes the most interesting ones. It’s important to investigate the nature of the outlier before deciding.
- If it is obvious that the outlier is due to incorrectly entered or measured data, you should drop the outlier:
For example, I once analyzed a data set in which a woman’s weight was recorded as 19 lbs. I knew that was physically impossible. Her true weight was probably 91, 119, or 190 lbs, but since I didn’t know which one, I dropped the outlier.
This also applies to a situation in which you know the datum did not accurately measure what you intended. For example, if you are testing people’s reaction times to an event, but you saw that the participant is not paying attention and randomly hitting the response key, you know it is not an accurate measurement.
- If the outlier does not change the results but does affect assumptions, you may drop the outlier. But note that in a footnote of your paper.
Neither the presence nor absence of the outlier in the graph below would change the regression line:
- More commonly, the outlier affects both results and assumptions. In this situation, it is not legitimate to simply drop the outlier. You may run the analysis both with and without it, but you should state in at least a footnote the dropping of any such data points and how the results changed.
- If the outlier creates a strong association, you should drop the outlier and should not report any association from your analysis.
In the following graph, the relationship between X and Y is clearly created by the outlier. Without it, there is no relationship between X and Y, so the regression coefficient does not truly describe the effect of X on Y.
So in those cases where you shouldn’t drop the outlier, what do you do?
One option is to try a transformation. Square root and log transformations both pull in high numbers. This can make assumptions work better if the outlier is a dependent variable and can reduce the impact of a single point if the outlier is an independent variable.
Another option is to try a different model. This should be done with caution, but it may be that a non-linear model fits better. For example, in example 3, perhaps an exponential curve fits the data with the outlier intact.
Whichever approach you take, you need to know your data and your research area well. Try different approaches, and see which make theoretical sense.