It’s really easy to mix up the concepts of association (as measured by correlation) and interaction. Or to assume if two variables interact, they must be associated. But it’s not actually true.
In statistics, they have different implications for the relationships among your variables. This is especially true when the variables you’re talking about are predictors in a regression or ANOVA model.
Association
Association between two variables means the values of one variable relate in some way to the values of the other. It is usually measured by correlation for two continuous variables and by cross tabulation and a Chi-square test for two categorical variables.
Unfortunately, there is no nice, descriptive measure for association between one (more…)
In the world of data analysis, there’s not always one clearly appropriate statistical analysis for every research question.
There are so many issues to take into account. They include the research question to be answered, the measurement of the variables, the study design, data limitations and issues, the audience, practical constraints like software availability, and the purpose of the data analysis.
So what do you do when a reviewer rejects your choice of data analysis? This reviewer can be your boss, your dissertation committee, a co-author, or journal reviewer or editor.
What do you do?
There are ultimately only two choices: You can redo the analysis their way. Or you can fight for your analysis. How do you choose?
The one absolute in this choice is that you have to honor the integrity of your data analysis and yourself.
Do not be persuaded to do an analysis that will produce inaccurate or misleading results, especially when readers will actually make decisions based on these results. (If no one will ever read your report, this is less crucial).
But even within that absolute, there are often choices. Keep in mind the two goals in data analysis:
- The analysis needs to accurately reflect the limits of the design and the data, while still answering the research question.
- The analysis needs to communicate the results to the audience.
When to fight for your analysis
So first and foremost, if your reviewer is asking you to do an analysis that does not appropriately take into account the design or the variables, you need to fight.
For example, a few years ago I worked with a researcher who had a study with repeated measurements on the same individuals. It had a small sample size and an unequal number of observations on each individual.
It was clear that to take into account the design and the unbalanced data, the appropriate analysis was a linear mixed model.
The researcher’s co-author questioned the use of the linear mixed model, mainly because he wasn’t familiar with it. He thought the researcher was attempting something fishy. His suggestion was to use an ad hoc technique of averaging over the multiple observations for each subject.
This was a situation where fighting was worth it.
Unnecessarily simplifying the analysis to please people who were unfamiliar with an appropriate method was not an option. The simpler model would have violated assumptions.
This was particularly important because the research was being submitted to a high-level journal.
So it was the researcher’s job to educate not only his coauthor, but the readers, in the form of explaining the analysis and its advantages, with citations, right in the paper.
When to Jump through Hoops
In contrast, sometimes the reviewer is not really asking for a completely different analysis. They just want a different way of running the same analysis or reporting different specific statistics.
For example a simple confirmatory factor analysis can be run in standard statistical software like SAS, SPSS, or Stata using a factor analysis command. Or it can be run it in structural equation modeling software like Amos or MPlus or using an SEM command in standard software.
The analysis is essentially the same, but the two types of software will report different statistics.
If your committee members are familiar with structural equation modeling, they probably want to see the type of statistics that structural equation modeling software will report. Running it this way has advantages.
These include overall model fit statistics like RMSEA or model chi-squares.
This is a situation where it may be easier, and produces no ill-effects, to jump through the hoop.
Running the analysis in the software they prefer won’t violate any assumptions or produce inaccurate results. This assumes you have access to that software and know how to use it.
If the reviewer can stop your research in its tracks, it may be worth it to rerun the analysis to get the statistics they want to see reported.
You do have to decide whether the cost of jumping through the hoop, in terms of time, money, and emotional energy, is worth it.
If the request is relatively minor, it usually is. If it’s a matter of rerunning every analysis you’ve done to indulge a committee member’s pickiness, it may be worth standing up for yourself and your analysis.
When you can’t talk to the reviewer
When you’re dealing with anonymous reviewers, the situation can get sticky. After all, you cannot ask them to clarify their concerns. And you have limited opportunities to explain the reasons for choosing your analysis.
It may be harder to discern if they are being overly picky, don’t understand the statistics themselves, or have a valid point.
If you choose to stand up for yourself, be well armed. Research the issue until you are absolutely confident in your approach (or until you’re convinced that you were missing something).
A few hours in the library or talking with a trusted expert is never a wasted investment. Compare that to running an unpublishable analysis to please a committee member or coauthor.
Often, the problem is actually not in the analysis you did, but in the way you explained it. It’s your job to explain why the analysis is appropriate and, if it’s unfamiliar to readers, what it does.
Rewrite that section, making it very clear. Ask someone to review it. Cite other research that uses or explains that statistical method.
Whatever you choose, be confident that you made the right decision, then move on.
Last month I did a webinar on Poisson and negative binomial models for count data. With a few hundred participants, we ran out of time to get through all the questions, so I’m answering some of them here on the blog.
This set of questions are all related to when it’s appropriate to treat count data as continuous and run the more familiar and simpler linear model.
Q: Do you have any guidelines or rules of thumb as far as how many discrete values an outcome variable can take on before it makes more sense to just treat it as continuous?
The issue usually isn’t a matter of how many values there are. (more…)
It seems every editor and her brother these days wants to see standardized effect size statistics reported in journal articles.
For ANOVAs, two of the most popular are Eta-squared and partial Eta-squared. In one way ANOVAs, they come out the same, but in more complicated models, their values, and their meanings differ.
SPSS only reports partial Eta-squared, and in earlier versions of the software it was (unfortunately) labeled Eta-squared. More recent versions have fixed the label, but still don’t offer Eta-squared as an option.
Luckily Eta-squared is very simple to calculate yourself based on the sums of squares in your ANOVA table. I’ve written another blog post with all the formulas. You can (more…)
Centering predictor variables is one of those simple but extremely useful practices that is easily overlooked.
It’s almost too simple.
Centering simply means subtracting a constant from every value of a variable. What it does is redefine the 0 point for that predictor to be whatever value you subtracted. It shifts the scale over, but retains the units.
The effect is that the slope between that predictor and the response variable doesn’t (more…)
I recently received this great question:
Question:
Hi Karen, ive purchased a lot of your material and read a lot of your pdf documents w.r.t. regression and interaction terms. Its, now, my general understanding that interaction for two or more categorical variables is best done with effects coding, and interactions cont v. categorical variables is usually handled via dummy coding. Further, i may mess this up a little but hopefully you’ll get my point and more importantly my question, i understand that
1) given a fitted line Y = b0 + b1 x1 + b2 x2 + b3 x1*x2, the interpretation for b3 is the diff of the effect of x1 on Y, when x2 changes one unit, if x1 and x2 are cont. ( also interpretation can be reversed in terms of x1 and x2). (more…)
