You may have heard of McNemar tests as a repeated measures version of a chi-square test of independence. This is basically true, and I wanted to show you how these two tests differ and what exactly, each one is testing.
First of all, although Chi-Square tests can be used for larger tables, McNemar tests can only be used for a 2×2 table. So we’re going to restrict the comparison to 2×2 tables. (more…)
A central concept in statistics is the level of measurement of a variable. It’s so important to everything you do with data that it’s usually taught within the first week in every intro stats class.
But even something so fundamental can be tricky once you start working with real data. (more…)
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.
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.
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:
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.
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’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.
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 off that the p-values 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…)
There are 4 questions you must answer to choose an appropriate statistical analysis.
1. What is your Research Question?
2. What is the scale of measurement of the variables used to answer the research question?
3. What is the Design? (between subjects, within subjects, etc.)
4. Are there any data issues? (missing, censored, truncated, etc.)
If you have not already, read about these in more detail.