Regression and anova, Applied Statistics

The first step in this case is to ensure that you are adequately clear on the General Linear Model and its relationship to both ANOVA and regression. The distinction is approximately equivalent to what Dr. Flaschner characterizes as the distinction between analysis of differences and analysis of associations. A good place to begin is:

Trochim, W. M. K. (2006). General linear model, Research Methods Knowledge Base.

As we said, in practice the distinction between the two procedures relies on the ability to categorize the criterion variable(s) as interval in nature and the predictor variables as either appropriately interval (for regression) or categorical (for ANOVA). Remember, one can always simplify a variable; reducing an interval scale to a set of categories may ease the analysis, although at a cost in information, since the total amount of variance available for analysis is reduced. But on the other hand, using dummy variables (0/1, no/yes dichotomous codes for particular categories - we discussed these in Module 1) can give the effect of restoring some of that lost analytical power. So most analyses can be framed either way.

Kathryn Cottingham and her colleagues have developed a useful guide to distinguishing between ANOVA and regression models that discusses each approach and when it seems most applicable.

It's a very practice-oriented approach.

But at the end of the day, or at least sometime in the middle of the afternoon (preferably before the start of the Cocktail Hour), we have to actually poke numbers into a computer, get numbers back, and make some sense of them. And that means picking a procedure in SPSS, following its conventions, and reporting within the framework of those conventions and the procedure, typically in the ways expected by our disciplinary peers who staff the review boards of journals and conferences. And here's the key issue: most of those peer reviewers were trained in statistics by either psychologists (who emphasized ANOVA) or sociologists (who emphasized regression) -- and heaven help you if you pick the wrong one!. However valuable the General Linear Model approach to data may be, odds are that almost any empirical business research article that you read will use either ANOVA or regression -- but not both.

Unless, of course, as is increasingly the case, that it uses Structural Equation Modeling -- which in a way punts the regression/ANOVA distinction away, but has its own set of issues concerning assumptions, limitations, sample size requirements, goodness of fit criteria, and a number of other problems -- all too often are swept under the proverbial rug by enthusiastic proponents of SEM, and both researchers and journal editors are anxious to seem trendy and methodologically up to date. But we'll defer consideration of SEM for RES610, if you choose to go there.

So here's how we'd like you to think about this problem -- with a sort of comprehensive literature review. This will entail a bit of a search on your part. You should locate a sample of perhaps five (plus or minus two) empirical research articles (that is, any articles that reported research requiring a statistical analysis of any sort) from respectable academic journals. These may be articles that relate to a topic that you're interested in, articles that you find during a systematic search, or articles that you read during RES600, ORG601 and/or ORG602 and/or any other courses that you had either here at Trident University or elsewhere), or any combination thereof. Ideally, they should represent a mix of the search strategies and statistical techniques; you'll have a more informative exercise, the more varied they are. Once you've identified your sample, you should look through them briefly; you don't need to perform a detailed analysis, but you should at least understand what's being done and why. The next step is to make a brief tabulation of the nature of the research questions being asked, the data employed, and the nature of the analysis being applied to the data toward their solution. Here is a brief illustration:


Research Question(s)


Analytical techniques

Kraut, Robert and others (1998) Internet Paradox: A Social Technology That Reduces Social Involvement and Psychological Well-Being? American Psychologist 53(9):1017-1031

Does the use of the Internet reduce amount of non-electronic social contact experienced by users?

longitudinal survey of households -- pre Internet and post Internet -- self-reports of social involvement, automatic recording of Internet use

regression - beta as test statistic -- use of dummy variables to encode categories

Case assignment expectations

This case assignment will help you better understand how to summarize the literature relevant to a specific topic in a succinct way. This practice is usually the first step to integrate the literature for a research project. Usually the number of articles increases as the literature review goes in depth. Therefore, it is a good practice to organize the relevant articles in tables to help you quickly refer to the appropriate articles.

As noted, a critique is a review and commentary on a particular article or piece of research. It is not necessarily critical in the negative sense, although you may need to comment negatively on some aspects; both positive and negative aspects should be treated. Just because something appears in print, even in an A-list journal, does not make it free from possible errors or beyond criticism; nothing should be necessarily taken at face value. Your informed commentary and analysis is as important as your summary of the material in the article -- simply repeating what the article says does not constitute an adequate critique. You are also expected to use the terminology of path analysis and regression correctly and clearly.

In this case, your critique should address at least the following issues, as well as any other points that you find relevant and worthy of comment:

  1. The degree to which the data and analyses in these studies systematically relate to the research questions being asked
  2. The correspondence between the data and the analyses suggested by Cottinghamet al. (2003).
  3. The reasons why regression and ANOVA continue to be described as largely separate models in most statistics texts and used as largely separate analysis procedures with a number of different formatting arrangements and even different reported coefficients in most statistical packages, including SPSS
  4. The difference between effect size and statistical significance, which we have touched on in earlier modules as well (note that there are somewhat different effect size coefficients for ANOVA and regression, although they can both be standardized to a measure like Cohen's d).
  5. How research courses such as this should approach the difference (if any) between the two procedures, and any suggestions you can make about ways in which the overall teaching of the general linear model could be improved to make it more comprehensible to you, and presumably to others.
  6. On the basis of your reading and observations and experience to date, which techniques are best adapted to the kinds of research questions with which you may be concerned when you approach your dissertation? Why?

Remember, this is an applied statistics course. Thus, explaining the statistical tools, interpreting coefficients, and understanding the properties of the data analysis are particularly important, and need your careful thought and comment, not just general or generic observations.

Posted Date: 2/22/2013 2:23:36 AM | Location : United States

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