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In the presence of skewed data distributions, one or another of the commonly used data transformations (square-root, log10, or reciprocal) can help to normalize the data. Any of the texts by Tabachnick & Fidell are a good source of information about score transformations. Of course the transformed scores take on different numerical values than the original scores, sometimes even resulting in score reflection--the lowest original scores become the highest transformed scores and the highest original scores become the lowest transformed scores. Reflected scores can be (and should be) re-reflected (again, see Tabachnick and Fidell, 2013) to solve that problem, but nothing will change the fact that the transformed scores will still take on different values than the original scores. This can be vexing in some applications. For instance, where the mean of a set of original IQ score might have a value of 100 and be perfectly interpretable ("average"), the transformed mean might be 10, not a directly meaningful value. One should not make too much of these changed values, though. Assuming that one has re-reflected reflected scores, high transformed scores still reflect greater amounts of the attribute and low transformed scores still reflect lessor amounts of the attribute. This is a point that is missed by some, who make far too much of the fact that transformed scores take on different numerical values than the original scores, to the point that they believe that the transformed scores no longer measure the same construct that was measured by the original scores. The quickest way to dispell this misimpression is to examine the correlation between original and transformed scores. That correlation typically runs in the upper 0.90's. It is axiomatic in statistics that, to the extent that two variables are correlated, they measure the same thing. Data transformations do not change the construct being measured; just the score values and the shape of the distribution of the scores.

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The "causal-comparative" design so popular in education DOES NOT ESTABLISH CAUSE-AND-EFFECT!

I was called upon the other day to write an argument to convince a dissertation committee chair of something I’d always assumed everyone knew: One can’t claim that a non-manipulated Independent Variable exerts a causal impact on a Dependent Variable. Only when the researcher randomly assigns cases to the Experimental and Control groups can one draw causal conclusions.

The causal-comparative design looks on its face very much like a simple experiment. To use Campbell and Stanley’s (1963) method of designation:

Treatment Group: X O
Comparison Group: O

What makes it a quasi-experimental design rather than a true experiment, is the absence of random assignment of cases to groups.

Suppose that one wished to evaluate the effectiveness of meditation in reducing trait anxiety. Using the causal-comparative approach, you’d identify a group of people who practiced meditation (the treatment X being evaluated) and a group of people who don’t practice meditation and then see if their scores on a trait anxiety measure O differ significantly.

Suppose that meditators are found to be significantly less anxious than nonmeditators. Would this indicate that it was their practice of meditation that caused this lowered anxiety? NO! It’s just as likely that people are already low in anxiety are drawn to meditation and that people who are high in anxiety are too jittery to sit still long enough to meditate! In other words, it is just as likely that people’s preexisting stress levels caused them to choose or shun meditation as it is that meditation caused lower levels of anxiety.

If the causal-comparative design does not establish that the IV and DV are causally related, what does it establish? Only that the IV and DV are correlated. Only a true experiment, with experimenter-controlled random assignment of cases to the meditation and control groups would provide a logical basis for drawing causal conclusions about meditation (or any other treatment whose effects are being evaluated.)

I'm happy to work with students at any stage of their research, whether it's at the proposal stage in selecting a design that really addresses the intended research questions, or later in the analysis of data. Please visit my website, http://www.DissertationStatsHelper.com for more details.

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