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I have some survey data and employees are divided into grades (from 1 to 7). At first glance, this appears to be a continuous variable. However, based on my knowledge of the organization, I know that levels 5 and above are managers, while those in grades 1 to 4 are lower level employees. From this variable, I would like to create a dummy varaible to use as an independent variable in a regression model. (I have done a number of t tests on various variables and shown that there are statistically significant differences between the two groups.)

My question is this: what statistical test (if any) can I use to show that there are actually two different groups rather than 7?

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    $\begingroup$ You might try clustering, perhaps hierarchical clustering, but I'm not sure statistical testing really answers the question you're interested in. You presumably don't think that across the four and three groups within those divisions the employees are perfectly homogenous, only that the groups more alike within the two main groups than across them. Presumably those levels (grades) are ordered categories on some measure; is that right? (That may affect your analysis.) What is it you want to show they're similar on? Is there some collection of variables you wish to compare? $\endgroup$
    – Glen_b
    Commented Jun 4, 2013 at 0:37
  • $\begingroup$ @Glen_b Thanks for asking for clarification. I would like to show that treating the levels variable as either a continuous variable or a categorical variable with 7 levels is inappropriate, and that two categories (one for general employees and 1 for managers) is a more appropriate representation of the sample (that respondents in groups 1~4 answer similarly across a number of variables, while those in 5~7 are also similar to each other, but different from those in 1~4). Hierarchical clustering is a good suggestion - thanks. $\endgroup$
    – kwela12
    Commented Jun 4, 2013 at 1:05

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There are a number of things you could do. You could do plain old likelihood ratio tests or compare AIC's (a penalized likelihood ratio test). You can use these to compare models. The AIC's have the advantage of penalizing the 2 level variable for complexity over the continuous variable.

m1 <- lm(y ~ x_as_2_categories)
m2 <- lm(y ~ x_as_7_categories)
anova(m1, m2)

You might want to look at some basic papers on this sort of testing.

A critical thing to note is that the 7 levels are likely not continuous (from your description) bur rather categorical. It appears that there is no 5.4 possible.

I realize that what I've described are simple models and you say you have survey data but that description is incredibly vague and difficult to make more precise recommendations on. The general idea is still applicable, generate multiple models and see which fits better. You'll want to read on statistical model comparison.

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  • $\begingroup$ This is the right idea, but the exposition is a little flawed by accepting the OP's characterization of the seven values as "continuous." They are not: they are categorical and ordered, as is clear from the last sentence in the question. (There's no such thing as a "grade $2 \pi$" in the employee hierarchy, for instance.) $\endgroup$
    – whuber ♦
    Commented Jun 4, 2013 at 1:59
  • $\begingroup$ I wonder if you wrote that after my last edit? (times are about the same). I don't know what the categories are so I didn't comment on that strongly. Maybe there is such a thing possible as 7.5 but it's just not recorded with that resolution. For example, I might have grades in school but I could also get grade and month and make a decimal value, or to the day. The fact that my particular measurement resolution isn't very good doesn't mean the variable isn't continuous. Otherwise you can argue it for any "continous" variable. $\endgroup$
    – John
    Commented Jun 4, 2013 at 3:03
  • $\begingroup$ @John Thank you for your answer. It is very helpful. I will follow the procedures you outlined. If the AIC test favors the two-level categorical approach it will improve the overall quality of the analysis greatly. My apologies for the vagueness of the question. $\endgroup$
    – kwela12
    Commented Jun 4, 2013 at 5:33
  • $\begingroup$ John, a "grade" in this context is an ordinal classification in the employee hierarchy, not a discrete approximation to some measurement. (+1) $\endgroup$
    – whuber ♦
    Commented Jun 4, 2013 at 12:28

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