German Exercise Materials for Methods I

Example: Levels of Measurement

Let’s take levels of measurement as an example. In Bortz’s classic, formal axioms are defined for levels of measurement, but there are no exercises. In more intuitively oriented books (e.g., Bühner and Ziegler, BZ or Sedlmeier and Renkewitz, SR), levels of measurement are explained with some catchy examples. But again, there are no exercises. In both books, you can only access the exercises by registering on the Pearson website. In both cases, after registering, I get the following message:

“Please note that teaching materials are exclusively reserved for registered instructors and teachers. You cannot access these materials.”

For SR, there are no exercises in the new edition. The exercises from the old edition can only be accessed awkwardly via https://www.pearson.de/studium/produkte/extras-online/dlm by entering the ISBN. There are 6 exercises for levels of measurement.

Unfortunately, I cannot find the promised exercises for BZ.

Both books are excellent for getting into a topic, but without exercises, you don’t really know what you know and what you don’t.

In my experience, you need to work through at least a dozen examples to fully understand levels of measurement. My workbook currently contains 18 examples, plus 3 tasks on permitted transformations. Of course, with solutions.

Do you know what the level of measurement is in the following case?

Healthy (=1), Neurotics (=2), Psychotics (=3)

Watch out, there are two possible solutions!

Detailed Solutions

Aren’t you also annoyed by books that contain exercises but no solutions? How are you supposed to check if you’re correct?

In my workbook, every task is solved model-like, just as I would mark them as correct in an exam.

Some particularly difficult tasks are explained in detail, with references to other sources.

Do you know the solution to this task?

In a study by Greeley (1994), the infidelity rate of men in the USA was estimated at 21% with a 95% confidence interval from 0.18 to 0.24. Why would it be wrong to say that the true value (the proportion of infidelity rate among men in the population) is within the given interval with a probability of 95%?

This cannot be answered in one sentence, although many instructors do. They simply say that the true value is either within the interval or not, so you cannot make a probability statement about it. But what does that mean? In my solution, I refer to three hot discussions on Stackexchange about this very question. At the same time, I try to give a concise answer: if you conduct a frequentist thought experiment for calculating confidence intervals, you will notice that the true value is a constant and must also be known. The true value is not a random variable, so a probability statement is not possible. In the case of the example above, we must assume for the calculation of a confidence interval that the true value in the population is 21%. If I make 100 confidence intervals, the true value always remains at 21%. The probability thus refers to the intervals, the true value is always the same.

The statement that the true value is within the interval with a certain probability would mean that the interval is kept constant (from 18% to 24%), but the true value changes. That is, of course, nonsense in this context and therefore the statement is not meaningful. However, in the solution, I refer to another procedure that makes such statements possible, but which has other problems (Bayesian statistics).

Free License

The workbook is published under a free license (CC-BY-SA). This means that anyone can use, modify, and redistribute the exercises as long as the license is not changed and the booklet is correctly cited. This facilitates collaboration between instructors.

Regular Updates

There is at least one update of the workbook every year because I use it in my own teaching. Improvements are incorporated, and new tasks are always added.