TU-L0022 - Statistical Research Methods D, Lecture, 2.11.2021-6.4.2022

One of the assumptions of classical test theory - and all the reliability indices based on that theory - is that the indicators of a scalar unidimensional measures of one construct.

So what does unidimensionality mean? Unidimensional basically means that we can meaningfully summarize the construct with a single number. So if you have multiple dimensions in the construct we need multiple numbers.

The idea is that each indicator - like in a classical test theory - they measure the same thing. The same thing is T and the indicators all capture T plus some random noise and this is the statistical model for unidimensional measurement. This is also known as the factor analysis model.

So why is unidimensionality important? Why can't you just summarize distinct things into into a single score? The reason can be understood with an example. So let's take a look at this example. We have a score defined as person's height plus person's weight and we take a sum. We call it the person's size.

So the problem is which one is bigger? The tall and skinny person or the short and fat person? We cannot really say because the concept of a big person relates to both of those concepts. You can say that a person is big if they're tall or they're big if they are just heavy. And let's also say my size is about 250 using this score. So what does it really tell about me?

I could be a tall and a skinny person. If we want to study whether I'm a good athlete or not, being tall and skinny or being short and fat, they probably have different performance consequences. If I'm tall and skinny I could be a good long distance runner. If I'm short and fat I could be a good in sports that require strength, for example.

So there are, these are two different kinds of people. We cannot say that these are equivalent. The idea of unidimensionality and unidimensional scale is that we can summarize all relevant information about the construct being studied with one number.

With person's size we need two numbers. We need at least two numbers: height and weight. We can also have shoe size and whatever but the height and weight are the two most important ones. Why is this important? It is because if we try to theorize the causes or consequences of person's size score, the causes and consequences of being heavy and being tall are different.

So for example if I would go to a try-out in a basketball team the coach would say that I'm too small for basketball. My size is 250, then the average size of a person in the team is 300. So I'm too small. So how do I make myself larger? I could eat more in which case my size will become a bigger. I would be a fat person and I still would make it in a team because the others would be tall and skinny in the team or anyway tall.

The same thing we can influence only one of those. So if you're saying that you have a cause of person's size then at least for the adult population the only way you can influence your size is by changing your weight by eating more and exercising less. So these concepts of height and weight are distinct dimensions of the higher level concept of person's size. It doesn't make any sense to take a sum of those.

This is relevant for business research because you oftentimes see construct such as entrepreneurial orientation which is defined as three main dimensions of innovativeness, proactiveness and risk-taking. You have product mix called marketing mix consisting of product, price, place and promotion and then you measure each of those dimensions separately. Sometimes researchers still generate one score that is supposed to summarize those dimensions. That makes as much sense as summarizing person's size as the sum of height and weight.