3.2 Measurement: Fundamentals

  • (Target) Population: Students at the university of Mannheim
  • Sample: Students in this classroom
  • Concept: Income
  • Measure: “How high is your income?”
    • Answer options are “> 800 Euro” (high) and “< 500 Euro” (low)
  • Variable: ..has values, e.g. 0 = “low” and 1 = “high”
  • Measurement process: Assign/group individuals to values of variable
    • Idea: Each value represents a cell
  • Data: Observations of individuals/units, grouped according to values (cells)
  • Q: What is the problem with the our income measure/question and answer scale?
  • Q: What is measurement error (think of true value)? Example?
  • Terminology: Unit vs. observation vs. unit of analysis10

Notes

Measurement is fundamental to any descriptive or causal research question. And we need to set down (and repeat) a few terms that we will use in our discussions. Doing research we normally have a population of interest that is the population we would like to learn about. Sometimes this population is also called target population. Let’s assume for now that our target population are students of the university of Mannheim. Unfortunately, we don’t have access to the entire population, however, we have easy access to a sample namely the students in this classroom (if you are not in a classroom simply imagine that you are). Subsequently, we are interested in income a phenomenon that we define and subsequently measure in a certain way. For instance, through the question “How high is your income?” and we provide respondents with two answer options “> 800 Euro (high)” and “< 500 Euro (low)”. The corresponding variable that we would probably call “income” contains the values that we assign to those categories, in our case 0 = “low” and 1 = “high”.
The terms concept, measure and variable help us determining what the actual measurement process involves. It involves observing individuals (getting observations) and assigning individuals to (grouping them into) values of that variable. Importantly, the measurement process occurs after we have decided how our concept should be defined and what measure we want to use for it. Our sample of observations then consists of individuals that we have grouped into/assigned to values of our variable (or several variables).

What can go wrong in this process? A first challenge concerns the translation of the concept into our measure. For instance, someone could argue that a simple 2-point scale (high, low) does the - more fine-grained - concept of income no justice. Importantly, the way we translate a concept into a measure has important implications for what kind of variation we find with this measure. Sometimes we may fail to register any meaningful variation because of unhelpful choices we made in this step.
A second challenge may concern measurement error namely the fact that we might missclassify our individuals and assign them to the wrong values of our variable. For instance, you could look around you and try to classify your fellow students in high income (above 800) and low income students (below 500) but there is some probability that they end up in the wrong category, i.e., are assigned the wrong value (What could be the reason for such measurment error?).

Now in applied causal research we encounter these problems quite often. For instance, taking our victimization example, it could be that some of the victims we spoke about did not answer truthfully and are assigned to the wrong group (the group of non-victims). The consequences are quite clear (they probably pull down the trust level of our group of apparent non-victims).

There are some additional relevant concepts that we will use later on. Unit normally describes the entity we are interested in, e.g., a particular individual Peter. Subsequently, we observe this unit, e.g., we measure Peter’s income at t = Feburary 2010, and would call this an observation. Another term you will encounter is unit of analysis which normally describes the data we enter into our statistical models. For instance, our unit could be Peter, and our units of analysis could be serveral observations of Peter’s income (every year) that we enter into a statistical model.

  1. Unit could be a particular individual Peter; Observation could be Peter’s income at t = February 2028; Unit of analysis would be the uni in our model such as i = Peter, or i = Peter*time if we have more measurement values for Peter.↩