3.6 Measurement: Exercise

  1. The most well known classification for levels of measurement, i.e. a “classification that describes the nature of information within the values assigned to variables” (Wikipedia) was provided by Stevens (1946). Please read the wikipedia article and summarize the classification. Also read the rest of the article.
  2. Above we argued that the variable education measured on a discrete scale with 11 values, can be conceptualized has having 11 cells to which we assign individuals as we measure their level of education. How many cells does a continuous variable have, e.g., think of height, weight or temperature?
  3. What are the object classes in R that correspond to the classification, e.g., by Stevens (1946) (nominal, ordinal, interval and ratio scales)?
  4. What is the variable time from a data perspective?
  5. Above we suggested that measurement can be conceptualized as assigning units, e.g., individuals, to values of a variable. Measurement error corresponds to mistakes in this assignment process. Take the data below…
    1. Let’s assume that you are interested in the mean of education. Calculate it!
    2. Peter’s and Fabrizio’s score are off by +2 (the true values are lower). How would you calculate the mean?
    3. Simone’s and Julia’s score contain error but you don’t know how much. How would you deal with that?
Unit Education (0-11)
Simone 2
Julia 5
Paul 2
Peter 4
Fabrizio 8
Diego 4

Notes

  • Lessons to be learned
    1. Something as fundamental as Steven’s 4 measurement levels was invented at some point
    2. Continuous variables…
    3. Statistical programming languages such as R are often linked to statistical theory
    4. Time seems different, but is just another variable/dimension
    5. Most robustness tests involve simple modification of the underlying data

References

Stevens, S S. 1946. “On the Theory of Scales of Measurement.” Science 103 (2684): 677–80.