Scales of measurement Flashcards
What is a measurement?
Measurements can be defined as a process where we limit data to be collected from a given phenomenon in such a way as to enable interpretation, and ultimately comparisons to a particular quantitative or qualitative standard. When dividing the data into categories, we are scaling the measurements. The scales used ultimately dictate the statistical procedures we can use when processing numerical data.
What is the Nominal scale?
The nominal scale is the easiest way to scale measures. Here we measure data by assigning names or divide into discrete categories. Using the categories girls and boys is nominal scaling. There are some issues however with nominal scaling. When processing numerical data, we must assign a number to each such discrete category. If girls are 1, and boys are 2, we get a situation where we can interpret boys to be more than girls which, fundamentally, makes little sense. The statistical procedures we can use for nominal scales are mode, percentage, and chi-square test. So, you can perform some statistics but not a great deal.
What is the Ordinal scale?
A better scaling technique is ordinal scaling. Here we can rank data as more/higher or less/lower. Instead of considering how many years people went to school we can instead consider their highest level of education (secondary school, high school, undergraduate, or graduate school). This makes more sense than simply considering the total years of education as the differences between each step up in education level probably differs, thus, simply considering the total number of years will provide less accuracy. Ordinal scaling enables statistical procedures such as median, percentile rank, and spearman’s rank order. The ordinal scale is useful for surveys where you perform calculations on a Likert scale, e.g., agree, somewhat agree, neutral, etc.
What is the Interval scale?
Interval scales uses equal units of measurement with an arbitrarily established zero point. Temperature measured in Celsius is carried out on an interval scale. Here we have an established zero point, and an increase from 10 to 20, is the same as an increase from 20 to 30. Consequently, there is no need to divide different values into separate categories as seen in ordinal scaling. Interval scales enable several statistical procedures like means, standard deviations, and Pearson product moment correlations.
What is the Ratio scale?
This is the ultimate scale. Like interval scales there are equal measurement units, however, there is an absolute zero where 0 means a total absence of the quality being measured, take distance as an example. Ratio scales can be express values in terms of fractions and multiplies.
How does the different scales compare?
Nominal scales only manage to say that one object is different from another. This only enables a limited set of statistical procedures for analysis. The higher order of measurement is the ordinal scale where we separate objects based on some attribute (more/higher or less/lower). Ordinal scales enable more statistical procedures but is still quite limited. Interval scales uses equal measures and an arbitrary point of zero. Here we have several statistical tools available. Finally, the highest order is the ratio scale. The main difference from the interval scale is the presence of an absolute zero. This enables us to express values in terms of fractions and multiples. Researchers will not always manage to move all variables to ratio or interval scale. However, they should always try to move them to the highest order possible.
