Scales of measurement
Scales of measurement
Table 1: Results of a vocabulary test among 10 students
Name | number of correct items | percentage of correct items | rank | mark | pass |
John | 20 | 1 | 1 | 1 | yes |
Peter | 19 | 0.95 | 2 | 2 + | yes |
Ellis | 15 | 0.75 | 3 | 3 | yes |
Sara | 14 | 0.7 | 4 | 3 | yes |
Martin | 13 | 0.65 | 5 | 3 - | yes |
Matty | 12 | 0.6 | 6 | 4 | yes |
Eve | 12 | 0.6 | 6 | 4 | yes |
Nancy | 10 | 0.5 | 7 | 5 | no |
Adam | 9 | 0.45 | 8 | 5 | no |
Mike | 2 | 0.1 | 9 | 6 | no |
Interval scale
- The number of correct items is displayed on an interval scale.
- An interval scale gives you the following information:
- who’s the best and who’s the worst student in the test (rank order),
- the interval between the individual students.
- Typical interval scale data are: number of years learning a foreign language, words per minute in a reading exercise, number of occurrences of a particular word in a corpus, temperature of water in degrees celsius, ...
- Changing the absolute scores from “raw points” (tokens) to relative percentages doesn’t change the scale of measurement.
- Rank is displayed on an ordinal scale: John is better than Peter, Peter is better than Ellis, etc.
- We cannot say by how much Peter is better than Ellis.
- We cannot calculate a mean rank.
- A typical ordinal scale item are grades at school: The interval between “gut (2)” and “befriedigend (3)” needn’t be the same as the one between “sehr gut (1)” and “gut (2)”.
- Pass or fail is shown on a nominal scale.
- Each result is assigned one category, in this case “yes” and “no”.
- Typical nominal scale data are: gender, native language, type of phrase, ...
- Even though you could encode “pass” as 1 and “fail” as 0, it makes no sense to calculate a mean score.
Interval scale: =, ≠, >, <, +, –, mode, median, arithmetic mean
Ordinal scale: =, ≠, >, <, mode, median
Nominal scale: =, ≠, mode
Transformations between scales
- You can transform a “higher” scale into a lower one, e.g. the interval scaled variable age into four individual age groups: up to 20, 21–40, 41–60, older than 60
- Whenever you do a downward transformation like this you’ll lose information!
- You cannot convert a “lower” scale upwards into a “higher” one!
Exercise 1: Which scale of measurement would you assume for the following variables?
- informant’s gender
- informant’s dialect
- number of occurrences of different types of relative clauses in a corpus
- grading of the same essays by different teachers
- length of headlines in The Sun and The Guardian
Figure 1: Percentage of EU citizens who can have a conversation in a foreign language (Source: Albert & Koster 2002: 76)
Son dəyişilmələr: Saturday, 14 December 2013, 3:51 PM