Chapter 1, Problem 7P

Four scales of measurement were introduced in this chapter, from simple classification on a nominal scale to the more informative measurements from a ratio scale.

1. a. What additional information is obtained from measurements on an ordinal scale compared to measurements on a nominal scale?
2. b. What additional information is obtained from measurement on an interval scale compared to measurements on an ordinal scale?
3. c. What additional information is obtained from measurements on a ratio scale compared to measurements on an interval scale?

To determine

The additional information obtained from measurements on an ordinal scale compared to measurements on a nominal scale.

Answer to Problem 7P

Measurements can be ranked on ordinal scale but observations cannot be ranked on nominal scale.

Explanation of Solution

Justification:

In nominal scale of measurement, observations are just categorized as per names. But in ordinal scale of measurement, observations can be ranked.

For example, different colors are categorized under nominal scale because different colors cannot be compared in terms of efficiency or performance.

Grades of students are categorized under ordinal scale of measurement because grade A is better than grade B.

Therefore, the additional information of comparing observations in terms of ranks when measurements are obtained from ordinal scale as compared to nominal scale.

To determine

The additional information obtained from measurements on an interval scale compared to measurements on an ordinal scale.

Answer to Problem 7P

Measurements can be compared in terms of difference in magnitude on interval scale but observations cannot be compared in terms of magnitude on ordinal scale.

Explanation of Solution

Justification:

In ordinal scale of measurement, observations can be ranked for comparison but in case of interval scale of measurement observations can be ranked and can be compared by difference in magnitude.

For example, Grades of students are categorized under ordinal scale of measurement because grade A is better than grade B.

Measurements of temperature are recorded on interval scale of measurement because the observations can be compared on the basis of difference in magnitude like 40 degree Celsius is 10 degree hotter than 30 degree Celsius.

Therefore, we get additional information of comparing observations in terms of difference in magnitude when measurements are obtained from interval scale as compared to ordinal scale.

To determine

The additional information obtained from measurements on a ratio scale compared to measurements on an interval scale.

Answer to Problem 7P

The zero point is arbitrary and can be located anywhere on interval scale of measurement but zero point is meaningful having meaning none on ratio scale of measurement.

Explanation of Solution

Justification:

In interval scale of measurement, observations are compared on the basis of difference in magnitude. The zero point is arbitrary and can be located anywhere.

For example, if variable X denotes the marks of students greater than 50. If some student has marks 59 then X is 9. Here zero point is 50.

In ratio scale of measurement, zero point is fixed and has general meaning none.

For example, if a person has zero salary it means he has zero rupees salary.

Therefore, the additional information of arbitrary zero point when measurements are obtained from interval scale and it means none in the ratio scale.