Scales Measurement Levels Overview

This question requires arranging different scenarios based on the level of measurement scales they represent, from the highest level to the lowest level. Understanding the characteristics of each scale is key to solving this problem.

Analyzing Measurement Scales in Scenarios

Let's break down each scenario:

• Scenario A: A researcher divides the sample into 'Urban' and 'Rural' areas. This involves categorizing data without any inherent order or numerical value between the categories. This represents a Nominal scale.
• Scenario B: A student scores 50 out of 60 marks in an English test. Marks represent a quantity with equal intervals between values (e.g., the difference between 40 and 50 marks is the same as between 10 and 20 marks) and a meaningful true zero (zero marks means no score). This is a Ratio scale.
• Scenario C: A cricketer is given the tenth rank as an all-rounder. Ranking indicates an order (e.g., 1st rank is better than 10th rank), but the intervals between ranks are not necessarily equal. The difference in performance between the 1st and 2nd ranked player might be different from the difference between the 9th and 10th ranked player. This is an Ordinal scale.
• Scenario D: The height of a building is double that of others. This involves a true zero point (zero height means no building) and equal, quantifiable intervals. The ratio between heights is meaningful (e.g., one building being "double" the height of another). This is also a Ratio scale.

Hierarchy of Measurement Scales

The generally accepted hierarchy of measurement scales, from highest level (most information) to lowest level (least information), is as follows:

• Ratio Scale: Possesses properties of interval scales plus a true zero point. Ratios between values are meaningful. (e.g., height, weight, age, marks).
• Interval Scale: Possesses ordered values with equal intervals between them, but lacks a true zero point. (e.g., temperature in Celsius or Fahrenheit).
• Ordinal Scale: Possesses ordered values, but the intervals between them are not necessarily equal. (e.g., ranks, satisfaction levels like 'good', 'better', 'best').
• Nominal Scale: Possesses categories without any inherent order or numerical value. (e.g., gender, nationality, types of residence).

Ordering the Scenarios by Scale Level

Based on the identified scales and their hierarchy:

• Both Scenario D and Scenario B are Ratio scales, which is the highest level.
• Scenario C is an Ordinal scale, placing it below the Ratio scales.
• Scenario A is a Nominal scale, representing the lowest level of measurement.

Therefore, arranging them from the higher level to the lower level of scales of measurement gives us the order: D, B, C, A.