Measurement Scales
Practice
1. Indicate the first letter (N, O, I, R) of the highest possible scale for each of the following measures, where N is lowest and R is highest:
Measure Highest Scale
a. Feet of snow Interval
b. Brands of carbonated soft drinks Nominal
c. Class rank at graduation Ordinal or Interval per measurement debate
d. GPA Interval
e. Speed of a baseball pitch Ratio
7. Are the following variables discrete or continuous? Mark “D” or “C” to indicate your answer.
Measure Variable Type
a. Inches of rainfall “C”
b. GPA “C”
c. Speed of base ball pitch “C”
d. Time taken to solve a puzzle “C”
e. Level of depression “D”
f. Number of angels that can fit on the head of a pin (Oops . .how’d that get in her again? You may skip this one. “D”
To determine the highest possible scale for each measure in the first question:
a. Feet of snow: The highest scale for measuring feet of snow would be Interval. This is because intervals between measurements are meaningful (e.g., the difference between 2 feet and 3 feet is the same as the difference between 5 feet and 6 feet). In this case, the scale is not Ratio because having 0 feet of snow does not indicate the absence of snow.
b. Brands of carbonated soft drinks: The highest scale for measuring brands of carbonated soft drinks would be Nominal. This is because the categories or brands are mutually exclusive and there is no inherent order or magnitude to the labels.
c. Class rank at graduation: The highest scale for measuring class rank at graduation could be either Ordinal or Interval, depending on the measurement debate. Ordinal scale allows for ordering and ranking, but does not specify the magnitude of difference between ranks. Interval scale, on the other hand, includes both ranking and precise equal intervals between ranks. The debate arises because there may be disagreements about whether the difference between the top-ranked student and the second-ranked student is the same as the difference between the 10th-ranked student and the 11th-ranked student.
d. GPA: The highest scale for measuring GPA would be Interval. This is because GPA is an ordered scale that includes precise intervals between grades (e.g., the difference between a B+ and an A- is the same as the difference between an A- and an A).
e. Speed of a baseball pitch: The highest scale for measuring the speed of a baseball pitch would be Ratio. This is because Ratio scale includes a true zero point (0 mph in this case), and ratios between measurements are meaningful (e.g., a pitch thrown at 100 mph is twice as fast as a pitch thrown at 50 mph).
For the second question, to determine whether the variables are discrete or continuous:
a. Inches of rainfall: This variable is continuous (C), as it can take any value on a continuous scale (e.g., 0.5 inches, 2.3 inches).
b. GPA: This variable is continuous (C), as it can take any value on a continuous scale (e.g., 3.2, 3.7).
c. Speed of a baseball pitch: This variable is continuous (C), as it can take any value on a continuous scale (e.g., 80 mph, 95 mph).
d. Time taken to solve a puzzle: This variable is continuous (C), as it can take any value on a continuous scale (e.g., 2 minutes, 5.5 minutes).
e. Level of depression: This variable is discrete (D), as it is typically measured using a limited number of ordered categories (e.g., mild, moderate, severe).
f. Number of angels that can fit on the head of a pin: Although this is a hypothetical example, it would be classified as discrete (D) as there are a limited number of possible whole numbers that can fit on the head of a pin.