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Measurement and measurement scales

The amount of motivation of an individual was measured by a self report scale that has 32 items each scaled as shown below:

0........1........2........3.......4..........5.........6...........7
never hardly ever sometimes very often

The following scores were obtained: Mishelle 192, Justin 128, Matthew 183, Cindy 51, Julie 218, John 102, Linda 0.

a. Is it accurate to conclude that John is twice as motivated as Cindy? Explain your answer being sure to include which scale of measurement is being used.
b. Is it accurate to conclude that John is twice as motivated as Cindy? please explain the answer.
c. Is it accurate to conclude that, because of her score of 0, Linda totally lacks motivation? please explain your answer.
d. Suppose that on item #27, Matthew had circled a rating of 5. What are the real upper and lower limits of this measurement?
e. Would a person's total motivation score - figured by adding up the numbers they circled for each item, be considered a discrete or a continuous variable? please explain the answer.
f. How could one measure motivation with a continuous variable? (Be creative, adding more decimal points on the scale is not correct).

Solution Preview

Measurement scales are numbering systems. They specify properties which determine what the numbers signify.
The properties involve concepts such as magnitude, interval size, and absolute zero .
Use and interpretation of the numbers depend on these underlying properties. For example, it makes sense to describe me as getting half as much salary as my neighbor. However it may not make sense to say that he is twice as intelligent as I am .

There are four types of numbering system, ordered from least to most informative.
? Nominal. These numbers represent categories,
? Ordinal. The magnitude of these is meaningful (higher is more than lower), but only as an order.
? Interval. The numeric distance between numbers is meaningful, although the absolute size of the number is not.
? Ratio. The order, intervals, and absolute size of numbers are significant.
The type of measurement being used here is the ordinal system

a. Is it accurate to conclude that John is twice as motivated as Cindy? Explain your answer being sure to include which scale of measurement is being used.

The scale of measurement being used is the ordinal scale.

In the Ordinal scale the order of objects is based on whether they have more, less, or the same.
One cannot tell about magnitude of difference between objects.
The ordinal scale ...

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