What Is Measurement?

Abstract

Most of us are familiar with measurement in the physical world, whether it is measuring today’s maximum temperature, the height of a child or the dimensions of a house, where numbers are given to represent “quantities” of some kind, on some scales, to convey properties of some attributes that are of interest to us.

Appendices

Discussion Points

• 1. Discuss whether latent variables should have a meaningful zero and why it may be difficult to define a zero.

• 2. Given that there could be a meaningful zero for test scores where zero means a student answered all questions incorrectly, are test scores ordinal, interval or ratio variables? If test scores are used as measures of an underlying ability, what level of measurement are test scores?

• 3. Is the following a “measurement” instrument? If so, what is the construct being measured?

Car Survey

“What characteristics led to your decision for the specific model?”

Tick four categories

	Customer 1	Customer 2	Customer 3	Customer 4
Economy	✓			✓
Handling		✓	✓	✓
Interior design	✓	✓
Exterior design	✓		✓	✓
Reliability		✓
Price			✓	✓
Comfort	✓
Safety		✓	✓

• 4. Is the following a “measurement” instrument? If so, what is the construct being measured?

Taxi Survey

Rating taxi rides

Melb airport to kew	Taxi 1	Taxi 2	Taxi 3	Taxi 4
Comfortable temperature	✓	✓	✘	✓
Driver’s certificate displayed	✓	✓	✘	✘
Uniform correct	✘	✓	✘	✓
Driver presentation	✓	✓	✘	✓
Pleasant odour	✓	✘	✘	✓
Internal cleanliness	✓	✓	✘	✓
External cleanliness	✓	✘	✘	✓
Vehicle handling	✓	✓	✘	✓
Driver quality	✓	✘	✘	✓
Correct change	✘	✘	✘	✓
Politeness	✓	✓	✘	✓
Peak time	✘	✘	✓	✓
Metered fare	$47.10	$48.40	$50.40	$51.00

• 5. Messick (1989) provided a definition of validity as “an integrated evaluative judgment of the degree to which empirical evidence and theoretical rationales support the adequacy and appropriateness of inferences and actions based on test scores or other modes of assessment.” Compare and contrast this definition of validity with what we have discussed in this chapter. Do you think this is a good definition of validity? Provide reasons for your answers.

Exercises

Q1. The following are some data collected in SACMEQ (Southern and Eastern Africa Consortium for Monitoring Educational Quality, UNESCO-IIEP 2004). For each variable, state whether the numerical coding as shown in the boxes provides nominal, ordinal, interval or ratio measures?

• 1. PENGLISH

  Do you speak English outside school?

  (Please tick only one box.)

  

• 2. XEXPER

  How many years altogether have you been teaching?

  (Please round to ‘1’ if it is less than 1 year.)

  

• 3. PCLASS

  Which Standard 6 class are you in this term?

  (Please tick only one box.)

  

• 4. PSTAY

  Where do you stay during the school week?

  (Please tick only one box.)

  

Q2. Which questionnaire titles in the following list would appear to be about “measurement” (as opposed to a survey)?

Q3. On a mathematics test of 40 questions, Jenny got a score of 14. Eric got a score of 28. Mary got a score of 30.

We can be reasonably confident to conclude that (write Yes or No in the space provide)

• 1. Jenny is not as good in mathematics as Eric and Mary are. [ ]

• 2. Mary is better at mathematics than Eric is. [ ]

• 3. Eric got twice as many questions right as Jenny did. [ ]

• 4. Eric’s mathematics ability is twice Jenny’s ability. [ ]

Q4. A movie guide rates movies by showing a number of stars. For example, a movie with 3-and-a-half stars is not as good as a movie with 4 stars (★★★★☆).

What is the most likely measurement level provided by this kind of ratings?

Q5. In the context of educational testing, the term “measurement error” usually refers to

Q6. In the context of educational testing, test reliability refers to

Q7. A student with limited proficiencies in English sat a Year 5 mathematics test and obtained a poor score due to language difficulties. Is this an issue related to test reliability or validity?

Q8. In a Grade 5 spelling test, there are 20 words. This is a very small sample of all the words Grade 5 students should know. If the test is used to measure students’ spelling proficiency in general, which of the following best describes the likely problems with this test?