Study Guide: Basic Concepts in Measurement

Question 1

Measurement

Answer 1

Assigning numbers to persons in such a way that some attributes of the persons being measured are faithfully reflected by some property of the numbers.

Question 2

Traits of Measurement

Answer 2

• Traits need to be quantifiable.

* Not all traits are easily identifiable

Question 3

Scales of Measurement

Answer 3

• Nominal
• Ordinal
• Interval
• Ratio

Question 4

Nominal Scale

Answer 4

• Numbers receive verbal label, but don’t signify any particular amount of a trait.
• “least valuable”, but useful for labeling
• Example: Coding Male vs. Female as 1 and 2

Question 5

Ordinal

Answer 5

• Numbers denote order/ranking, but not the amount of a trait, and there is no consistent distance between numbers.
• Example: List of contestants’ race times–there is an order/rank, but the time between scores has no consistency.

Question 6

Interval

Answer 6

• Numerical differences in scores represent equal differences in the trait being measured.
• Does not have a true zero
• Example: Temperature–there are set and standard differences between numbers, but “0” does not mean the lack of temperature!

Question 7

Ratio

Answer 7

• Has a true zero point that represents the absence of a trait.
• Can make proportional statements (twice the score = twice the attribute)

Example: Income, GPA, Years of Experience

Question 8

What scale meets the minimum criteria for statistical measurement?

Answer 8

Interval scale

Question 9

Measures of Central Tendency

Answer 9

• Mean
• Median
• Mode

Question 10

In a normal distribution…

Answer 10

mean=median=mode

Question 11

What measure of central tendency is most often utilized?

Answer 11

Mean!
*Takes all data points into account

• Highlights importance of outliers
• Larger sample sizes can absorb more of a difference between data points

Question 12

What is the normal curve and why is it important?

Answer 12

• A theoretical distribution of human traits in nature.
• More abnormal=less precise scores become.
• it gives a standard to compare against

Question 13

Variability

Answer 13

• Everyone differs…and we can measure it!

* Measures the degree of variance (like outliers), deviation from average score.

Question 14

How to calculate Variability

Answer 14

• The sum of squared deviations from the mean, divided by number of scores
• Also, the square of standard deviation

sigma^2 = [ E(X-u)^2 ] // N

Question 15

Z-score

Answer 15

Returns the squared measure of variability to the original metric (how many deviations from the mean)

Question 16

How to calculate Z-score

Answer 16

z= x-u // standard deviation

Question 17

Standard Deviation

Answer 17

• The understanding of the percentage of people that fell above and below the mean
• Measures the amount of variation or dispersion from the average
• Calculated: Square root of the variance. (square root of the above calculation)

Question 18

Benefits of Z-score

Answer 18

• Normalizes distribution

* Able to compare tests with different metrics

Question 19

Correlation

Answer 19

• How is one score on one measure associated with a score on another measure
• Ranges from -1 to +1

Question 20

Prediction

Answer 20

• Can often be on different scales of measurement

* Linear regression: Allows for an adjustment for different scales of measurement.

Question 21

Intercorrelation

Answer 21

Factor Analysis: identifies the underlying variables that account for correlations between test scores

Question 22

Types of Norms

Answer 22

• Equivalency

* Reference

Question 23

Equivalency

Answer 23

The group with which the individual’s score is most consistent (grade equivalence, age equivalence)

Question 24

Reference

Answer 24

How the individual performed compared to those from the norm group (percentile)

Question 25

Cautions of Norms

Answer 25

• Beware of over-interpreting equivalency scores
• Be sure to use the norm group most appropriate and representative
• It is all relative info!