Scales of Measurement

1
Scales of Measurement
2
Correlation

• Measured with Pearson product moment correlation
  coefficient (denoted by r)
• Conceptually, r X Y covary X Y
  vary separately

3
Example
X Y XY 1 3 3 2 6 12 4 4 16 5 7 35 12 20
66
4
Positive Correlation
Beer Sales
Temperature
5
Negative Correlation
Coffee Sales
Temperature
6
No Correlation
Grocery Sales
Temperature
7
Restricted Range
Job Performance
Selection Device
8
Coefficient of Determination
Predictor
Criterion
r2
X
Y
9
Linear Regression

• Provides simplified description of relationship
  between X and Y.
• Can be used for prediction.
• Can be presented as a simple equation (Y bX
  a)
• b slope
• a intercept

10
Measurement Concepts Reliability

• The stability or consistency of scores in
  measurement
• Test theory suggests that a score has two
  components true score and error
• Xo Xt Xe
• rxx Xt Xo

11
Types of Reliability

• Test-retest
• Alternate Forms
• Split-half (internal consistency)
• Kuder-Richardson and Alpha

12
Measurement Concepts Validity

• The degree to which the test truly measures
  what it is supposed to measure.
• Operationalized as the correlation between the
  predictor and the criterion (rxy)

13
Validation Strategies

• Criterion-related (predictive and concurrent)
• Content
• Construct

14
Criterion Development
Criterion Relevance
Ultimate Criterion
Actual Criterion
Criterion Deficiency
Criterion Contamination
15
Sources of Criterion Contamination

• Measurement Errors
• Bias

16
Other Statistical Concepts

• Factor Analysis
• Meta-Analysis

17
Group Mean Difference No Test Bias
18
Group Mean DifferenceSlope Bias
19
Group Mean DifferenceIntercept Bias
20
Group Mean DifferenceIntercept Bias
21
Other Measurement Issues in Recruitment and
Selection

• Adverse Impact
• Minimum Cutoff Scores
• Validity Generalization