Chapter 6 Norm-Referenced Measurement

Topics for Discussion Reliability Consistency Repeatability Validity Truthfulness Objectivity Inter-rater reliability

Observed, Error, and True Scores Observed Score = True Score + Error Score

Reliability Reliability is that proportion of observed score variance that is true score variance

Table 6-1 Systolic Blood Pressure Recordings for 10 Subjects Subject Observed BP = True BP + Error BP Sum (  ) Mean (M) Variance (S 2 ) S

Interclass Reliability Pearson Product Moment Test Retest Equivalence Split Halves

Table 6-2 Sit-up Performance for 10 Subjects Subject Trial 1 Trial Sum (  ) Mean S Variance (S 2 ) r xx’ =.927

Spearman Brown Prophecy Formula k = the number of items I WANT to estimate the reliability for divided by the number of items I HAVE reliability for

Table 6-3 Odd and Even Scores for 10 Subjects Subject Odd Even Sum (  )9286 Mean S Variance (S 2 ) r xx’ =.639

Table 6-4 Values of r kk From Spearman-Brown Prophecy Formula r K (change in test length)

Table 6-5 Effect of a Constant Change in Measures Subject Trial 1 Trial Sum (  ) Mean S Variance (S 2 ) r xx’ = 1.00

Intraclass Reliability ANOVA Model Cronbach's alpha coefficient Alpha Coefficient

Intraclass (ANOVA) Reliabilities Common terms you will encounter Alpha Reliability Kuder Richardson Formula 20 (KR 20 ) Kuder-Richardson Formula 21 (KR 21 ) ANOVA reliabilities

Table 6-6 Calculating the Alpha Coefficient Subject Trial 1 Trial 2 Trial 3 Total  X  X S

Calculating the Alpha Coefficient

Index of Reliability The theoretical correlation between observed scores and true scores

Table 6-7 Student Scores on a 10-Item Multiple-Choice Quiz Subject Total Items

Standard Error of Measurement Reflects the degree to which a person's observed score fluctuates as a result of errors of measurement

Factors Affecting Test Reliability 1)Fatigue 2)Practice 3)Subject variability 4)Time between testing 5)Circumstances surrounding the testing periods 6)Appropriate difficulty for testing subjects 7)Precision of measurement 8)Environmental conditions

Decline in Reliability for the Harvard Alumni Activity Survey as the Time Between Testing Periods Increases Months Between Test-Retest

Validity Types Content-Related Validity Criterion-Related Validity Statistical or correlational concurrent predictive Construct-Related Validity

Standard Error of Estimate Standard Error Standard Error of Prediction

Standard Errors SE of Measurement SE of Estimate

Methods of Obtaining a Criterion Measure Actual participation e.g., golf, archery Perform the criterion known valid criterion (e.g., treadmill performance) Expert judges panel judges Tournament participation Round robin Known valid test

Table 6-8 Correlation Matrix for Development of a Golf Skill Test (From Green et al., 1987) Playing golf Long puttChip shotPitch shotMiddle distance shot Drive Playing golf 1.00 Long putt Chip shot Pitch shot Middle distance shot Drive What are these? Concurrent Validity coefficients

Table 6-9 Concurrent Validity Coefficients for Golf Test 2-item battery Middle distance shot Pitch shot.72 3-item battery Middle distance shot Pitch shot Long putt.76 4-item battery Middle distance shot Pitch shot Long putt Chip shot.77

Correlations Between IQs of Related or Unrelated Children as a Function of Genetic Similarity and Similarity of Environment Identical twins - reared together.88 Identical twins - reared apart.75 Fraternal twins - same sex.53 Fraternal twins - opposite sex.53 Siblings - reared together.49 Siblings - reared apart.46 Parent with child.52 Foster parent with child.19 Unrelated - reared together.16 From Glass & Stanley, 1970, p. 119

Figure 6.1 Diagram of Validity and Reliability Terms

Interpreting the “r” you obtain

Concurrent Validity This square represents variance in performance in a skill (e.g., golf)

Concurrent Validity The different colors and patterns represent different parts of a skills test battery to measure the criterion (e.g., golf)

Concurrent Validity The orange color represents ERROR or unexplained variance in the criterion (e.g., golf) Error

Concurrent Validity ACDB Consider the Concurrent validity of the above 4 possible skills test batteries

Concurrent Validity ACDB Which test battery would you be LEAST likely to use? Why? D – it has the MOST error and requires 4 tests to be administered

Concurrent Validity ACDB Which test battery would you be MOST likely to use? Why? C – it has the LEAST error but it requires 3 tests to be administered

Concurrent Validity ACDB Which test battery would you use if you are limited in time? A or B – requires 1 or 2 tests to be administered but you lose some validity

Interpret these correlations Actual golf score Putting Trial 1 Putting Trial 2 Driving Trial 1 Driving Trial 2 Observer 1 Observer 2 Actual golf score 1.00 Putting T Putting T Driving T Driving T Observer Observer What are these? Concurrent Validity coefficients Criterion

Interpret these correlations Actual golf score Putting Trial 1 Putting Trial 2 Driving Trial 1 Driving Trial 2 Observer 1 Observer 2 Actual golf score 1.00 Putting T Putting T Driving T Driving T Observer Observer What are these? Reliability coefficients

Interpret these correlations Actual golf score Putting Trial 1 Putting Trial 2 Driving Trial 1 Driving Trial 2 Observer 1 Observer 2 Actual golf score 1.00 Putting T Putting T Driving T Driving T Observer Observer What is this? Objectivity coefficient

Example of Reliability Study (Rikli et al., RQES, 1992) K1234 DistanceGender 1/2 mileM F /4 mileM F mileM F Grade

SPSS Examples