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Correlation & Prediction REVIEWPowerPoint Presentation

Correlation & Prediction REVIEW

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Correlation & PredictionREVIEW

- Correlation
- Bivariate Direct/Indirect Cause/Effect
- Strength of relationships (is + stronger than negative?)
- Coefficient of determination (r2); Predicts what?
- Linear vs Curvilinear relationships

Table 5-2Variable Classification

IndependentDependent

Presumed cause Presumed effect

The antecedent The consequence

Manipulated/measured by researcher Outcome (measured)

Predicted from Predicted to

Predictor Criterion

X Y

Some Examples

- Chi-SquareGender and knee injuries in collegiate basketball players
- Independent t-testDifferences in girls and boys (independent groups; mutually exclusive)
- Dependent t-testPre and Post measurement of same group or matched pairs (siblings)
- One-Way ANOVADefensive ability (1, 2 or 3) and throwing distance (IV of >2 levels)

Topics for Discussion

- Reliability (variance & PPM correlation support reliability & validity) Consistency Repeatability
- Validity Truthfulness
- Objectivity Inter-rater reliability

Observed, Error, and True Scores

Observed Score = True Score + Error Score

ALL scores have true and error portions

- There is variation in observed, true & error scores
- Error can be + or – (increase/decrease observed scores)
- Error scores contribute LITTLE to observed variation
- S2o = S2t + S2e

ReliabilityTHIS IS HUGE!!!!

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

TIP: use algebra to move S2t to stand alone

S2o = S2t + S2e

Table 6-1Systolic Blood Pressure Recordings for 10 Subjects

Subject Observed BP = True BP + Error BP

1 103 105 -2

2 117 115 +2

3 116 120 -4

4 123 125 -2

5 127 125 +2

6 125 125 0

7 135 125 +10

8 126 130 -4

9 133 135 -2

10 145 145 0

Sum (S) 1250 1250 0

Mean (M) 125.0 125.0 0

Variance (S2) 133.6 116.716.9

S 11.6 10.8 4.1

Reliability Coefficients

- Interclass Reliability
- Correlates 2 trials

- Intraclass Reliability
- Correlates >2 trials

Interclass Reliability (Pearson Product Moment)

- Test Retest (administer test 2x & correlate scores)
- See Excel document (Norm-ref msmt examples)
- Time, fatigue, practice effect

- Equivalence (create 2 “equivalent” test forms)
- Odd/Even test items on a single test
- Addresses most of the test/retest issues
- Reduces test size 50%

- Split Halves
- Spearman-Brown prophecy formula

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 6-3Odd and Even Scores for 10 Subjects

Subject Odd Even

1 12 13

2 9 11

3 10 8

4 9 6

5 11 8

6 7 10

7 9 9

8 12 10

9 5 4

10 8 7

Sum (S) 92 86

Mean 9.2 8.6

S 2.2 2.6

Variance (S2) 4.8 6.7

Assume a 30-item test

rxx’ = .639

(low but test is only 15 items)

Are these two trials consistent?

Subject Trial 1 Trial 2

1 15 25

2 17 27

3 10 20

4 20 30

5 23 33

6 26 36

7 27 37

8 30 40

9 32 42

10 33 43

Sum (S) 233 333

Mean 23.3 33.3

S 7.7 7.7

Variance (S2) 59.1 59.1

All scores changed by 10 points

If reliability= consistency, how can you calculate reliability considering a constant change in scores?

rxx’ = 1.00

Intraclass Reliability ANOVA ModelCronbach's alpha coefficient

Alpha Coefficient

K = # trials (different than in the Spearman-Brown prophecy formula)

Intraclass (ANOVA) ReliabilitiesCommon terms you will encounter

- Alpha Reliability
- Kuder Richardson Formula 20 (KR20) (items scored 0/1)
- Kuder-Richardson Formula 21 (KR21)
- ANOVA reliabilities

All are calculated the same: partition total variance in scores into

PEOPLEtotal variance between participants (total or observed S2)

TRIALS variance across trials (error S2)

PEOPLE-BY-TRIALS not everyone performs equally differently across trials (error S2)

Table 6-6 scores intoCalculating the Alpha Coefficient

Subject Trial 1 Trial 2 Trial 3 Total

1 3 5 3 11

2 2 2 2 6

3 6 5 3 14

4 5 3 5 13

5 3 4 4 11

SX 19 19 17 55

SX2 83 79 63 643

S22.70 1.70 1.30 9.50

K = # trials

Calculating the Alpha Coefficient scores into

Index of Reliability scores into

The theoretical correlation between

observed scores and true scores

Square root of the reliability coefficient

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