Correlation prediction review
Download
1 / 21

Correlation & Prediction REVIEW - PowerPoint PPT Presentation


  • 83 Views
  • Uploaded on

Correlation & Prediction REVIEW. Correlation Bivariate Direct/Indirect Cause/Effect Strength of relationships (is + stronger than negative?) Coefficient of determination (r 2 ); Predicts what? Linear vs Curvilinear relationships. Table 5-2 Variable Classification. Independent Dependent

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about ' Correlation & Prediction REVIEW' - gray-boone


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
Correlation prediction review
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 2 variable classification
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
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)


Norm referenced measurement

Norm-Referenced Measurement

HPER 3150

Dr. Ayers


Topics for discussion
Topics for Discussion

  • Reliability (variance & PPM correlation support reliability & validity) Consistency Repeatability

  • Validity Truthfulness

  • Objectivity Inter-rater reliability


Observed error and true scores
Observed, Error, and True Scores

Observed Score = True Score + Error Score

ALL scores have true and error portions



Reliability this is huge
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 1 systolic blood pressure recordings for 10 subjects
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
Reliability Coefficients

  • Interclass Reliability

    • Correlates 2 trials

  • Intraclass Reliability

    • Correlates >2 trials


Interclass reliability pearson product moment
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
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
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
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 model cronbach s alpha coefficient
Intraclass Reliability ANOVA ModelCronbach's alpha coefficient

Alpha Coefficient

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


Intraclass anova reliabilities common terms you will encounter
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 calculating the alpha coefficient
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



Index of reliability
Index of Reliability scores into

The theoretical correlation between

observed scores and true scores

Square root of the reliability coefficient


ad