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SHOWTIME!

SHOWTIME!. STATISTICAL TOOLS IN EVALUATION. CORRELATION TECHNIQUE SIMPLE PREDICTION TESTS OF DIFFERENCE. DETERMINING RELATIONSHIPS BETWEEN SCORES. • MANY SITUTATIONS WHERE ONE MAY WANT TO KNOW THE RELATIONSHIP BETWEEN: • SCORES ON TWO SIMILAR TESTS (I.E., RELIABILITY MEASURE)

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SHOWTIME!

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  1. SHOWTIME!

  2. STATISTICAL TOOLS IN EVALUATION CORRELATION TECHNIQUE SIMPLE PREDICTION TESTS OF DIFFERENCE

  3. DETERMINING RELATIONSHIPS BETWEEN SCORES • MANY SITUTATIONS WHERE ONE MAY WANT TO KNOW THE RELATIONSHIP BETWEEN: • SCORES ON TWO SIMILAR TESTS (I.E., RELIABILITY MEASURE) • OR TWO DIFFERENT TESTS (AMOUNT OF SHARED VARIANCE OR INFORMATION OF TWO TESTS) “if there are seven tests in a battery of tests and two of the tests are highly related, the battery could be reduced to six tests with no loss of information”

  4. DETERMINING RELATIONSHIPS BETWEEN SCORES - GRAPHING TECHNIQUE • PLOTTING OF THE SCORES FOR TWO TESTS OF EACH INDIVIDUAL IN A GRAPH • THE CLOSER ALL PLOTTED POINTS ARE TO THE TREND LINE, THE HIGHER OR LARGER THE RELATIONSHIP • WHEN THE PLOTTED POINTS RESEMBLE A CIRCLE MAKING IT IMPOSSIBLE TO DRAW A TREND LINE, THERE IS NO LINEAR RELATIONSHIP BETWEEN THE TWO MEASURES BEING GRAPHED

  5. DETERMINING RELATIONSHIPS BETWEEN SCORES - GRAPHING TECHNIQUE

  6. DETERMINING RELATIONSHIPS BETWEEN SCORES - GRAPHING TECHNIQUE

  7. DETERMINING RELATIONSHIPS BETWEEN SCORES - GRAPHING TECHNIQUE

  8. DETERMINING RELATIONSHIPS BETWEEN SCORES - GRAPHING TECHNIQUE OF A LARGE DATA BASES USING A COMPUTER

  9. DETERMINING RELATIONSHIPS BETWEEN SCORES - GRAPHING TECHNIQUE OF A LARGE DATA BASES USING A COMPUTER

  10. CORRELATION TECHNIQUE • MATHEMATICAL TECHNIQUE FOR DETERMINING THE RELATIONSHIP BETWEEN TWO SETS OF SCORES • PEARSON PRODUCT-MOMENT CORRELATION USED WITH RATIO AND INVERVAL DATA • SPEARMAN’S RHO OR RANK ORDER CORRELATION TECHNIQUE USED WITH ORDINAL DATA

  11. PEARSON PRODUCT-MOMENT FORMULA

  12. CALCULATION USING PEARSON PRODUCT-MOMENT FORMULA

  13. CALCULATION USING PEARSON PRODUCT-MOMENT FORMULA

  14. CALCULATION USING PEARSON PRODUCT-MOMENT FORMULA

  15. TWO CHARACTERISTICS OF CORRELATIONAL COEFFICIENTS • DIRECTION OF THE RELATIONSHIP IS INDICATED BY WHETHER THE CORRELATION COEFFICIENT IS POSITIVE OR NEGATIVE • POSITIVE COEFFICIENT INDICATES THAT AN INCREASE IN SCORES ON ONE MEASURE IS ACCOMPANIED BY AN INCREASE IN SCORES ON THE OTHER MEASURE OR THAT A DECREASE IN SCORES ON ONE MEASURE IS ACCOMPANIED BY A DECREASE IN SCORES ON THE OTHER MEASURE • NEGATIVE COEFFICIENT INDICATES THAT AN INCREASE IN SCORES ON ONE MEASURE IS ACCOMPANIED BY A DECREASE IN SCORES ON THE OTHER MEASURE - EXISTS BECAUSE OF OPPOSITE SCORING SCALES OR A TRUE NEGATIVE RELATIONSHIP EXISTS • STRENGTH OF THE RELATIONSHIP IS INDICATED BY HOW CLOSE THE COEFFICIENT IS TO 1; THE CLOSER THE COEFFICIENT IS TO 1, THE STRONGER THE RELATIONSHIP BETWEEN THE TWO VARIABLES

  16. INTERPREATATION OF CORRELATIONCOEFFICIENT • A HIGH CORRELATION (r) BETWEEN TWO VARIABLES DOES NOT DOES NOT IMPLY A CAUSE- AND EFFECT-RELATIONSHIP • A STRONG CORRELATION (r) BETWEEN SHOE SIZE AND MATH ABILITY IN K-12 STUDENTS DOES NOT MEAN THAT AN INCREASE IN SHOE SIZE WILL INCREASE MATH ABILITY • COEFFICIENT OF DETERMINATION (r2) IS THE TRUE INDICATOR OF THE DEGREE OF RELATIONSHIP • INDICATES THE AMOUNT OF VARIABILITY IN ONE MEASURE THAT IS EXPLAINED BY THE OTHER MEASURE • IF r = .90 BETWEEN HEIGHT AND BODY WEIGHT, THE COEFFICIENT OF DETERMINAITON (r2) EQUALS .81 MEANING THAT 81% OF THE VARIABILITY IN BODY WEIGHT SCORES IS DUE TO THE INDIVIDUALS’ HAVING DIFFERENT HEIGHT • AS r DECREASES, r2 DROPS DRAMATICALLY AS AN r = .60 HAS AN r2 = .36 or 36% AND r = .40 HAS AN r2 = .16 or 16% • BASED ON THE ASSUMPTION THAT THE RELATIONSHIP BETWEEN THE TWO VARIABLES IS LINEAR

  17. SIMPLE PREDICATION OF AN UNKNOWN SCORE (Y’) FOR AN A KNOWN MEASURE (X)

  18. SIMPLE PREDICATION OF AN UNKNOWN SCORE (Y’) FOR AN A KNOWN MEASURE (X)

  19. QUESTIONS OR COMMENTS?? THANK YOU!!

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