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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)

• 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”

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

DETERMINING RELATIONSHIPS BETWEEN SCORES - GRAPHING TECHNIQUE

DETERMINING RELATIONSHIPS BETWEEN SCORES - GRAPHING TECHNIQUE

DETERMINING RELATIONSHIPS BETWEEN SCORES - GRAPHING TECHNIQUE

DETERMINING RELATIONSHIPS BETWEEN SCORES - GRAPHING TECHNIQUE OF A LARGE

DATA BASES USING A COMPUTER

DETERMINING RELATIONSHIPS BETWEEN SCORES - GRAPHING TECHNIQUE OF A LARGE

DATA BASES USING A COMPUTER

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

PEARSON PRODUCT-MOMENT FORMULA

CALCULATION USING PEARSON PRODUCT-MOMENT FORMULA

CALCULATION USING PEARSON PRODUCT-MOMENT FORMULA

CALCULATION USING PEARSON PRODUCT-MOMENT FORMULA

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

INTERPREATATION OF CORRELATION COEFFICIENT

• 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 = .60HAS 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

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

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

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