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 (r 2 ) 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 (r 2 ) EQUALS .81
MEANING THAT 81% OF THE VARIABILITY IN BODY
WEIGHT SCORES IS DUE TO THE INDIVIDUALS’ HAVING
DIFFERENT HEIGHT
• AS r DECREASES, r 2 DROPS DRAMATICALLY AS AN r = .60
HAS AN r 2 = .36 or 36% AND r = .40 HAS AN r 2 = .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)

QUESTIONS OR COMMENTS??
THANK YOU!!