GENERAL MEASUREMENT CONCEPTS

ELEMENTS OF SCORE ANALYSIS

• TYPES OF SCORES

• COMMON UNIT OF MEASURE

• THREE STEPS OF ANALYZING A SET OF SCORES

• CALCULATORS AND COMPUTERS

WHY ANALYSIS TEST SCORES?

“FOR A LARGE GROUP A SIMPLE LIST OF SCORES HAS NO MEANING”

“OVERALL GROUP PERFORMANCE AND/OR IMPROVEMENT CAN ONLY BE INTERPRETED BY CONDENSING THE INFORMATION AND APPLYING DESCRIPTIVE STATISTICS TO IT”

WHY ANALYSIS TEST SCORES?

“ONCE THE OVERALL GROUP PERFORMANCE IS DETERMINED, INDIVIDUAL PERFORMANCE CAN THEN BE EVALUATED IN RELATION IN RELATION TO THE OVERALL GROUP PERFORMANCE”

TYPES OF SCORES

• CONTINUOUS SCORES

• DISCRETE SCORES

CONTINUOUS SCORES

• HAVE POTENTIALLY AN INFINITE NUMBER OF VALUES AS THEY CAN BE MEASURED WITH VARYING DEGREES OF ACCURACY

• BETWEEN ANY TWO VALUES EXIST COUNTLESS VALUES THAT CAN BE EXPRESSRED AS FRACTIONS

• EXAMPLES: TIME, WEIGHT, & LENGTH

CONTINUOUS SCORES

• MOST CONTINUOUS SCORES ARE ROUNDED OFF TO THE NEAREST UNIT OF MEASUREMENT WHEN RECORDED

• 5 OR MORE IS ROUNDED UP AND 4 OR LESS IS ROUNDED DOWN

• EXAMPLE ROUNDING TO A WHOLE NUMBER: 1.6 = 2; 1.4 = 1

DISCRETE SCORES

• LIMETED TO A SPECIFIC NUMBER OF VALUES

• ARE NOT EXPRESSED IN FRACTIONS

• EXAMPLES - FREE THROWS MADE IN BASKETBALL OR SUCCESSFUL THROWS AT A TARGET

OTHER CLASSIFICATION OF SCORES

• RATIO

• INTERVAL

• ORDINAL

• NOMINAL

RATIO SCORES• COMMON UNIT OF MEASUREMENT

BETWEEN EACH SCORE

• TRUE ZERO POINT

• STATEMENTS ABOUT EQUALITY OF RATIOS CAN BE MADE: 1 SCORE CAN BE REFERRED TO AS 2 TIMES GREATER THAN ANOTHER SCORE

• EXAMPLES INCLUDE DISTANCE, TIME, WEIGHT, AND LENGTH

INTERVAL SCORES

• COMMON UNIT OF MEASUREMENT BETWEEN EACH SCORE

• NO TRUE ZERO (A SCORE OF ZERO ON A KNOWLEDGE TEST DOES NOT INDICATE TOTAL LACK OF KNOWLEDGE) AND HENCE STATEMENTS ABOUT EQUALITY OF RATIOS CAN NOT BE MADE

“MOST PHYSICAL PEFORMANCE SCORES ARE EITHER RATIO OR INTERVAL SCORES”

ORDINAL SCORES

• DO NOT HAVE A COMMON UNIT OF MEASUREMENT BETWEEN SCORES AND DO NOT HAVE A TRUE ZERO

• THERE IS AN ORDER IN THE SCORES THAT MAKES IT POSSIBLE TO DESCRIBE OR LIST ONE SCORE HIGHER THAN THE OTHER SCORE

• EXAMPLE: CLASS RANK ON A PUSH-UP TEST

NOMINAL SCORES

• CANNOT BE RANKED ORDER

• MUTUALLY EXCLUSIVE SCORES

• CANNOT SAY THAT ONE SCORE IS BETTER THAN ANOTHER SCORE

• EXAMPLES: SPORT PREFERENCE, GENDER, AND ETHNICITY

COMMON UNITS OF MEASURE

• SCORES MUST BE RECORDED IN A SINGLE UNIT OF MEASUREMENT SUCH AS CENTIMETERS RATHER THAN METERS AND CENTIMETERS

• USUALLY RECORDED IN THE SMALLER ONE SUCH AS CENTIMETERS

• RECORDING SCORES IN THE SMALLER UNIT OF MEASURE AS THEY ARE COLLECTED IS LESS TIME-CONSUMING THAN CONVERTING THEM INTO THAT FORM LATER

SELECTING A CRITERION SCORE

MEAN SCORE VERSUS BEST SCORE

• CRITERION SCORE IS THE MEASURE USED TO INDICATE A PERSON’S ABILITY

• GENERALLY A BETTER INDICATOR WHEN DEVELOPED FROM MORE THAN 1 TRIAL (I.E., MEAN SCORE FROM MORE THAN 1 TRIAL)

• RELIABILITY INCREASES AS THE NUMBER OF MEASURES INCREASES

MEAN SCORE VERSUS BEST SCORE

• GENERALLY THE MOST RELIABILE CRITERION SCORE AND THE BEST INDICATOR OF TRUE ABILITY (TYPICAL PERFORMANCE) MAY BE THE MEAN SCORE OF MULTIPLE TRIALS AS THE SUM OF THE ERRORS OF MEASURMENT IS ZERO

• NOTE: OBSERVED SCORE EQUALS TRUE SCORE PLUS ERROR SCORE

MEAN SCORE VERSUS BEST SCORE

• FOR MULTIPLE-TRIAL PHYSICAL PERFORMANCE TESTS WHERE MAXIMAL ABILITY RATHER THAN TYPICAL ABILITY IS DESIRED, AND THE EQUIPMENT AND SCORING PROCEDURE ARE HIGHLY ACCURATE, THE BEST SCORE IS THE BEST INDICATOR OF A PERSON’S TRUE ABILITY AS A PERSON CANNOT SCORE BETTER THAN HER OR HIS PHYSIOLOGICAL CAPACITY

• TYPICAL OF MANY PHYSIOLOGICAL MEASUREMENTS TAKEN IN A LABORATORY SETTING)

MEAN SCORE VERSUS BEST SCORE

• IF THE BEST SCORE IS USED AS THE CRITERION SCORE:

- IT SHOULD BE BASED ON MULTIPLE TRIALS

- IT IS NOT THE SAME TRIAL FOR EACH PERSON

MEAN SCORE VERSUS BEST SCORE• DEPEDNING ON THE SITUATION AND WHAT THE

TEST ADMINISTRATOR BELIEVES IS MOST APPROPRIATE, AN INDIVIDUAL’S CRITERION SCORE FROM MULTIPLE TRIAL TESTS MAY BE DETERMINED IN ANY OF THE FOLLOWING WAYS:- MEAN OF ALL TRIAL SCORES- BEST SCORE OF ALL TRIAL SCORES- MEAN OF THE SELECTED TRIAL

SCORES BASED ON THE TRIALS ON WHICH THE GROUP SCORED BEST

- MEAN OF THE SELECTED TRIAL SCORES BASED ON THE TRIALS ON WHICH THE INDIVIDUAL SCORED BEST

THREE STEPS OF ANALYZING A SET OF TEST SCORES

• SELECT THE APPROPRIATE ANALYSIS TECHNIQUE

• COMPLETE CALCULATIONS WITH THE ANALSYS TECHNIQUE

• INTERPRET THE RESULTS OF THE ANALYSIS TECHNIQUE

CALCULATORS AND COMPUTERS

• SCORE ANALYSIS SHOULD BE ACCURATE AND QUICK

• CALCULATORS WORK WELL WITH SMALL DATA SETS; BUT WITH LARGER DATA SETS THE USE OF CALCULATORS BECOME MORE TIME-CONSUMING AND MORE MISTAKES TEND TO BE MADE

• COMPUTERS WITH DATA ANALYSIS SOFTWARE SUCH AS SPSS ARE VERY FAST AND ACCURATE

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