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Percentiles

Percentiles. Percentages. Latin roots Cent = one hundred Percent = by the hundred Comparing raw score with a conceptual scale of 100 points Provides a reference for any raw score in relation to the rest of the scores. Percentile.

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Percentiles

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  1. Percentiles

  2. Percentages • Latin roots • Cent = one hundred • Percent = by the hundred • Comparing raw score with a conceptual scale of 100 points • Provides a reference for any raw score in relation to the rest of the scores

  3. Percentile • “Defined as a point or position on a continuous scale of 100 theoretical divisions such that a certain fraction of the population of raw scores lies at or below that point.” • 75th percentile • 50th percentile • 33rd percentile

  4. Percentile as a Standard Score • Standard score - score derived from raw data and has a known basis for comparison • Allows us to compare scores more easily • What is more meaningful? • Balance index of 3.5 • Score was in the 65th percentile

  5. Standard Scores • Allow us to • Evaluate raw scores • Compare two sets of data that are based on different units of measure • Example • 3.5 on balance index • 120 Ft. lbs. of isokinetic torque in quadriceps

  6. Problems of Interpretation • Problem occurs at extreme ends of the scale for data sets with large numbers of scores • Ceiling effect • Learning curve • Easier to make improvements at beginning and middle of curve • More difficult at top • Plateau in curve

  7. Common Percentile Divisions • Quartiles • Deciles

  8. Calculating Using Percentiles • Rank order distributions • 10, 9, 9, 7, 7, 7, 6, 5, 5, 5, 4, 4, 3, 3, 1 • N = 15 • What percentile is the score 6? • What about 5? • What about 7? • Calculating raw score from percentile

  9. Calculating Using Percentiles • Simple frequency distributions • add number in frequency column from score

  10. Summary • Converting raw scores to standard scores is common • Standard scores allow us to compare 2 sets of data based on different units of measure • Percentile scores are most common standard score used

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