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Percentiles

Percentiles. Add meaning to a raw score How does a score compare relative to a specific group?. Percentile. A point or position on a continuous scale of 100 theoretical divisions such that a certain fraction of the group of raw scores lies at or below that point.

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Percentiles

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  1. Percentiles Add meaning to a raw score How does a score compare relative to a specific group? HK 396 - Dr. Sasho MacKenzie

  2. Percentile • A point or position on a continuous scale of 100 theoretical divisions such that a certain fraction of the group of raw scores lies at or below that point. • If a score is at the 75th percentile, then it is greater than or equal to 75% of all the scores. HK 396 - Dr. Sasho MacKenzie

  3. Why use Percentiles? • People are very familiar with the scale that ranges from 0 to 100. • Percent values have instant meaning. • He sank 1292 out of 1407 free throws, is less clear than… • He sank 92% of his free throws HK 396 - Dr. Sasho MacKenzie

  4. Percentiles are Standard Scores • A standard score is a score that is derived from raw data and has a known basis of comparison. • Percents are one type of standard score. • For percents, the center is 50% and the range is from 0% to 100%. • Raw scores are measured values, standard scores are derived from raw scores and provide more information. HK 396 - Dr. Sasho MacKenzie

  5. Standard Scores allow… • Instant evaluation of a raw score • Comparison of scores having different units of measurement. • Is bench pressing 200 lbs more impressive than squatting 300 lbs? • More info (mean and SD) is required to answer this question • Or, we could convert the scores to percentiles HK 396 - Dr. Sasho MacKenzie

  6. Lifts in Percentiles… • 200 lb bench is at the 70th percentile. • 300 lb squat is at the 60th percentile. • Therefore, the person has a “better” bench relative to the group. HK 396 - Dr. Sasho MacKenzie

  7. How to calculate Percentiles • Start with a list of raw scores. • Sort the scores from highest to lowest. • This is also called ranking the scores • Choose a particular score to convert. • Count the number of scores that fall at or below the chosen score. • Divide the count by the total number of scores and multiply by 100. HK 396 - Dr. Sasho MacKenzie

  8. Percentile for 300 lb Squat • There are 9 scores at or below 300 lbs. • There are 15 scores in total • Percentile = (9/15)*100 • Percentile = 60% • A 300 lb squat is better than 60% of the group. HK 396 - Dr. Sasho MacKenzie

  9. What about duplicate scores? • Still use “at or below” the score • Percentile = (8/15)*100 • Percentile = 53% • Both individuals have the same squat of 260 lbs, so they are both at the 53rd percentile. • Round percentile to nearest integer. HK 396 - Dr. Sasho MacKenzie

  10. Software Programs • Software programs, such as Excel, use functions such as PERCENTRANK(), and PERCENTILE() to help determine percentiles of a group. • They are based on equations that are slightly more complex than the previous method, but the basic idea is the same. HK 396 - Dr. Sasho MacKenzie

  11. Ceiling Effect and Score Improvement • Is it more difficult for a 100 m sprinter to improve their time from 11.4 to 11.0 s or from 10.2 to 9.8 s? • Both have an improvement of 0.4 s, but improving from 10.2 to 9.8 s is more difficult. • In contradiction, the sprinter’s change in percentile would be less when improving from 10.2 to 9.8 s. • This is known as the ceiling effect. HK 396 - Dr. Sasho MacKenzie

  12. 300 250 200 150 100 50 0 10.6 12.6 9.8 10.2 11.0 11.4 11.8 12.2 13.0 Time (s) 97 90 84 70 50 30 16 10 3 Percentile Male NCAA 100 m Sprint Frequency HK 396 - Dr. Sasho MacKenzie

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