Add meaning to a raw score Percentiles Add meaning to a raw score How does a score compare relative to a specific group? 8/10/2019 HK 396 - Dr. Sasho MacKenzie

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. 8/10/2019 HK 396 - Dr. Sasho MacKenzie

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 8/10/2019 HK 396 - Dr. Sasho MacKenzie

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. 8/10/2019 HK 396 - Dr. Sasho MacKenzie

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 8/10/2019 HK 396 - Dr. Sasho MacKenzie

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. 8/10/2019 HK 396 - Dr. Sasho MacKenzie

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. 8/10/2019 HK 396 - Dr. Sasho MacKenzie

Percentile for 300 lb Squat Rank Lbs 1 375 2 365 3 360 4 330 5 320 6 315 7 300 8 260 9 10 250 11 240 12 220 13 185 14 180 15 170 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. 8/10/2019 HK 396 - Dr. Sasho MacKenzie

What about duplicate scores? Rank Lbs 1 375 2 365 3 360 4 330 5 320 6 315 7 300 8 260 9 10 250 11 240 12 220 13 185 14 180 15 170 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. 8/10/2019 HK 396 - Dr. Sasho MacKenzie

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. 8/10/2019 HK 396 - Dr. Sasho MacKenzie

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. 8/10/2019 HK 396 - Dr. Sasho MacKenzie

Male NCAA 100 m Sprint Frequency Time (s) Percentile 9.8 11.4 10.6 11.0 10.2 11.8 12.6 13.0 12.2 50 100 150 200 250 300 Frequency 97 50 84 70 90 30 10 3 16 Percentile 8/10/2019 HK 396 - Dr. Sasho MacKenzie