1. 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 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.
8/10/2019
HK 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
8/10/2019
HK 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.
8/10/2019
HK 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
8/10/2019
HK 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.
8/10/2019
HK 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.
8/10/2019
HK Dr. Sasho MacKenzie

8. 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 Dr. Sasho MacKenzie

9. 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 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.
8/10/2019
HK 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.
8/10/2019
HK Dr. Sasho MacKenzie

12. 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 Dr. Sasho MacKenzie