Percentage
A percentage is a ratio expressed as parts per 100: the number of occurrences divided by the total, multiplied by 100.
Percentage is a derived measure, built from two counts. The formula is: (number of target events ÷ total number) × 100. In teaching programs the most common form is percentage correct: correct responses divided by total opportunities, times 100. If a client answers 7 of 10 trials correctly, that is 70% correct. Interval data are also reported as percentages (scored intervals ÷ total intervals × 100), and so is interobserver agreement.
Percentage is useful when the number of opportunities varies from session to session or is set by the teacher, as in discrete-trial teaching. It puts results on the same 0 to 100 scale, which makes them easy to graph and compare with a mastery criterion such as 80% across three sessions.
Percentage has two important limits. First, it hides the size of the total: 1 of 2 and 50 of 100 are both 50%, but the second is far more convincing. Small totals make each response swing the percentage widely, which is why mastery criteria often require a minimum number of trials. Second, it says nothing about time, so it cannot show how fast a client responded. RBTs should record the actual counts as well as the percentage so the supervisor can see both.
Example and non-example
| Example | An RBT runs 12 trials of a receptive identification program; the client is correct on 9. The percentage correct is 9 ÷ 12 × 100 = 75%. |
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| Non-example | Reporting that a client asked for help 9 times in 45 minutes (0.2 per minute) is a rate, because it divides by time, not by a total. |
Don't confuse it with
| Rate | Percentage divides by the total number of opportunities or intervals; rate divides by time. |
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| Trials to criterion | Percentage summarizes performance in one session; trials to criterion counts how many trials it took to reach a goal. |
Test yourself
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Question 1During a 20-minute independent work period, an RBT's duration data show that a student was working for a total of 14 minutes. What percentage of the period was the student working?
Show answer
D: 70%. Divide the duration of the behavior by the length of the observation and multiply by 100: 14 ÷ 20 = 0.70, or 70%.
- A: 14 is the number of minutes worked, not a percentage of the period.
- B: 30% is the share of the period the student was not working (6 of 20 minutes).
- C: 60% would mean 12 minutes of work out of 20.
Task A.1 · 40-hour curriculum section C
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Question 2Data from partial interval, whole interval and momentary time sampling procedures are usually summarized as:
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A: the percentage of intervals scored. Each interval is scored as an occurrence or a nonoccurrence. The summary is the number of scored intervals divided by the total number of intervals, times 100.
- B: Responses per minute is rate, which needs a count of every response; interval procedures do not count responses.
- C: Average length per response is mean duration, which requires timing each occurrence.
- D: Time from cue to response is latency, a continuous measure.
Task A.2 · 40-hour curriculum section C
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Question 3An RBT uses partial interval recording with 30 intervals. Hitting is marked in 12 of them. What should the RBT report?
Show answer
C: 40% of intervals. Divide scored intervals by total intervals and multiply by 100: 12 ÷ 30 = 0.40, or 40% of intervals.
- A: 12 is the number of scored intervals, not a percentage.
- B: 18 is the number of intervals without hitting, not a percentage.
- D: 60% would mean 18 of the 30 intervals were scored.
Task A.2 · 40-hour curriculum section C
Answer every question to see your score.
On the RBT exam
This term belongs to task A.6 Calculating and summarizing data in content area A, Data Collection and Graphing, which is 13 of the 75 scored questions.