Tally marks and stopwatch times are raw data. Before your supervisor can compare one session to the next, those numbers usually need to be summarized. This lesson covers the three summaries you will calculate most often as an RBT: rate, mean duration, and percentage.
Why it matters
A count of 20 means very little on its own. Twenty requests in 10 minutes is a lot; twenty requests in a full school day is not. Summaries put every session on the same scale so a graph shows real change instead of differences in session length or number of trials.
Your supervisor makes the treatment decisions, but those decisions rest on the numbers you calculate and enter. A wrong denominator or a unit mix-up can make a skill look mastered when it is not, or make a behavior look worse than it is.
Key ideas
- Every summary is a division problem. The skill is knowing what goes on top and what goes on the bottom.
- Rate: count ÷ observation time.
- Mean duration per episode: total duration ÷ number of episodes.
- Percentage: (part ÷ total) × 100.
- Match the summary to the data. Rate fits behavior that can happen at any time, such as hitting or requesting, especially when session length varies. Percentage fits data with a set number of opportunities, such as discrete trials or task-analysis steps. Duration summaries fit behavior where how long it lasts matters.
- Use one unit before you calculate. Convert minutes and seconds to the same unit first. A time of 1 minute 30 seconds is 90 seconds or 1.5 minutes, never "1.30 minutes."
- Keep the raw numbers. Report a percentage along with the count behind it (for example, 17 of 20). A percentage built on only two or three opportunities can swing wildly from one response.
- Combine before you divide. To get one percentage across several sessions, add all the correct responses and all the opportunities, then divide. Averaging session percentages gives a short session too much weight.
- Calculate, don't interpret beyond your role. Enter accurate summaries and flag anything that looks unusual. Deciding what the data mean for the program is your supervisor's job.
Definitions
- Rate: the number of responses per unit of time, such as per minute or per hour. Rate lets you compare sessions of different lengths. Many ABA texts use frequency to mean the same thing, but some data sheets use "frequency" for a raw count, so check which your program means.
- Total duration: the sum of the time across all episodes in a session. It shows how much of the session the behavior took up. See duration.
- Mean duration per episode: total duration divided by the number of episodes. It shows how long a typical episode lasted.
- Percentage: a part divided by a total, multiplied by 100. Common forms are percentage correct (correct trials ÷ total trials), percentage of task-analysis steps completed independently, and percentage of session time.
- Percentage of intervals: the number of intervals scored ÷ the total number of intervals, × 100. It is an estimate based on interval recording or momentary time sampling, not an exact percentage of time.
Examples from a session
Three summaries, three learners
- Rate (clinic): Noah, age 4, hands over a picture card to request 30 times during a 2-hour session. His rate is 30 ÷ 2 = 15 requests per hour, or 0.25 per minute.
- Mean duration (home): Grace, age 10, has three episodes of crying lasting 2, 4, and 6 minutes. Total duration is 12 minutes. Mean duration is 12 ÷ 3 = 4 minutes per episode. In a 60-minute session, crying took up 12 ÷ 60 × 100 = 20% of the time.
- Percentage (school): Diego, age 16, practices reading a bus schedule. He answers 15 of 20 trials correctly and independently, so his percentage correct is 15 ÷ 20 × 100 = 75%.
Notice how each summary answers a different question. Noah's rate tells the team how often. Grace's total and mean durations tell them how much time and how long each time. Diego's percentage tells them how accurate he is when given a set number of chances.
Non-example (mixed units): Episodes last 1 minute 30 seconds, 2 minutes, and 45 seconds. Writing them as 1.30 + 2 + 0.45 and dividing by 3 gives 1.25 minutes, which is wrong. Convert to seconds first: 90 + 120 + 45 = 255 seconds, and 255 ÷ 3 = 85 seconds, or 1 minute 25 seconds.
Common mistakes / exam traps
- Flipping the division. Rate is count ÷ time, not time ÷ count. Eighteen responses in 45 minutes is 0.4 per minute, not 2.5.
- Counting prompted responses as correct. When the data sheet scores only independent responses as correct, prompted trials go in the denominator but not in the numerator.
- Dividing by trials planned instead of trials run. If a session ends after 20 of 25 planned trials, divide by 20. Trials that never happened are not opportunities.
- Averaging percentages across sessions. Two of 2 correct (100%) and 17 of 20 correct (85%) is not 92.5% overall. It is 19 of 22, about 86%.
- Treating interval data as exact time. If partial-interval recording scores behavior in 30% of intervals, that does not mean the behavior lasted 30% of the session. Partial-interval recording tends to overestimate, and whole-interval recording tends to underestimate.
- Comparing raw counts across sessions of different lengths. Convert to rate first.
Exam trap
Rate vs. mean duration vs. percentage: watch the denominator. Rate divides by time, mean duration divides by the number of episodes, and percentage divides by the total number of opportunities, steps, intervals, or minutes.
Exam trap
Total duration vs. mean duration: total duration is the sum of every episode (how much of the session), and mean duration divides that sum by the number of episodes (how long a typical one lasted). If a question asks "per episode" and your answer is the sum, you stopped one step early.
Quick check
During a 45-minute session, a learner has three tantrums lasting 3, 5, and 7 minutes. What is the mean duration per tantrum?