A.6 Calculate & Summarize

By RBThub February 23, 2026

Raw data is like raw ingredients. You can't just hand a BCBA a bag of flour and an egg and call it a cake. You have to mix it, bake it, and present it.

In ABA, "Frequency" (the raw count) is often useless on its own. We need to Calculate (do the math) and Summarize (make it readable). This section teaches you how to turn raw numbers into Rates and Percentages.

Executive Summary

This video serves as a "Math Class for RBTs." It breaks down the three essential calculations you will use daily: Rate (standardizing frequency over time), Mean Duration (calculating average time), and Percent Correct (measuring accuracy). Understanding these ensures you are providing the BCBA with usable data, not just raw noise.

⏱️ Video Timeline

00:00
Introduction to Rate
Why raw counts are misleading. Rate standardizes data (e.g., "10 hits" vs. "10 hits per hour").
02:20
Calculating Rate
Formula: Count ÷ Time. Examples include hand raising and aggression.
06:31
Mean (Average) Duration
How to find the average length of a behavior (Total Duration ÷ Occurrences). Useful for tantrums.
10:18
Percent Correct
Used for Discrete Trial Training (DTT) and quizzes. Formula: Corrects ÷ Opportunities × 100.

🔑 Key Insights

Rate: Use this when session times vary. (2 hours vs. 4 hours).
Mean Duration: Do we want the behavior to get shorter (tantrums) or longer (studying)?
Percentage: The gold standard for measuring skill acquisition (learning new things).
The Goal: Data must drive decisions. If the rate isn't going down, the intervention isn't working.

❓ Frequently Asked Questions

Q: Why not just use Frequency?
A: Because sessions have different lengths. 10 behaviors in 1 hour is very different from 10 behaviors in 8 hours. Rate fixes this.
Q: Can I combine these?
A: Yes! You might track the Rate of tantrums (how often) AND the Mean Duration (how long).

1. Calculating Rate

Formula: Count ÷ Time = Rate
The "Human" Translation: Think of a speedometer. "60 miles" is just a distance (Frequency). "60 miles per hour" is a speed (Rate). Rate tells us the tempo of the behavior.
FREQUENCY TIME 10 Hits ÷ 2 Hours = 5 / hr RATE
Example

Scenario: The client hit 10 times during a 2-hour session.
Math: 10 (Count) ÷ 2 (Hours) = 5 hits per hour.

2. Calculating Percentage

Formula: (Correct Responses ÷ Total Opportunities) × 100
The "Human" Translation: This is just like a school test grade. If you got 8 questions right out of 10, you got an 80%.
CORRECT TOTAL TRIALS 8 Correct 10 Total x 100 = 80%
Example

Scenario: You asked the client to "Touch Nose" 10 times. They did it correctly 8 times.
Math: 8 ÷ 10 = 0.8 -> 80%.

📝 Knowledge Check

Grab your calculator (or use your brain)!

Q1: A client screamed 20 times in a 4-hour session. What is the Rate?

Answer: 5 screams per hour.
20 ÷ 4 = 5.

Q2: Why is "Percentage" better than "Count" for a spelling test?

Answer: Because the list might have different numbers of words. 10/10 is better than 10/20. Percentage standardizes the score.
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Calculations Quiz

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