1. Introduction to Behavior Data Interpretation

Effective behavior intervention relies on accurate interpretation of collected data. This comprehensive guide provides educators and behavior analysts with the tools and techniques necessary to transform raw behavioral data into actionable insights that drive student success.

🎯 Core Principle

Data interpretation is not about finding what we expect to see, but rather discovering what the data actually tells us about student behavior and intervention effectiveness.

Why Data Interpretation Matters

Proper data interpretation enables us to:

Identify functional relationships between interventions and behavior change
Detect emerging patterns before they become significant problems
Make objective decisions about intervention modifications
Communicate progress effectively to stakeholders
Ensure interventions are truly effective, not just coincidentally timed

The Interpretation Process

Stage	Key Activities	Common Pitfalls
1. Data Preparation	Clean data, check for missing values, organize by date/session	Including unreliable data points
2. Visual Inspection	Create graphs, identify obvious patterns	Over-interpreting random variation
3. Systematic Analysis	Apply visual analysis rules, calculate statistics	Ignoring clinical significance
4. Contextualization	Consider environmental factors, student history	Overlooking external variables
5. Decision Making	Determine intervention effectiveness, plan next steps	Making hasty decisions

Types of Behavioral Data

📋 Common Data Types

Frequency/Rate: Number of occurrences per unit time
Duration: How long behavior lasts
Latency: Time between prompt and response
Intensity: Magnitude or force of behavior
Percentage: Proportion of opportunities or intervals
Trials to Criterion: Learning acquisition data

2. Visual Analysis Fundamentals

Visual analysis is the primary method for interpreting single-subject design data in behavior analysis. This systematic approach allows practitioners to identify meaningful patterns and changes in behavior over time without relying solely on statistical tests.

The Six Components of Visual Analysis

1️⃣ Level

The mean or average value of data within a phase

2️⃣ Trend

The direction and slope of the data path (increasing, decreasing, or flat)

3️⃣ Variability

The degree of fluctuation or bounce in the data

4️⃣ Immediacy of Effect

How quickly behavior changes after intervention introduction

5️⃣ Overlap

The proportion of data points that overlap between phases

6️⃣ Consistency

Similar patterns across similar phases or conditions

Creating Effective Graphs

Graph Element	Best Practice	Purpose
X-Axis	Time dimension (sessions, days, dates)	Shows progression over time
Y-Axis	Behavior measure (0 to max observed + 20%)	Displays behavior magnitude
Phase Lines	Solid vertical lines between conditions	Indicates intervention changes
Data Points	Connected with lines, different shapes for conditions	Shows individual measurements
Labels	Clear, descriptive phase labels	Identifies conditions

Example: Well-Constructed Behavior Graph

💡 Pro Tip

Always include at least 5 data points in baseline and intervention phases for reliable visual analysis. Fewer points make it difficult to establish patterns and assess stability.

3. Identifying Behavior Patterns

Recognizing patterns in behavioral data is crucial for understanding the function of behaviors and predicting future occurrences. This chapter explores common patterns and their implications for intervention.

Common Behavioral Patterns

1. Cyclical Patterns

🔄 Characteristics

Regular ups and downs in behavior frequency
Often tied to schedule or routine changes
May indicate setting events or biological rhythms

Example: Monday spikes in challenging behavior after weekends

Intervention Implication: Focus on transition supports and Monday morning routines

2. Extinction Burst

📈 Characteristics

Temporary increase in behavior when reinforcement is removed
Often accompanied by increased intensity or variation
Typically followed by decrease if intervention maintained

Example: Tantrums increase initially when attention is withheld

Intervention Implication: Prepare team for increase; maintain consistency

3. Scalloped Pattern

〰️ Characteristics

Low rates after reinforcement, increasing as next opportunity approaches
Common with fixed-interval schedules
Indicates schedule control

Example: Work completion increases just before scheduled breaks

Intervention Implication: Consider variable-ratio reinforcement schedule

Pattern Detection Strategies

Strategy	When to Use	How to Apply
Moving Average	High variability data	Calculate 3-5 point average to smooth data
Split-Middle Line	Determining trend	Divide phase in half, find median of each, connect
Envelope Analysis	Assessing variability	Draw lines connecting peaks and valleys
Lag Analysis	Delayed effects	Compare behavior to events from previous sessions

⚠️ Caution

Avoid "seeing" patterns that don't exist. Random variation can sometimes appear meaningful. Look for patterns that repeat across multiple phases or conditions before drawing conclusions.

Environmental Pattern Analysis

Environmental Factors Checklist

Time of day effects (morning vs. afternoon)
Day of week patterns
Before/after specific activities
Staffing changes or substitutes
Peer presence or absence
Weather or seasonal effects
Medication timing
Hunger/satiation states

4. Trend Analysis Techniques

Trend analysis reveals the direction and rate of behavior change over time, essential for evaluating intervention effectiveness and predicting future behavior patterns.

Determining Trend Direction

Trend = (Last 3 data points average - First 3 data points average) / Number of sessions

Trend Classifications

Trend Type	Description	Interpretation
Accelerating ↗	Increasing slope over time	Behavior increasing rapidly
Decelerating ↘	Decreasing slope over time	Behavior decreasing rapidly
Stable →	Minimal slope (±5% of mean)	No significant change
Variable ↝	Inconsistent direction	Unstable pattern
Curvilinear ⤴	Changing slope direction	Initial change then plateau

Split-Middle Method

📐 Step-by-Step Process

Divide data points in phase into two equal halves
Find median date and median rate for each half
Mark these two points on the graph
Draw line through both points
Adjust line up or down so 50% of points fall above and below

Trend Stability Criteria

80% Rule

A trend is considered stable if at least 80% of data points fall within 15% of the trend line. This criterion helps determine when to change phases or modify interventions.

Celeration Line

Celeration = (Behavior at Time 2 / Behavior at Time 1) ^ (1 / Days Between)

Celeration values:

×2.0: Behavior doubling each period
×1.0: No change
×0.5: Behavior halving each period

💡 Best Practice

Project trend lines from baseline into intervention phases (dashed line) to visualize what would have happened without intervention. This helps assess intervention impact.

5. Level and Variability Assessment

Understanding the level (central tendency) and variability (spread) of data is fundamental to determining intervention effectiveness and making phase change decisions.

Measuring Level

Measure	Calculation	When to Use
Mean	Sum of all values / Number of values	Stable data without outliers
Median	Middle value when ordered	Data with outliers or trends
Mode	Most frequent value	Discrete categories
Trimmed Mean	Mean excluding top/bottom 10%	Occasional extreme values

Level Change Analysis

Level Change = Median(Intervention) - Median(Baseline)
Percentage Change = (Level Change / Median(Baseline)) × 100

Assessing Variability

Range-Based Measures

Range: Maximum - Minimum
Interquartile Range: 75th percentile - 25th percentile
Stability Envelope: Mean ± 15% of mean

Variance-Based Measures

Standard Deviation = √(Σ(x - mean)² / n)
Coefficient of Variation = (SD / Mean) × 100

Stability Criteria

Data is considered stable when:

80% of points fall within 15% of median level
No more than 25% variation from session to session
Coefficient of variation < 30%

Bounce and Cyclicity

Identifying Problematic Variability

Pattern	Concern Level	Action
Low bounce (CV < 20%)	Low	Proceed with analysis
Moderate bounce (CV 20-50%)	Medium	Look for patterns
High bounce (CV > 50%)	High	Investigate measurement issues
Extreme outliers	Very High	Verify data accuracy

⚠️ Important Note

High variability often indicates:

Multiple functions of behavior
Environmental inconsistency
Measurement problems
Competing interventions

Address variability before concluding intervention ineffectiveness.

6. Phase Change Analysis

Analyzing changes between phases (baseline to intervention, or between different interventions) is critical for determining intervention effectiveness and making data-based decisions.

The Six Questions of Phase Change

1. Is there a change in level?

Compare median or mean values between phases. A meaningful change typically exceeds 25% of baseline level.

2. Is there a change in trend?

Compare trend lines between phases. Look for changes in direction or slope steepness.

3. Is there a change in variability?

Compare stability envelopes. Reduced variability often indicates better behavioral control.

4. Is there immediacy of effect?

Examine first 3-5 data points after phase change. Immediate changes suggest strong intervention effects.

5. Is there overlap between phases?

Calculate percentage of data points that overlap. Less overlap indicates stronger effects.

6. Is the pattern consistent?

In reversal or multiple baseline designs, look for similar effects across replications.

Calculating Effect Sizes

Method	Formula	Interpretation
Percentage of Non-overlapping Data (PND)	% of intervention points exceeding baseline max/min	>90% very effective, 70-90% effective, <70% questionable
Percentage of All Non-overlapping Data (PAND)	% of all data points that don't overlap	>75% large effect, 50-75% medium, <50% small
Improvement Rate Difference (IRD)	Improvement in intervention - Improvement in baseline	>0.70 large, 0.50-0.70 moderate, <0.50 small

Phase Change Decision Rules

When to Change Phases

Baseline: Stable or counter-therapeutic trend (minimum 5 points)
Intervention: Stable trend in desired direction (minimum 5 points)
Crisis: Immediate change needed for safety
Plateau: No progress for 7+ sessions
Deterioration: Three consecutive points in wrong direction

💡 Pro Tip

Document all phase change decisions with rationale. Include environmental events, team decisions, and any protocol modifications to aid future interpretation.

7. Statistical Approaches

While visual analysis remains primary in single-subject designs, statistical methods can supplement interpretation and provide additional confidence in decision-making.

When to Use Statistics

High stakes decisions (placement changes, medication)
Subtle effects difficult to detect visually
Research or publication requirements
Comparing across multiple students or studies

Common Statistical Tests

Test	Purpose	Requirements
C Statistic	Detect trend in baseline	8+ data points
Tau-U	Measure effect controlling for baseline trend	5+ points per phase
Regression Analysis	Model trend and level changes	20+ total data points
Time Series Analysis	Account for autocorrelation	50+ data points

Autocorrelation

⚠️ Critical Consideration

Behavioral data often shows autocorrelation (today's behavior predicts tomorrow's). This violates assumptions of many statistical tests. Always check for autocorrelation before applying traditional statistics.

Lag-1 Autocorrelation = r₁ = Σ(xᵢ - x̄)(xᵢ₊₁ - x̄) / Σ(xᵢ - x̄)²

Effect Size Calculations

Standard Mean Difference (SMD)

SMD = (Mean_intervention - Mean_baseline) / SD_baseline

Interpretation: >0.8 large, 0.5-0.8 medium, <0.5 small

Reliable Change Index (RCI)

RCI = (X₂ - X₁) / √(2 × SE²)

Values >1.96 indicate statistically reliable change

Clinical vs. Statistical Significance

Remember: Context Matters

A statistically significant decrease from 100 to 95 aggressive incidents may be less meaningful than a non-significant decrease from 10 to 2 incidents. Always consider:

Social validity (does it matter to stakeholders?)
Clinical importance (does it improve quality of life?)
Practical significance (is the change noticeable?)

8. Making Data-Driven Decisions

Transforming data interpretation into actionable decisions requires systematic evaluation processes and clear decision rules that balance multiple considerations.

The Decision Framework

DECIDE Model

Define the decision needed
Examine the data thoroughly
Consider alternative explanations
Identify action options
Determine best course
Evaluate decision outcomes

Common Decision Points

Decision Type	Data Indicators	Action Criteria
Continue Current	Positive trend, decreasing variability	3+ consecutive points in desired direction
Modify Intervention	Plateau after initial progress	No change for 5+ sessions
Intensify Support	Insufficient progress rate	Below aimline for 3 consecutive points
Fade Support	Sustained improvement	At goal level for 10+ sessions
Change Strategy	No improvement or worsening	3+ points in wrong direction

Creating Aimlines

Daily Progress Needed = (Goal - Current Level) / Days Available

📊 Example Aimline Calculation

Current: 20% task completion
Goal: 80% task completion
Timeline: 30 school days
Daily progress needed: (80-20)/30 = 2% per day

Draw line from current level to goal, check actual progress against this line weekly.

Response to Intervention (RTI) Decisions

Tier Movement Criteria

Move to less intensive: Met goal for 4+ weeks
Maintain current tier: Making adequate progress
Move to more intensive: Below aimline for 3+ weeks
Consider evaluation: No response to Tier 3 for 6+ weeks

Team Decision-Making Protocol

Present Data: Share graphs with clear phase labels
Summarize Patterns: Describe level, trend, variability
Highlight Concerns: Note any decision points reached
Propose Options: Present 2-3 evidence-based alternatives
Consensus Building: Discuss pros/cons of each option
Document Decision: Record rationale and success criteria

💡 Decision Tip

When data are ambiguous, err on the side of less restrictive interventions while increasing data collection frequency to clarify patterns more quickly.

9. Reporting and Communication

Effective communication of data interpretation ensures all stakeholders understand student progress and support consistent implementation of interventions.

Audience-Specific Reporting

Audience	Focus	Format
Parents/Families	Progress toward goals, celebrations, next steps	Simple graphs, narrative summary, concrete examples
Administrators	Compliance, outcomes, resource needs	Dashboard summary, trend data, brief bullets
Team Members	Implementation details, data patterns, decisions needed	Detailed graphs, phase analysis, action items
Students	Personal progress, achievements, goals	Visual progress charts, sticker charts, self-monitoring

Progress Report Template

📝 Standard Progress Report Sections

Summary Statement
- Current performance level
- Progress toward goal
- Overall trend (improving/maintaining/declining)
Data Display
- Clear graph with phases labeled
- Goal line indicated
- Key data points highlighted
Interpretation
- Pattern description
- Environmental factors
- Intervention effectiveness
Recommendations
- Continue/modify/change decisions
- Specific next steps
- Timeline for review

Visual Communication Best Practices

📊 Graph Guidelines

Use color coding consistently (green=good, red=concern)
Include clear titles and axis labels
Highlight significant events with annotations
Show confidence intervals when appropriate
Provide context with comparison data

Writing Data Narratives

The DESC Method

Describe what the data show objectively
Explain the patterns and trends
Support with specific examples
Conclude with clear recommendations

Example Narrative

Sample Data Summary

"During baseline (Sessions 1-5), Johnny's on-task behavior averaged 35% of observed intervals, with high variability (range: 20-50%). Following implementation of the self-monitoring intervention (Sessions 6-15), on-task behavior immediately increased to 60% and showed a steady upward trend, reaching 85% by Session 15. Variability also decreased substantially (SD reduced from 12% to 5%). This 50% improvement exceeds our goal of 70% on-task behavior. We recommend continuing the current intervention while beginning to fade prompts for self-monitoring."

10. Tools and Resources

This chapter provides practical tools and resources to support accurate data interpretation and professional development in behavior analysis.

Essential Software Tools

Tool Category	Options	Best For
Data Collection	Classroom Pulse, BehaviorSnap, Catalyst	Real-time data entry and organization
Graphing	Excel, Google Sheets, GraphPad	Creating publication-quality graphs
Statistical Analysis	R, SPSS, SAS	Advanced statistical calculations
Visual Analysis	Tau-U Calculator, PND Calculator	Effect size calculations

Quick Reference Formulas

Percentage of Intervals: (Intervals with behavior / Total intervals) × 100

Rate: Frequency / Time

Trend Line Slope: (Y₂ - Y₁) / (X₂ - X₁)

Mean Level Change: Mean(Phase B) - Mean(Phase A)

Variability Ratio: SD(Phase B) / SD(Phase A)

Interpretation Checklist

Complete Analysis Checklist

Graph created with proper labels and phases
Visual analysis of level, trend, and variability
Effect size calculated
Environmental factors considered
Alternative explanations explored
Clinical significance evaluated
Recommendations developed
Report written for stakeholders

Professional Development Resources

Journals: Journal of Applied Behavior Analysis, Behavior Analysis in Practice
Books: "Single Case Research Methodology" (Ledford & Gast)
Online Courses: FIT Visual Analysis Training, UNT Graphing Tutorials
Professional Organizations: ABAI, APBA, CEC
Conferences: Annual ABAI Convention, State ABA conferences

Troubleshooting Common Issues

Problem	Possible Causes	Solutions
Can't detect pattern	High variability, insufficient data	Collect more data, examine environmental factors
Conflicting trends	Multiple behaviors, competing interventions	Separate data by context, simplify intervention
Plateau in progress	Ceiling effect, motivation loss	Adjust goals, modify reinforcement
Data drift	Observer bias, definition creep	Retrain observers, clarify definitions

Data Interpretation Guide

Table of Contents

1. Introduction to Behavior Data Interpretation

🎯 Core Principle

Why Data Interpretation Matters

The Interpretation Process

Types of Behavioral Data

📋 Common Data Types

2. Visual Analysis Fundamentals

The Six Components of Visual Analysis

1️⃣ Level

2️⃣ Trend

3️⃣ Variability

4️⃣ Immediacy of Effect

5️⃣ Overlap

6️⃣ Consistency

Creating Effective Graphs

💡 Pro Tip

3. Identifying Behavior Patterns

Common Behavioral Patterns

1. Cyclical Patterns

🔄 Characteristics

2. Extinction Burst

📈 Characteristics

3. Scalloped Pattern

〰️ Characteristics

Pattern Detection Strategies

⚠️ Caution

Environmental Pattern Analysis

Environmental Factors Checklist

4. Trend Analysis Techniques

Determining Trend Direction

Trend Classifications

Split-Middle Method

📐 Step-by-Step Process

Trend Stability Criteria

80% Rule

Celeration Line

💡 Best Practice

5. Level and Variability Assessment

Measuring Level

Level Change Analysis

Assessing Variability

Range-Based Measures

Variance-Based Measures

Stability Criteria

Bounce and Cyclicity

Identifying Problematic Variability

⚠️ Important Note

6. Phase Change Analysis

The Six Questions of Phase Change

1. Is there a change in level?

2. Is there a change in trend?

3. Is there a change in variability?

4. Is there immediacy of effect?

5. Is there overlap between phases?

6. Is the pattern consistent?

Calculating Effect Sizes

Phase Change Decision Rules

When to Change Phases

💡 Pro Tip

7. Statistical Approaches

When to Use Statistics

Common Statistical Tests

Autocorrelation

⚠️ Critical Consideration

Effect Size Calculations

Standard Mean Difference (SMD)

Reliable Change Index (RCI)

Clinical vs. Statistical Significance

Remember: Context Matters

8. Making Data-Driven Decisions

The Decision Framework

DECIDE Model

Common Decision Points

Creating Aimlines

📊 Example Aimline Calculation

Response to Intervention (RTI) Decisions

Tier Movement Criteria

Team Decision-Making Protocol