• Medium in which behavior analyst works
• Results of Measurement
• Empirical basis for decision making
• Difficult to understand behavior through raw data this is why we use graphs.

• Visual format for displaying data.
• Reveals relations between a series of measurements and relevant variables.
• Helps people make sense of quantitative information.
• How behavior analysts organize, store, interpret, and communicate the results of their work.

3 Purposes of Graphs

C. A. I/D.

1. Communicate: Communicates our data
2. Assess: Helps us to assess data correctly.
3. IV/DV: Shows how the DV and IV are related to each other.

1. Give you n immediate picture of an individual's behavior.
2. Allows you to explore interesting variations in behavior as they are occurring.
3. Acts as a judgmental aid to help you interpret the results of a study or treatment.
4. Acts as a conservative method for determining the significance of behavior change, because a behavior change that is statistically significant may not look impressive on a graph.
5. Allows for an independent judgment and evaluation of the data.

5 Types of ABA Graphs

L. B. Cr. Sc. scc. Sp.

1. Line Graphs
2. Bar Graphs
3. Cumulative Records
4. Semilogarithmic Charts
   • standard Celeration Charts
5. Scatter Plot

5 Types of ABA Graphs

L. B. Cr. Sc. scc. Sp.

Equal Interval Graph 

•  

  Equal Interval Graph 

  AKA Arithmetic Chart, Add-Subtract Chart

   

  1. Line
  2. Bar
  3. Cumulative Records
  4. Scatter Plot

• Graphs in which the distance between any 2 consecutive points on BOTH THE X-AXIS AND Y-AXIS are always the same.
• All intervals are the same size.
• Equal Interval Graphs:
  • Line
  • Bar
  • Cumulative Records
  • Scatter Plot
• Non-Equal INterval Graph:
  • Logarithmic scales, including semilogarithmic scales, (e.g., standard celeration chart), look at behavior change through proportionate or relative change.

Equal Interval Graphs

1. Line
2. Bar
3. Cumulative Records
4. Scatter Plot

• Most common graph in ABA.
• Comparing data points lets us examine level, trend, variability.
• Based on the CARTESIAN PLANE.
  • CARTESIAN PLANE: 2-dimensional area formed by 2 perpendicular lines that intersect.
• Use a balanced ratio between the height and width of the axes.
• Y-axis should be shorter than X-axis.
• Each point on a line graph shows the level of some quantifiable dimension of the DV in relation to the IV in effect when the data was recorded.

7 Parts of a line Graph

1. Horizontal Axis
2. Vertical Axis
3. Condition Change Line
4. Condition Labels
5. Data Points
6. Data Path
7. Figure Caption

7 Parts of a line Graph

1. Horizontal Axis
2. Vertical Axis
3. Condition Change Line
4. Condition Labels
5. Data Points
6. Data Path
7. Figure Caption

1. Horizontal Axis: (AKA X-Axis, Abscissa):

(X & A before Y & O)

• Represents passage of time (in equal intervals) and the presence, absence, or value of the IV.

7 Parts of a line Graph

1. Horizontal Axis
2. Vertical Axis
3. Condition Change Line
4. Condition Labels
5. Data Points
6. Data Path
7. Figure Caption

2. Vertical Axis (AKA Y-Axis, Ordinate):

(X & A before Y & O)

• Represents the full range on values of the DV (i.e., the quantifiable aspect of the target behavior). 
• Scaling of this axis is important to see changes in the level, trend, and variability in the data.
• Origin: Intersection of the horizontal and vertical axis.
  • Usually represents 0 value of DV.

7 Parts of a line Graph

1. Horizontal Axis
2. Vertical Axis
3. Condition Change Line
4. Condition Labels
5. Data Points
6. Data Path
7. Figure Caption

3. Condition Change Lines

• Vertical line drawn upwards from the X-Axis to show points in time at which changes in the IV occurred. 
  • Solid Lines: Major Changes
  • Dashed Lines: Minor Changes

7 Parts of a line Graph

1. Horizontal Axis
2. Vertical Axis
3. Condition Change Line
4. Condition Labels
5. Data Points
6. Data Path
7. Figure Caption

4. Condition Labels:

• A label written at the top and parallel to the X-Axis, that describes the experimental conditions in effect during each phase of research.

7 Parts of a line Graph

1. Horizontal Axis
2. Vertical Axis
3. Condition Change Line
4. Condition Labels
5. Data Points
6. Data Path
7. Figure Caption

5. Data Points:

• Each data point on the graph has two meanings:
  1. A quantifiable measure of the target behavior recorded during a given observation period.
  2. The time and/or experimental conditions under which that particular measurement was conducted.
• If there is more that 1 set of data on the graph, different symbols (♦×) are used to show this, ∅ colors on graphs.
• Coordinates of data point in graphs are always displayed as (x,y). 

7 Parts of a line Graph

1. Horizontal Axis
2. Vertical Axis
3. Condition Change Line
4. Condition Labels
5. Data Points
6. Data Path
7. Figure Caption

6. Data Path:

• Connects successive data points with a straight line. Illustrates level and trend of behavior between 2 consecutive data points.
• Data path should be examined to interpret graphs.
• Maximum of 4 data paths can / should be displayed on one set of axes. 

7 Parts of a line Graph

1. Horizontal Axis
2. Vertical Axis
3. Condition Change Line
4. Condition Labels
5. Data Points
6. Data Path
7. Figure Caption

7. Figure Caption

• Concise statement that provides information to identify the IV and DV. 
• Also explains symbols used and unplanned events.
• Printed below graph.

5 Types of ABA Graphs

L. B. Cr. Sc. scc. Sp.

Equal Interval Graphs

1. Line
2. Bar
3. Cumulative Records
4. Scatter Plot

• Based on the CARTESIAN PLANE.
  • CARTESIAN PLANE: 2-dimensional area formed by 2 perpendicular lines that intersect.
• There are NO distinct data points representing successive response measures through time.
• Does NOT ALLOW for analysis of variability and trend in behavior.
• USE BAR GRAPHS WHEN YOU WANT OYUR DATA TO EFFECTIVELY COMMUNICATE RELEVANT QUANTITATIVE RELATIONS:
  1. Displaying separate sets of data that are not related to each other.
  2. Summarizing performance within a condition or a group of individuals. 

5 Types of ABA Graphs

L. B. Cr. Sc. scc. Sp.

Equal Interval Graphs

1. Line
2. Bar
3. Cumulative Records
4. Scatter Plot

• Developed by Skinner to record data in EAB research 1957.
• "Cumulative Recorder" displays cumulative data.
• Cumulative Records used for rate/frequency data.
• Cumulative Recorder allows a subject to draw his/her own graph.
• Called "cumulative" because you keep adding on responses during each observation period to the total number of all previously recorded responses.
• The Y-Axis represents teh total number of responses recorded since the very start of data collection.
• When total number of responses exceeds upper limit of the Y-Axis scale; data path resets to 0 and begins to record again.

2 Types of Cumulative Record Response Rates

1. Overall Response Rate
2. Local Response Rate

• Steeper slope → higher response rate
• Rate / Frequency: Number of responses / time. 

1. Overall Response Rate: An average rate of response over a given time period, such as during a specific session of phase in a study.
   • Calculated by dividing the total # of responses recorded during the period by the # of observation periods indicated on the X-Axis.
2. Local Response Rate: An average rate of responding during periods of time smaller than that for which an overall response rate has been given.
   
   • Same calculation as overall response rate, but only using a small portion of teh data on the graph.

5 Types of ABA Graphs

L. B. Cr. Sc. scc. Sp.

4. Semilogarithmic Charts (AKA Ratio Chart, Multiply-Divide Chart)

• LOGARITHMIC SCALES look at behavior change through PROPORTIONAL or RELATIVE change.
  • X-Axis = In equal intervals (like other graphs)
  • Y-Axis = Scaled LOGARITHMICALLY
• Semilogarithmic Scale: Graphs in which one axis is scaled proportionally (e.g., Standard Celeration Chart). 
• On a semilogarithmic chart, all behavior changes of equal proportion are shown by equal vertical distances on the vertical axis.
• Data that is shown as an exponential curve on an equal interval chart is shown as a straight line on a semilogarithmic chart.

5 Types of ABA Graphs

L. B. Cr. Sc. scc. Sp.

4.1. Standard Celeration Chart

• A type of SEMILOGARITHMIC CHART.
• Ogden Lindsley created it to be used in the ABA educational methodology; Precision Teaching.
• Academic and Social behaviors are charted. 
• Provide a standardized means of charting and analyzing how frequency of behavior changes over time.
• Scales go up by multiples of 2,4,6,8,16, 32 etc. or 10, 100, 1,000 etc.
• Students SELF-MONITOR their progress by recording data that makes a graph that displays the number of items performed correctly and the number of error made within fixed periods of time distributed across the day or week.
• GOAL: To increase the number correct and decrease the number incorrect within the same set.
• Allows data to be squeezed into progressively tighter bundles.

5 Types of ABA Graphs

L. B. Cr. Sc. scc. Sp.

5. Scatter Plot

• Show relative distribution of individual measures in a data set.
• Data points unconnected.
• Depict changes in value on one axis correlated with changes in value on the other axis.
• Use scatter plots when you want data to effectively communicate the following relevant quantitative relations:
  • The temporal distribution of the behavior
  • Grouping of individual data points may also help to identify elusive environmental stimuli.

3 Fundamental Properties of Behavior Change

L. T. V.

1. Level
2. Trend
3. Variability

3 Fundamental Properties of Behavior Change

1. Level
2. Trend
3. Variability

1. Level

• Value on the VERTICAL axis around which a series of data measures converge.
• A change in level is illustrated when the data's average value changes.
• An analysis of level answers the question: "How much has behavior changed?
• Levels in data are examined by analyzing data's mean, median, range
  1. Mean Level Line: Horizontal line drawn through the data points on the vertical axis equaling the AVERAGE or MEAN value of teh data.
  2. Median Level Line: Horizontal line drawn through the data points on the vertical axis that shows the most typical (middle) performance within a condition.
     • Better to use when data has extreme outliers.

3 Fundamental Properties of Behavior Change

1. Level
2. Trend 
3. Variability

2. Trend

• OVERALL direction taken by the data path.
• The general direction and rate of increase or decrease in which data move over time.
• An analysis of trend answers the question: "In what direction is the change headed?"
• Described in terms of their:
  • Direction:
    • Increasing
    • Decreasing
    • Zero trend
  • Degree:
    • Gradual
    • Steep
  • Extend of Variability of data points around the trend.
• TREND LINE(or LINE OF PROGRESS): Straight line drawn through the data to show the trend.
  • To draw trend lines:
    • Freehand (not very accurate)
    • Mathematical formula: Ordinary Least-Squares Linear Regression Equation (time consuming and complicated)
    • Split-Middle Line of Progress (best) (page 208 PTBAE)

3 Fundamental Properties of Behavior Change

1. Level
2. Trend 
3. Variability

3. Variability

• The extent to which the data 'bounces around' on the graph.
• An analysis of variability answers teh question: "How consistent is the change that is taking place?"
• Frequency and degree to which multiple measures of behavior yield different outcomes.
  • High degree of variability = Little or no control over the factors influencing behavior.

Visual Analysis of Temporal Relations

of Data Within and Between Conditions

• Visual analysis of temporal relations of data WITHIN conditions:
  • Examining the data w/in each condition, determine the level, trend, and variability in each condition.
• Visual analysis of temporal relations of data BETWEEN conditions:
  • Comparing the data in the different conditions, determine whether change in trend level and variability occurred and to what extent any changes were significant.