Module 2

Figure 6.2 Major Parts of a Simple Line Graph

(1) Horizontal axis (2) Vertical axis (3)Axis labels (4) Condition change lines (5) Condition labels (6) Data points (7) Data Path (8) Figure caption

Precision teaching, has been developed for use with the Standard Celeration Chart

- Learning is best measured as a change in response rate - Learning is most often occurs through proportional changes in behavior - Past changes in performance can project future learning

Parts of a Line Graph

-Horizontal axis -Vertical axis -Condition change lines Condition labels -Phase and condition -Data points -Data path -Figure Caption

Fundamental Properties of Behavior Change

-Level -Trend -Variability

Types of Graphs Utilized in ABA

-Line graph -Bar graphs -Cumulative record -Semilogarithmic charts ◦ Standard Celeration -Chart Scatterplots

Data

-Medium with which the behavior analyst works -Empirical basis for decision making

Line Graph Variations

-Two or more dimensions of the same behavior -Two or more different behaviors -Measure of the same behavior under different conditions -Changing values of the independent variable -Same behavior of two or more participants

Purpose and Benefits of Graphic Displays of Behavioral Data

1. Gives the practitioner immediate access to an ongoing visual record of the participant's behavior 2. Enables the researcher to explore interesting variation in behavior as they occur 3. Judgmental aids: interpret results of a study 4. Determining the significance of behavior change 5. Enable independent judgements and interpretations of the significance of behavior change 6. Provide feedback to the people whose behavior the graph depict 7. Facilitate communication, dissemination, and a comprehension of behavior change among a wide variety of recipients

Lecture Verification #1 Name all three fundamental properties of behavior change.

1. Level 2. Trend 3. Variability

Cumulative graph may be preferable in four situation:

1. When the total number of responses emitted over time is important 2. When used as a source of feedback for clients 3. When the target behavior can occur or not occur once per observation session 4. Reveal the intricate relations between behavior and environmental variables

A line graph should have a scale of _____________________ between the y-axis and the x-axis.

2:3

Celeration

A factor by which frequency multiples or divides per unit of time

Miguel wants to create a standardized visual display that will demonstrate frequency over time. His best option would be: A. Standard Celeration Chart B. Bar Graph C. Scatterplot D. Line

A. Standard Celeration Chart

The same behavior under different and alternating experimental conditions

Allows direct visual comparisons of differences, as well as relative changes in performance over time

Constructing Line Graphs

An effective graph presents data ◦ Accurately ◦ Completely ◦ Clearly ◦ Makes visual analysis as easy as possible ◦ Does not create distortion or bias interpretation

Michelle wants to create a visual display that will compare the same behavior of two or more participants. Her best option would be: A. Standard Cerleration Chart B. Line Graph C. Scatterplot D. None of the above

B. Line Graph

Jerome wants to create a visual display to help determine what time of day his client exhibits higher frequencies of the target behavior. His best option would be: A. Line Graph B. Scatterplot C. Standard Cerleration Chart D. Cumulative Record

B. Scatterplot

Present a measure of central tendency

Bar Graphs

Used frequently to summarize the performance of a participant of group of participants during different conditions

Bar Graphs

Line Graph

Based on the Cartesian plane ◦ Two-dimensional area formed by intersecting lines ◦ Points on the plane represent relationships -Level of the dependent variable when the independent variable was in effect ◦ Comparisons of data points reveals the presence or absence of changes in level, trend, and/or variability

Dominique wants to create a visual display that will display discrete sets of data that are not related to one another. Her best option would be: A. Line Graph B. Standard Celeration Chart C. Bar Graph D. Scatterplot

C. Bar Graph

A factor by which frequency multiples or divides per unit of time

Celeration

Linear measure of frequency change across time

Celeration

What's standard about the standard celeration chart?

Consistent display of celeration

Lecture Verification #2 This type of graph is also known as a histogram and is useful in summarizing behavioral data allowing for a quick comparison of performance across participants and/or conditions. A) line graph B) scatterplot C) Cumulative record D) Bar graph

D) Bar graph

Sam wants to create a visual display that will capture cumulitive responses. Her best option would be: A. Standard Celeration Chart B. Line Graph C. Bar Graph D. Cumulative Record

D. Cumulative Record

Empirical basis for decision making

Data

Medium with which the behavior analyst works

Data

Results of measurement

Data

Direct and Repeated Measurement of Behavior

Data ◦ Medium with which the behavior analyst works ◦ Results of measurement ◦ Empirical basis for decision making ◦ Singular -Datum is ◦ Plural -Data are

Data (Plural)

Data are

Data (Singular)

Datum is

Standard Celeration Chart

Developed by Ogden Lindsley Standardized method for ◦ Charting & analyzing how frequency of behavior changes over time Four standard charts ◦ Difference in scaling on horizontal axis -Daily chart -Weekly chart -Monthly chart -Yearly chart What's standard about the standard celeration chart? ◦ Consistent display of celeration Celeration ◦ Linear measure of frequency change across time ◦ A factor by which frequency multiples or divides per unit of time -Acceleration - accelerating performance -Deceleration - decelerating performance Standard chart ◦ Six, X 10 cycles (vertical axis) -1 per 24 hrs -1,000 per minute ◦ Bottom left to top right corner -Slope of 34° - celeration value X2

Cumulative Record

Developed by Skinner ◦ Primary means of data collection in EAB ◦ Cumulative recorder -Experimental subject draws its own graph ◦ Shows the number of responses on the ordinate against time on the abscissa ◦ Number of responses recorded and added to the total number of responses recorded during previous observations -Cumulative ◦ Y-Axis (vertical axis) -Represents the total number of responses recorded since the start of data collection ◦ Display -Total number of responses at any given point in time ◦ Relative rates of response -The steeper the slope, the higher the response rate ~Overall response rate ~Local response rate

Two or more dimensions of the same behavior

Enables visual analysis of the dependent variable on the same graph

Constructing Line Graphs Figure Caption & Printing

Figure caption ◦ Printed below the graph ◦ Concise, complete description of figure -Direct viewers attention to features of the graph that may be overlooked ~E.g., scale changes -Describe the meaning of any added symbols Print graphs in one color - black

Display relationships between dependent variable and independent variable

Graphic displays

Facilitates of accurate analyses

Graphic displays

Primary function communication

Graphic displays

Summarization of data collected

Graphic displays

Simple formats for visually displaying relationships among and between a series of measurements and relevant variables of quantitative information

Graphs

Level

Indicated by the relationship of the data points with the vertical axis. -High, Moderate, Low (Think about measuring the average height)(

Indicated by the relationship of the data points with the vertical axis.

Level

Most common graphic format

Line Graph

Two-dimensional area formed by the intersection of two perpendicular reference lines, called axes

Line Graph

What is the most commonly used graph in applied behavior analysis?

Line graph

_____________________ are the based on the Cartesian plane, a two-dimensional area formed by the intersection of two perpendicular lines and uses on data points.

Line graphs

Celeration

Linear measure of frequency change across time

The behavior of two or more participants

Maximum of four different data paths can be displayed effectively on one set of axes

Trend

Overall direction of data path. -increasing, decreasing, zero trend

Constructing Line Graphs Data Points & Data Paths

Place each data point in the exact coordinate of the horizontal and vertical axis Use bold, easily discernable symbols ◦ Use a different symbol for each set of data Draw data paths using a straight line ◦ The center of each data point in a given data set to the center of the next data point in the same set DO NOT CONNECT DATA POINTS IF... ◦ Points fall on either side of a condition change line ◦ A significant span of time passed and behavior was not measured ◦ There was a discontinuity in time in the horizontal axis (e.g., school vacation) -Data were not collected, lost, etc. ◦ It is follow-up or post-check data -Unless intersession time span same as original experiment ◦ Data points fall beyond the values described by the vertical axis Use different styles of lines for multiple data paths on the same graph Clearly identify what each data path represents ◦ Use arrows or a legend

Standard Celeration Chart & Precision Teaching

Precision Teaching ◦ Instructional decision-making system ◦ Developed for use with standard celeration chart Position ◦ Learning best measured as a change in response rate ◦ Learning most often occurs through proportional changes in behavior ◦ Past changes can predict future learning Chart uses estimations for most frequency values

Variability

Range of data points around the mean. -Increasing variability makes it difficult to predict future patterns, which is necessary to achieve experimental control.

Suitable for displaying proportional change

Ratio Charts

Semilogarithmic Charts

Ratio or multiply-divide charts ◦ One axis is scaled proportionally ◦ Double response rate 4 to 8 same as 50 to 100 All behavior changes of equal proportion are shown by equal vertical distances on the vertical axis

Graphic display that shows the relative distribution of individual measures in a data set with respect to the variables depicted by the x- and y-axes

Scatterplots

Show how much changes in the value of the variable depicted by one axis correlate with changes in the value of the variable represented by the other axis

Scatterplots

Scatterplot

Shows relative distribution of individual measures in a data set Data points are unconnected Depicts changes in value on one axis correlated with changes in value on the other axis Patterns suggest certain relationships ◦ Sometimes used to discover the temporal distribution of the target behavior

Displays celeration, a linear measure of frequency change across time; frequency multiplies or divides per unit of time

Standard Celeration Chart

Provide a standardized means of charting and analyzing how frequency of behavior changes over time

Standard Celeration Chart

Overall direction of data path.

Trend

True or False: Applied behavior analysts quantify behavior change with direct and repeated measurements

True

True or False: Because behavior change is dynamic and ongoing, behavior analysts strive for direct and continues contact with the target behavior

True

True or False: Each point on a line graph shows the level of some quantifiable dimension of the target behavior in relation to a specified point in time and/or environmental condition

True

True or False: Graphic displays of behavioral data are an effective means of illustrating and communicating three fundamental properties of behavior change

True

True or False: Making valid and reliable decisions from raw data is difficult and inefficient

True

True or False: The data obtained throughout a behavior change program provide the empirical basis for every important decision

True

Constructing Line Graphs Drawing, scaling, & labeling axes

Use a balanced ratio between the height and width of the axes Relative length of the vertical axis to horizontal axis Horizontal axis ◦ Mark equal intervals ◦ Left to right chronological succession of equal time periods or response opportunities ◦ Use regularly spaced tic marks Scaling of vertical axis ◦ Most significant feature of the graph ◦ Mark the origin at zero ◦ Mark the full range of values represented in the data set ◦ If relatively small changes in performance are socially significant -Y-Axis should reflect a smaller range of values

Two or more different behaviors

Used to facilitate simultaneous comparison of the effects of experimental manipulations on two or more different behaviors

Range of data points around the mean.

Variability

Interpreting Graphically Displayed Behavioral Data

Visual analysis ◦ Did behavior change in a meaningful way? -If so, to what extent can that change in behavior be attributed to the independent variable? ◦ Identification of -Variability -Level -Trend "It is impossible to interpret graphic data without being influenced by various characteristics of the graph itself." ◦ Johnson & Pennypacker, 1993b, p. 320 Read the graph ◦ Figure caption ◦ Condition & axis labels ◦ Location of numerical value & relative significance of scale breaks Visually track each data path ◦ Are data paths properly connected? ◦ Is the graph distorted? Visual analysis ◦ Within conditions -Number of data points -Nature & extent of variability in the data -Absolute & relative level of the behavioral measure -Direction & degree of any trends in the data Visual analysis ◦ Between conditions -Level ~Mean or median level lines -Trend -Stability/Variability ~Across similar conditions Level ◦ Value on the vertical axis around which a series of data points converge ◦ Stability -When data points fall at or near a specific level ◦ Mean or median lines -Added to represent overall average or typical performance -Use with caution - can obscure important variability Trend ◦ Overall direction taken by the data path -Direction ~Increasing, decreasing, or zero trend -Degree ~Gradual or steep -Extent of variability ◦ Trend line or line of progress -Freehand, least-squares regression equation, or split-middle line of progress Variability/Stability ◦ 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

Cumulative Record

When to use cumulative graph over noncumulative graph ◦ Progress toward a specific goal can be measured in cumulative units -E.g., Number of new words learned, quarters saved ◦ Graph is used as personal feedback -Total progress and relative rate of performance easily detected ◦ Target behavior can only occur once per observation period -Yes/No ◦ Intricate details between behavior & environmental variables are of interest -E.g., Within session analyses

Each data point on a _____________________ represents the total number of responses emitted by the subject since measurement began.

cumulative record

The bar graph shares most of the line graph's features except it does not have distinct _____________________ points representing successive response measures through time.

data

Applied behavior analysts quantify behavior change with _____________________ and _____________________ measurements - The product of these measurements is called data

direct, repeated

The data obtained throughout a behavior change program provide the _____________________ _____________________ for every important decision - Continue with current intervention - Implement a different intervention

empirical basis

The Standard Celeration Chart is a multiply/divide graph that enables the standardized charting of celeration, a linear measure of _____________________ change over time, a factor by which frequency multiples and divides per unit of time.

frequency

According to Johnston and Pennypacker (2009), graphs have one fundamental purpose: to affect the_____________________behavior of the graph reader.

interpretive

Condition change lines should be placed to the _____________________ of the data point representing the last measure prior to the change in conditions.

right

A _____________________ shows the relative distribution of individual measure in a data set with respect to the variables depicted by the x and y axes.

scatterplot

Even though it is still prevalent in the field, you should refrain from using "sessions" as a label on the horizontal access and instead be sure that you use a unit of_____________________.

time

An essential structure to the line graph is that the _____________________ axis is clearly labeled with a quantitative measure and the _____________________ axis is labeled with a time unit.

vertical horizontal

Constructing Line Graphs (1 of 4)

• An effective graph presents the data accurately, completely and clearly • Drawing, scaling and labeling axes - A vertical axis approximately two-thirds the length of the horizontal axis - The horizontal axis should be marked in equal intervals, each unit representing, from left to right, the chronological succession of equal time periods in which behavior was measured - Discontinuities in the progression of time should be indicated on the horizontal axis by a scale break - The social significance of various levels of behavior change for the behavior being graphed should be considered when scaling the vertical axis - Label the horizontal and vertical axes

Scatterplots

• Graphic display that shows the relative distribution of individual measures in a data set with respect to the variables depicted by the x- and y-axes • Data points are unconnected • Show how much changes in the value of the variable depicted by one axis correlate with changes in the value of the variable represented by the other axis • Sometimes use scatterplots to discover the temporal distribution of a target behavior

Parts of a Basic Line Graph

• Horizontal Axis: Also called x-axis, a straight horizontal line that often represents time, presence, absence, and/or value of the independent variable • Vertical Axis: Also called y-axis, a vertical line drawn upward from the left-hand end of the horizontal axis. Most often represents a range of value of the dependent variable • Axis Labels: Brief descriptions of the dimensions represented by each axis • Condition Change Lines: Vertical lines drawn from the horizontal axis to show points in time at which changes in the independent variable occurred • Condition Labels: Single words or brief descriptive phrases printed along the top of the graph. These identity the experimental condition • Data Points: Represents a quantifiable measure of the target behavior recorded and the time and/or experimental conditions • Data Path: Connecting successive data points within a given condition with a straight line • Figure Caption: Concise statement identify the independent and dependent variables

Constructing Line Graphs (2 of 4)

• Identify experimental conditions - Condition change lines; vertical lines extending upward from the horizontal axis indicate changes in treatment or experimental procedures - Condition labels; identifying the conditions in effect during each period of an experiment

Constructing Graphs with Computer Software

• Most computer generated graphs are produced with Microsoft Excel software • Save time • Enable more frequent data-based decisions

Constructing Line Graphs (3 of 4)

• Plot data points and draw data paths - Ensure that each data point is exactly on the coordinate it represents - Data points should be marked with bold symbols - Data paths are created by drawing a straight line from each data point to the next data point in the same set, except: ▪ Data points falling on either side of a condition change line ▪ Across a significant span of time in which behavior was not measured ▪ Across discontinuities of time in the horizontal axis ▪ Data points on either side of a regularly scheduled measurement period in which data were not collected, lost, destroyed, or not available ▪ Follow-up or postcheck data points

Constructing Line Graphs (4 of 4)

• Plot data points and draw data paths - When multiple data paths are displayed on the same graph, different styles of lines, in addition to different symbols for the data points, may be used to help distinguish one data path from another • Write figure caption - Concise but complete description of the figure • Print graph - Graphs should be printed in only one color - black

Cumulative Records

• Skinner invented the cumulative recorder, a device that automatically draws a graph of a subject's rate of behavior • A cumulative record is constructed by adding the number of responses recorded during each observation period to the total number of responses recorded during all previous observation periods • The steeper the slope, the higher the response • Overall response rate is the average rate of response over a given time period • Local response rate refers to the rate of response during periods smaller than that for which an overall rate has been given. • Cumulative graph may be preferable in four situation: 1. When the total number of responses emitted over time is important 2. When used as a source of feedback for clients 3. When the target behavior can occur or not occur once per observation session 4. Reveal the intricate relations between behavior and environmental variables

Ratio Charts

• Suitable for displaying proportional change • Ratio scale, equal vertical distances correspond to equal ratios of change in the variable being measured • The horizontal axis is marked off in equal intervals and only the vertical axis has a ration scaling

Variations of the Simple Line Graph: Multiple Data Paths

• Two or more dimensions of the same behavior - Enables visual analysis of the dependent variable on the same graph • Two or more different behaviors - Used to facilitate simultaneous comparison of the effects of experimental manipulations on two or more different behaviors • The same behavior under different and alternating experimental conditions - Allows direct visual comparisons of differences, as well as relative changes in performance over time • Changes in target behavior relative to the changing values of an independent variable • The behavior of two or more participants - Maximum of four different data paths can be displayed effectively on one set of axes

What are the benefits of graphic display and visual analysis of behavioral data?

◦ Immediate access to record of behavior ◦ Variations prompt exploration ◦ Provides judgmental aid -Relatively easy to learn, no predetermined level for determining significance of change, no mathematical properties required ◦ Conservative method ◦ Encourages independent judgment & interpretation ◦ Effective source of feedback

Bar Graph

◦ No distinct data points representing successive response measures through time ◦ Functions -Displaying and comparing discrete sets of data that ARE NOT related by a common underlying dimension by which the horizontal axis can be scaled (Example) -Visual summary of participant or group performance during different experimental conditions ◦ Provides efficient summary of data ◦ DOES NOT allow for analysis of variability & trends in behavior

Graphic displays

◦ Primary function communication ◦ Display relationships between dependent variable and independent variable ◦ Summarization of data collected ◦ Facilitates of accurate analyses