Data
 medium with which the behavior analyst works
 results of measurement
 empirical basis for decision making
Graphs Purposes and Benefits
 visual format for displaying data
 reveals relations between a seires of measurements and relevant variables
 how behavior analysts, organize, store, interpret, and communicate the results of our work
 3 purposes of graphs: CAID
 Communicate data
 Assess data correctly
 IV and DV (how they are related to each other)
 5 Benefits of Graphs
 immediate picture of individual's behavior
 allows you to explore variations in behavior as they are occuring
 acts as a judgmental aid to help you interpret the results of a study or treatment
 acts a conservative method for determining the significance of behavior change  behavior change that is statistically significant may not look impressive on a graph
 allows for an independent judgment and evaluation of the data
 Communicate data
 Assess data correctly
 IV and DV (how they are related to each other)
 immediate picture of individual's behavior
 allows you to explore variations in behavior as they are occuring
 acts as a judgmental aid to help you interpret the results of a study or treatment
 acts a conservative method for determining the significance of behavior change  behavior change that is statistically significant may not look impressive on a graph
 allows for an independent judgment and evaluation of the data
5 Types of ABA Graphs
LBCSS Little Boys Sure Can Scream
 Line Graphs
 Bar Graphs
 Semilogarithmic Charts
 Cumulative Recrods
 Standard Celeration Chart
Equal Interval Graphs
(Arithmetic Charts; AddSubtract Charts)
 graphs in which the distance between any 2 consecutive points on both the x and y axis are always the same
 all intervals are the same size
 4 types of equal interval graphs:
 line graphs
 bar graphs
 cumulative records
 scatter plots
 nonequal interval graphs
 logarithmic and semilogarithmic (standard celeration chart)
 look at behavior change through proportionate or relative change
Line Graphs
(Frequency Polygons)
 most common graph in ABA
 based on the cartesian plane 2 dimensional area formed by 2 perpendicular lines that intersect
 use a balanced ratio between the hieght and width of the axes
 y axis should be shorter than x axis
 each point on the line graph shows the level of some quantifiable dimension of the DV in relation to the IV in effect when the data was recorded
 comparing data points lets us examine level, trend, and variability
 communicate the following relevant quantitative relations
 data that can be scaled along some dimension, such as time or the order of responses in a sequence
7 Parts of a Line Graph
 Horizontal Axis (X Axis; Abscissa)

represents the passage of time and the presence, absence, or value of the IV
 left to right passing of time in equal intervals
 utilize a scale break (//) to represent discontinuities in time
 Vertical Axis (Y Axis; Ordinate)
 represents the full range of values of the DV (i.e. the quanitfiable aspect of the target behavior)
 on an equal interval line graph, the scaling of the y axis is really important to see changes in level, trend, and variability

ORIGIN intersection of the horizontal and vertical axis
 represents the zero value of the DV
 Condition Change Lines
 the vertical lines drawn upward from the x axis to show poiints in time at which changes in the IV occured
 solid line = major change
 dashed line = minor change
 Condition Labels
 Data Points
 each data point has two meanings
 a quanitfiable measure of the target behavior recorded during a given obsercation period
 the time and/or experimental conditions under which that particular measurement was conducted
 coordinates of a data point are displayed as (x,y)
 Data Path
 connects successive data points with a straight line
 illustrates level and tred of behavior between two consecutive data points
 max of 4 data paths per graph
 Figure Caption
 concise statement that provides information to identify the IV and DV
 explains symbols
 represents the passage of time and the presence, absence, or value of the IV
 left to right passing of time in equal intervals
 utilize a scale break (//) to represent discontinuities in time
 represents the full range of values of the DV (i.e. the quanitfiable aspect of the target behavior)
 on an equal interval line graph, the scaling of the y axis is really important to see changes in level, trend, and variability

ORIGIN intersection of the horizontal and vertical axis
 represents the zero value of the DV
 the vertical lines drawn upward from the x axis to show poiints in time at which changes in the IV occured
 solid line = major change
 dashed line = minor change
 each data point has two meanings
 a quanitfiable measure of the target behavior recorded during a given obsercation period
 the time and/or experimental conditions under which that particular measurement was conducted
 coordinates of a data point are displayed as (x,y)
 connects successive data points with a straight line
 illustrates level and tred of behavior between two consecutive data points
 max of 4 data paths per graph
 concise statement that provides information to identify the IV and DV
 explains symbols
When NOT to connect points on a line graph
 data points fall on either side of a condition change line
 time has passed and the behavior was not measured
 there was a discontinuity in time of the x axis
 data were not collected, lost, etc
 it is follow up or post check data
Line Graph Variations
 two or more dimensions of the same behavior
 two or more different behaviors
 measure the same behavior under different conditions
 changing values of the IV
 same behavior of two or more participants
Bar Graphs
(Histograms)
 based on the cartesian plane (as in line graphs) but no distinct data points
 use bar graphs when:
 displaying separate sets of data that ARE NOT related to each other
 summarizing performance within a condition or a group of individuals
Cumulative Records
 developed by Skinner to record data in EAB research as a device called the cumulative recorder
 cumulative because responses keep getting added during the observation period to the total number of previously recorded responses
 the steeper the slope, the higher the rate of responding
 the y axis value represents the total number of respnses recorded since the very start of data collectionuntil the graph hits its upper limit and it resets to zero and begins to rise again
 cumulative records generally are used for rate/frequency data
2 Types of Cumulative Record Response Rates
 Overall Response Rate
 an average rate of response over a given time period such as druing a specific session or 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
 Local Response Rate
 an average rate of response 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 the data on the graph
 an average rate of response over a given time period such as druing a specific session or 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
 an average rate of response 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 the data on the graph
When to Use a Cumulative Record
 the target behavior can be measured in cumulative units (ex. number of cans recycled)
 the target behavior only occurs once per observation period
 the cumulative record shows how rapidly or slowly the target responses are repeated
 the cumulative record can be used as personal feedback (e.g. self management programs)
 the effects of the IV are easier to detect on a cumulative record
 reveal more intricate details between behavior and environmental variables
 reveal more intricate details between behavior and environmental variables
Semilogarithmic Charts
(Ratio Chart; MultiplyDivide Chart)
 logarithmic scales look at behavior change through PROPORTIONAL or RELATIVE change
 x axis = equal intervals
 y axis = scaled LOGARITHMICALLY
 SEMIlogarithmic graphs in which one axis is scaled logarithmically
 all behavior changes of equal proportion are shown by equal vertical distances on the vertical axis
 Ex. a doubling of response rate from four to eight responses/minute would appear on a semilogarithmic chart as the same amount of change as doubling from 50 to 100 responses/minute
 data that is shown as an exponential curve on an equal interval chart is a straight line on a semilogarithmic chart
 all behavior changes of equal proportion are shown by equal vertical distances on the vertical axis
Standard Celeration Chart
 a type of semilogarithmic chart created by Ogden Lindsley to be used in Precision Teaching to chart academic and social behaviors
 provides a standardized means of charting and analyzing how frequency of behavior changes over time
 instead of going up by 10's, the scales go up by MULTIPLES
 students can selfmonitor their progress within a fixed period of time
 allows for data to be squeezed into progressively tighter and tighter bundles and the slope looks the same whether you start iwth a very high or a very low level of behavior
 Ex. one child's correct responding improved from 2 to 4 and the other from 10 to 20. on the graph, both would show having improved 100%
 Ex. one child's correct responding improved from 2 to 4 and the other from 10 to 20. on the graph, both would show having improved 100%
When to use a Standard Celeration Chart
 use when your primary concern is promoting rate of responding
 research shows the more rapid and fluent the rate of correct responding, the more durable the learning
Scatter Plots
 shows relative distribution of individual measures in a data set
 data points are NOT connected
 depict changes in vlaue on one axis correlated with changes in vlaue on the other axis
 use when you want your data to effectively communicate the following relevant quantitative relations
 the temporal distribution of the bheavior
 the grouping of the individual data points may help to identify elusive enviornmental stimuli
 the temporal distribution of the bheavior
 the grouping of the individual data points may help to identify elusive enviornmental stimuli
Ethical Warning for Choosing Graphs
you must use the method that demonstrates the most ethical and valid representation of the target behaviorNOT a graph that skews the target behavior
3 Fundamental Properties of Behavior Change in Graphs
LTV
 Level
 Trend
 Variability
Level
(one of the 3 Fundamental Properties of Behavior Change in Graphs)
 the 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
 Levels are examined by looking at mean, median, and/or range

Two types of Level Lines

Mean Level Line horizontal line drawn through the data points of the vertical axis equaling the average or mean vlaue of the data
 caution may obscure important variability

Median Level Line horizontal line drawn through the data points on the vertical axis that shows the most typical performance within a condition
 better than the mean level line when your data has extreme outliers

Mean Level Line horizontal line drawn through the data points of the vertical axis equaling the average or mean vlaue of the data
Trend
(one of the 3 Fundamental Properties of Behavior Change in Graphs)
 overall direction taken by the path
 the general direction and rate of increase or decrease in which data move over time
 Trend is described in terms of:
 Direction
 increasing
 decreasing
 zero trend
 Degree
 gradual
 steep
 extend of variability around the trend
 Direction
 TREND LINE (LINE OF PROGRESS)  straight line drawn through the data to show the trend
 freehand
 mathematical formula Ordinary Least Swuares Linear Regression Equation
 Split Middle Line of progress (best method for drawing trend line)
6 Steps to a Split Middle Line of Progress
CDMMQS
 Count count how many data points are on the graph
 Divide divide the graph in half with a vertical line
 Mid Rate for each half of the graph, find the middle values on the y asiz for each half of the data points
 Mid Date for each half of the data, draw a vertical line for the middle points
 Quarterly Intersect Line of Progress  connect the 2 intersections of mid date and mid rate
 Split MIddle Line of Progress  shift the quarterly intersect line up for down (keep it paralell to itself) so that an equal number of points fall above and below it
Variability
(one of the 3 Fundamental Properties of Behavior Change in Graphs)
 the extent to which the data bounce around the graph
 question to ask how consistent is the change that is taking place
 frequency and degree to which multiple meausres 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