Chapter 6
On a cumulative record the steeper the slope
..the higher the response rate
Each data point on a graph represents two facts
1. A quntifiable measure of the target behavior recorded during an observation period 2. Tthe time and/or experimental conditions under which that particular measurement was conducted
Eventhough cumulative records derieved from continous recording are the most descriptive displays of behavioral data available, two other features of behavior in addition to the comparison of very high rates, can be difficult to determine on some cumulative graphs1. One although he total number of responses
1. Although the total number of responses since data collection began can be easily seen on a cumulative graph, the number of responses recorded for any given session can be hard to ascertain, given the number of data points and scaling of the vertical axis 2. The gradual changes in slope from one rate to another can be hard to detect on cumulative graphs
Data paths are created by drawing a straight line from the center of each data point in a given data set to the center of the next data point in the same set
1. Data points falling on either side of the condition change line are not connected 2. Data points should not be connected across a sinificant span of time in which behavior was not measured 3. Data points should not be connected across disconuities of time across the horizontal axis 4. Data points on either side of regularly scheduled measurement period in which data were not collected or were lost, destroyed, or otherwise not available should not be joined together 5. Follow up or post check data points should not be connected with another unless they represent successive measures obtained during the rest of the experiment If a data point falls beyond the values described by the vertical axis scale, breaks should be made in data path connecting that data point with those that fall within the described range
Visual analysis of data from an applied behavioral analysis study is conducted to answer two questions
1. Did the behavior change in a meaningful way 2. If so, what extent can that change in behavior be attributted to the independent variable
Parts of a basic line graph
1. Horizontal axis 2. Vertical axis 3. Condition change lines 4. Condition labels 5 Data points 6. Data path 7. Figure caption
Visual formats for graphic display of data most often used in ABA are
1. Line graphs 2. bar graphs 3. cumaltive records 4. semilogarthic charts 5. Scatter plots
Six benifits of graphic display
1. Plotting each measure of behavior on a graph right after the observational period provides the practitioner or researcher with immediate access to an ongoing visual record of the participants behavior 2. Direct and continual contact with the data in a readily analyzable format enables the researcher as well as the teacher to explore interesting variations in behavior as they occur 3. Graphs are judgemental aids, devices that help practioners of experimenter interpret the results of a study or treatment 4. Visual analysis is a conservative method for determining the significance of behavior change 5. graphs enable the encourage independent judgments of the meaning 6. Effective source of feedback to the people whose behavior change they represent
Data given a condition are examined to determine
1. The number of data points 2. The nature and extent of variability in the data 3. The absolute and relative level of the behavioral measure 4. The direction and degree of any trends in the data
Certain fundental properties common to all behavioral data
1. Trend 2. Level 3. Variability
Graphs with multipkl data paths are used frequently in ABA to show
1. Two or more dimensions of behavior 2. Two or more different behaviors 3. The same behavior under different and alternating experimental conditions 4. Cchanges in the target behavior relative to the changing values of independent variables 5. The behavior of two or more participants
Bar graphs serve two major functions
1. Used for displaying and comparing discrete sets of data that are not related to one another by a common underlying dimension by which horizontal axis can be scaled 2. To give a visual summary of the performance of a participant or group of participants during different conditions of an experiment
Four situations in which a cumulative graph may be preferable to a noncumulative graph
1. When the total number of responses made over time is important or when progress toward a specific goal can be measured in cumulative units of behavior 2. When the graph is used as a source of feedback for the participant 3. When the target behavior is one that can occir only once per observation session(check) 4. Can reveal the intricate relations between the behavior and environmental variables
When multiple data sets are plotted on the same sets of axes
a different geometric symbol should be used for each set of data
When the same manipulation of an independent variable occurs at different points along the horizontal axes of multiple tier graphs
a dog leg connecting the condition change lines from one tier to the next makes it easy to follow the sequence and timing events in the experiment
When many different values must be plotted within a small distance on the vertical axis
a graph paper with many grid lones per inch should be used
The y axis most often represents
a range of values of the dependent variable, which in applied behavioral analysis is always some quantifiable dimension of behavior
However, when two sets of data with widely different and no overlaping ranges are displayed against the same y axis
a scale break can be used to seperate the range of measures encompassed by each data set
Dsicontinous in the progression of time on the horizontal axis should be indicated by
a scale break, an open spot in the axis with a squiggly line at each end
visual analysis
a systematic examination to interpret graphically displayed data
When measurement occurs across consecutive observations rather than standard units of time, the horizontal axis still serves as
a visual representation of the progression of time because the data plotted against it have been recorded one after the other
Should a data point fall beyond the range of values described by the vertical axis scale, it is plotted just
above the scale it transcends with the actual value of the measurement printed in parentheses next to the data point
The relative legth of the vertical axis to the horizontal axis, in combination with the scaling of the axes, determines the degree to which a graph will
accentuate or minimize the variability in a given data set
When Cummulative records are plotted by hand or created with a computer graphing program, which is most often the case the number of responses recorded during each observation period is
added to the total number of responses recorded during all previous observation periods
Condition change lines should be placed
after the data point representing the last measure prior to the change conditions signified by the line and before the data point representing the first measure obtained after the change procedure
On multiple graphs, one label identifying the diminsion portrayed on
all of the vertical axes can be centered along the axes of the graph
Each equally spaced unit on the horizontal axis should represent
an equal passage of time
A brief label printed
and centered to the left and parallel to the vertical axis, should identify the dimension by which the axis is scaled
Logarithmic scales are well suited to display
and communicate proportional change
In general less lengthy phases are required of experiments investigating realtions between previously studied
and well established variables if the results are also similiar to those of pervious studies
On a logarithmic scale equal relative changes in the variable being measured
are represented by equal distances
The legibility of graph is enhanced by a balanced ratio
between the height and widthso the data are neither too close together nor too spread apart
The vertical axis should not be extended
beyond the hatch mark indicating the highest value on the axis scale
The symbols for each dach data set should be selected so that the value of each data point
can be determined when data points fall near or on the same conditions on the graph
Unplanned events that occur during an experiment or treatment program, as well as minor changes in procedure that do not warrant a condition change line
can be indicated by placing small arrows, asterisks, or other symbols next to the relevant data points
Also there is little purpose in repeated measurement in situations in which the subject
cannot logically perform the behavior
Lables identifying the conditions in effect during each period of an experiment are
centered above the space delineated by the condition change lines. Whenever space permits, condition labels should be parallel to the horizontal axis
In multi tier graphs, equal distances on each vertical axis should represent equal changes in behavior to aid the
comparison of data across tiers
The social significance of various levels of behavior change for the behavior being graphed should be
considered in scaling the vertical axis
Must maintain direct and continous
contact with the behavior under investigation
In most instances, scale breaks should not be used on the vertical axis, especially if a
data path would cross th break
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 distuinguish one data path from another
Graphing an individuals behavior on the same set of axes allows
discrete visual comparisons of differences in absolute levels of responding at any given time as well as relative changes in performance over time
Dpending on the levels and variability of the data encompassed by each data paths can be
displayedeffectively on one set of axes, however there is no rule
The horizontal axis should be marked in
equal inervals, with each unit representing from left to right the chronological succession of equal time periods or response opportunities in which the behavior was measured and from which an interpretation of behavioral change is to be made
The exception occurs when the total number of responses has
exceeded the upper limit of the y axis
Horizontal numbering of regularly spaced tic marks on the vertical axis
facilitates use of the scale
Cumulative records are almost always used with
frequency data, although other dimensions of behavior such as duration and latency, can be displayed
Variability
how often and the extent to which multiple measures of behavior yield different outcomes
The dimenesion by which the horizontal axis is scaled should be identified
in a breif label printed and centered below the parallel to the axis
Grpahs should be printed
in only one color, black and white
Condition labels
in the form of single words or brief descriptive phrases, are printed along the top of the graph and parallel to the horizontal axis
Figure caption
is a consise statement that, in combination with the axis and conditon label, provides the reader with sufficient information to identify the independent and dependent variable
Scatteplots
is a graphic display that shows relative distribution of individual measures in data set with respect to the variables depicted by the x and y axes
Overall response rate
is the average rate of responding over a given period of time, such as during a specificsession, phase, or condition of an experiment.
Data
is the medium with which BCBA's work.
Nor are many data points required to demonstrate that behavior did not occur when in fact
it had no opportunity to occur
Increasing the distance on the vertical axis between each unit of measurement
magnifies the variability in the data
Therefore one shoulf use a median level line instead of a
mean level line to graphically represent the central tendency of a series of data points that include several outliers, either high or low
Contracting the units of measurement on the vertical axis
minimizes the protrayal of variability axis
The bar graph does not have distinct data points representing successive response measures through time. Bbar graphs can take a wide variety of forms to allow quick and easy comparisons
of performance across participants and/or conditions
Also, whenever possible similiar positions
on each vertical axis of multiple tier graphs should represent similiar absolute values of the dependent variable
Scatter plots 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
Line graph
or frequency polygon, is the most common format for displaying data in ABA
Bar graph
or histogram, is a simple and versatile format for graphically summarizing behavioral data
Cummulative records show the
overall and local response rates
The behavior represented by each data path should be clearly identified either by
printed labels with arrows drawn to the data path or by a legend showing models of the symbols and line styles
semi logarithmic chart
refers to graphs in which only one axis is scaled proportionally
Local response rate
refers to the rate of response during periods of time smaller than for which an overall rate has been given
Data path
represents the lvel and trend of behavior between successive data points, and it is a primary focus of attention in the interpretation and analysis of graphed data
As a rule, fewer data points are needed in subsequent replications of an experiment if the data depict the
same level and trend in performance that were noted in earlier applications of the condition
The graph maker should plot the data
set against several different vertical axis scales, watching distortion of the graphic display that might lead to wrong interpretations
When relatively minor changes occur within in overall condition, dashed vertical lines
should be used to distinguish minor changes from major changes, which are shown by solid lines
Condition change lines
show points in time which changes in the independent variable occurred
On semi log charts all behavior changes of equal proportional are
shown by equal vertical distances on the vertical axis, regardless of the abolute value of those changes
Scale breaks on the x axis can also be used to
signal periods of time when data were not collected or when regularly spaced data points represent consecutive measurements made at unequal intervals
Graphs
simple formats for visually displaying realtionships among and between a series of measurements and relevant vriables
When the data set includes sveral measures of 0
starting the vertical axis at a point slightly above the horizontal axis keeps the data points from falling directly on the axis
Patterns of data points falling along the lines on the plane or clusters
suggest certain realtionships
Bar graphs sacrifice the the presentation of variability and trends in behavior, in exchange for the efficiency of
summarizing and comparing large amounts of data in a simple, easy to interpret format. They should be viewed with the understanding that they mask important variability in the data
The data obtained throughout a behavior change program or a research study are means for that contact, they form
the basis for every important decision
To producd a visual representation of an overall rate on a cumulative graph
the first and last data points of a given series of observations should be connected with a straight line
Familiarity with the response class measured and the conditions under which it was measured may be
the graph viewers buggest aid in determining how many data points constitute believability
In ABA, each point in a line graph shows
the level of some quantifiable dimensionn of the target behavior in relation to a specified point in time and/or environmental conditions
As a general rule, the more measurements of the dependent variable per unit of time and the longer the period of time in which measurement occured
the more confidence once can have in the data path's estimation of the true course of behavior change
Rate is
the number of esponses emitted per unit of time, usually reported as reponses per minute in ABA
In scientific usage the word data means
the result of measurement, usually in quatified form
Vertical axis
the vertical axis also called the y axis is a vertical line
If relatively small numerical changes in performance are socially significant
the y axis scale should reflect a smaller range of values
When two data sets travel the same path
their lines should be drawn close to and parallel with one another to help clarify the situation
Multiple data point graphs are also used
to show changes in behavior relative to changing values of the independent variable
Ethical concerns do not permit the repeated measurement of certain behaviors
under experimental conditions in which there is little or no expectation for improvement
Rrelative rates of responding can be determined by
visually comparing one slope to another, the steeper the slope, the higher rate of response
Cumulative records
was developed by Skinner as the primary means of data collection in the experimental analysis of behavior. A device called the cumulative recorder enables a subject to actually draw its own graph
A vertical axis that is approximately two thirds the length of the horizontal axis
works well for most graphs
When the differences in behavioral measures from one tier to another
would result in overly long vertical axis, a scale break can be used to highlight the differences in absolute values, gain aiding a point to point comparison of y axis positions
Horizontal axis
x axis , is a straight horizontal line that most often represents the passage of time and presence, or absence, and/or value of the independent variable