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