4- displaying and interpreting behavioral data Flashcards
Dimensionless quantities
Partial interval, whole interval, momentary time sample
A systematic form of data examination, characterized by visual inspection of graphical displays of those data
Visual data analysis
1 embedded in text
2 summary form, usually as a structured data table, numerical representation
- graphical form (A visual representation of data)
Types of data display
Equal interval line graph
Cumulative records
Bar graph
Semilogarithmic graphs
Graphic displays used in ABA
Based on a “Cartesian” plane, a two dimensional area formed by the intersection of two perpendicular lines (One vertical, one horizontal)
They form a + shape
Invented by Renee Descartes
Equal interval line graph
Any point within the plane of the chart represents a specific relationship between the two variables (Dimensions) Measured along each of the axis lines
AKA Equal-Interval line graph
Simple line graph
Most commonly use format for charting ABA data
Used to evaluate treatment effectiveness
Used in functional analysis
Common uses of line graphs
The horizontal X – axis The vertical Y – axis Data points The data path Condition and condition phase change line Condition and phase change labels Figure legend
Parts of an equal interval line graph
X – axis
The abscissa
Represents the passage of time
Horizontal axis
Data analysis animates the discipline of ABA the way the nervous system animates
The human body
In APA, it allows for the evaluation of the effects on behavior, I’ve experimental or clinical manipulation.
Typically, these data are presented as repeated measures overtime
Visual analysis
- Taking an overview of an entire data display, noting it’s general characteristics such as a type of display, range and continuity of each axis, specific variables under consideration, and,
- Specific data inspection and analysis such as evaluating Trends, level, and variability of data, both within and across phases.
Visual analysis: The process
- Was very meaningful change in behavior?
2. To what extent can the change be attributable to a specific environmental change
Visual analysis; the purpose
Termed criterion by inspection
Cornerstone of behavior analytic research and practice
Visual analysis
Ryan engage in an average of to ask of flipping furniture for six hour school day, over the course Of the ten-day baseline face. The range was between zero and four per day. During the 15 days of the first intervention phase, Ryan engaged in…
Example of data in text
A.k.a. chart, is a relatively simple visual format for displaying data
Provides visual representations of relationships between a series of measurements and relevant variables
Device used for organizing summarizing interpreting and communicating the results of ABA
Graphs
Provides immediate access to an ongoing visual record of behavior and that’s promotes the continuous evaluation
Unexpected variations in data can lead to more complete analysis
They aid in judgment and interpretation of data more quickly and with less training then required by statistical evaluation
More conservative than statistical analysis
Provide Visual feedback to person whose behavior is being graphed and the individuals who are collecting the data
Tables and data are embedded within a text may be use as adjunct to graphs
Some benefits of using graphs
A type of Bar Graph
Histogram
A type of Standard celeration chart
Semilogarithmic graph
Marked according to the needs of the behavior analyst, to promote the most useful analysis
Can be marked as consecutive calendar days, weeks, or months; or by consecutive school days or by sessions classes or any specified recorded observation. Over a period of time
X axis units
Y – axis
The ordinate
Represents range of values of dependent variable, some quantified dimension of the target behavior
Moving from the zero point upwards along the LetterY axis, each point represents an increase value of the DV (the target bx)
The vertical axis don’t care
Equal movements up represent equal increases in behavior, on an equal intervals chart
Behavior should be expressed in whole time units, such as per hour or per minute rather than expressed in nonstandard units such as per class or procession
Y – Axis units
Dad expressed in procession or per class rates kind of problems
Session or class to rations can vary making them difficult to compare
Number of hours observed in some daily data can vary. Day today data points may not be comparable
For instance, weekday daily data versus weekend the data observations often very
Problems with non-standard units
Data may be graphed over consecutive days, classes, sessions, or observation. As, for example, the number of face slept for an hour, per day or number of Mands per minute per session.
That’s a rate such as hits two others per hour, is measured up the Y axis While the passage of time, per consecutive day, is marked along the X axis
Solution to problems with nonstandard units
Typically runs from zero, the intersection point with the X – axis, up to some number which is chosen by the creator of the graph
How is this number chosen?
What can happen if the incorrect number selected as the top of the range for the graphical display? Can go off the chart
Y – axis range
No convention exist. It depends on the specific behavior being charged
Led to the development of the standard celeration chart at least in part. Including Mands per day can go quickly from one up to hundreds. This makes a Y axis difficult to arrange
For equal interval line graphs, with clearly defined learning objectives, extend the Y axis range enough above the learning goal to allow for excellence – usually 25% to 33% above
Example, for target rate of 30 correct responses per minute on single digit multiplication table flashcards, have your range go up to 40 or so
The Proper Range: Acquisition Targets
Sometimes small variations at high values of the dependent variable can be enhanced by simple trick of graph manipulation
Can also be done on the X axis to make it appear that data taken months apart or temporarily contiguous
Bad idea
The break in the Y axis.
An individually measured value of the target behavior ( the DV) at a given point in time.
marks the intersection of values of two measurements, one marked along the Y axis and the other on the X axis
Example, there were 26 face laps (DV Measure on Y axis) during observation 4. (Time measure on X axis). See slide.
Data points.
The slide called a data point equals the intersection of X value and a Y value
Different shapes maybe used to represent different dependent variables
Useful in helping to distinguish between data paths
Different colors are nice…But do not copy or fax well
Data points
Series of straight lines connecting success of data points within a phase or condition.
Represents the relationship between the independent variable and the dependent variable
The primary focus for analysis and interpretation
Each line represents an estimate of the behavior
Connects data points
Each line represents an estimate of the chorus taken by the behavior between each point.
The more data points collected, the more confidence can be placed in the story of the behavior depicted by the data path.
Data Path
Represent one of two types of occurrence;
- Major changes occur in the independent variable –i.e. The introduction or discontinuation of An intervention.
- A major, usually permanent, change in the environment. eg.,The person moves residences, or sustains a permanent physical injury.
Phase changes
They document phase changes. They are a vital part of any chart
Solid vertical line placed at a point along the X axis indicating the point in time when the phase change occurred.
Allows for a clear visual separation between the data charted before the phase change, and the data collected after the phase change
Changes in the INDEPENDENT VARIABLE!
Phase change lines
Represents one of two types of occurrence:
MINOR changes occur in the INDEPENDENT VARIABLE. i.e., change in some parameter of an on-going intervention
Or
A minor, usually temporary, change in the environment. Example, the person is temporarily ill or goes on vacation.
Condition changes
Documents minor changes or vital changes.
A dotted vertical line is placed at a point along the X axis indicating the point in time of the change
Typically changes within phases. Thus, charts may contain only phase change lines, or May contain both…
Phase and condition change lines
Condition change lines.
Cooper continues to define the distinction between the condition and phase change lines.
JABA has utilize this distinction less and less
Dotted vertical lines now represent both condition and phase change lines in the majority of published articles on ABA
The board is unlikely to maintain this distinction for the purposes of the test, but we teach it not only as best practice, but because it enhances your ability to analyze data.
We will make the distinction on our test
Changing conventions
states what response measure was used to measure the dependent variable – the target behavior such as,
rate of hits per hour, number of Mands , or percentage of recorded intervals during which screaming occurred
Y axis label
States what time periods are represented by each success data point.
Such as, days, weeks, sessions
X axis label
Brief and placed at the top of the chart, and identify each separate major phase of treatment. Such as baseline, DRA, D/C haldol
Phase label
Mark changes occurring within a phase. Such as changes in FR schedule, dosages.
Should be easily understood.
Condition label
A concise statement that provide you with:
Sufficient information to identify the dependent variable’s and the independent variables, and
Possibly other salient information necessary to visually interpret the data
Figure legends
A general rule of thumb, do not connect across periods on the X axis where no data exist Regardless as to whether data were collected and loss, we’re not collected, or at the behavior did not have the opportunity to occur, such as days missed at school
This convention has Evald over time
On Connecting data points
What are we looking for?
What do we look at?
How do we analyze data?
Equal interval line graph characteristics
Answers two basic questions:
- Was there a meaningful change in behavior?
- did the target behavior significantly change in rate, or some other measure, between one phase/condition and the next?
a. A rough standard of significant change is a doubling or having but only as a guideline - To what extent can the change be attributable to a specific environmental change?
—-Was the change due to the independent variable, (the environmental manipulation? ) How sure can we be – was this a systematic manipulation?
Visual analysis: the purpose
When analyzing a graph visually we must look at 4 characteristics of the data plotted on the chart
- Level
- Variability
- Trend
- The number of data points
Visual analysis of a graph
The mean, or rarely the median value, of a set of data points
A flat horizontal line drawn through a data set at the average value, a.k.a., the mean value of those data points
Level
We are discussing the directionality of a line drawn through a set data points
Trend
Discussing the bounce of a set of data points within phases or conditions
Variability
Add up all eight data points.
6+10+7+10+6+7+6+8 =60
Divide 60 by the total number of data points, 8
60÷8 = 7.5
Draw your level line at 7.5
Computing the average value -Level line
- Between phases and or conditions, levels of data can change.
- Visual inspection of this mean shift in level can’t allow you to evaluate the effect of the change in the Independent variable
Shift in level
Mean level lines are most common.
However, median level lines are also used, especially when outlying data points skew the level line in a way that makes it not representative of the data set as a whole.
And those outliers usually require some additional analysis
Median level
Refers to the overall direction taken by the data path through a set of data points
Described in terms of the direction of the path through the data: increasing, decreasing or zero no trend
never described as first increasing then decreasing, those would be two different …
Trend: direction of the data
States what time periods are represented by each successive data point.
The direction and degree in a series of graphically displayed data points can be visually represented with a straight line drawn through the data
Usually the best fit line is used.
Trend ? Level?
A trend line, typically drawn freehand
They bisect the data, with close to an equal number of data points above the line as below the line.
Linsley 1985 suggested ignoring the one or two data points outside the more typical range of the data set
The best fit line
Mathematical way to calculate trend
Sometimes referred to as the Quarter intersect method
Split middle line of progress
One of the ways to visually analyze data is to Look at the presence or absence of an effect on the trend by a phase or condition change: I.e., a change in the independent variable (environmental manipulation)
Example, no change in trend even if levels change between phases, can indicate no meaningful change in the behavior
Conversely, a change in trend alone (Without a change in level or variability) Can constitute a significant change
Trends not affected by the IV.
And
Trends affected by the independent variable
The extent to which measures of behavior under the same environmental conditions diverge from one another.
Stability is the opposite of this
The greater the _______, the greater the need for additional data
Variability
Ratio of the X axis to the Y axis
4:3
X-axis should be:
______ times the length of the Y axis
which is a……… Increase
______ Ratio
- 6
- 5%
4: 3
The greater the variability, the greater the need for…
Additional data
Variability is determined around a central reference:
The trend line
Variability is not defined by the full range of the data set
The minimum number of data points necessary to establish a trend, variability or a level of data.
Three
Are always reported as percentages of record at intervals during which the criterion of the interval was met.
Percentages need no conversion to standard units
Dimensionless quantities such as partial interval, whole interval, momentary time sample
Developed by Skinner as the primary means of data collection and analysis in EAB laboratory research.
Cumulative record
Primarily used in EAB
Each response move the ink stylus one unit, click, along its track.
When it reaches the end of the track it reset to zero and begins moving again, one click at a time.
Paper moves under the stylus at a steady rate
Cumulative recorder
Rate is indicated by slope, not Y axis value
The slope of the line represents responses per minute
Cumulative recorder
At high rates, slopes above 75 to 80°, major changes in rate can be very difficult to distinguish. Remember, 90° would be an infinite rate.
Local rates, number of responses for any given session on a long-term record, can be difficult to distinguish.
Gradual changes in slope, rate, can be difficult to distinguish
Cumulative record problems
Was there a change and variability?
Was there a change in trend?
Was there a change in level
Questions
Vertical axis represents the value of a DEPENDENT variable
HOWEVER,
The HORIZONTAL axis represents a phase, condition, or classification variable.
does NOT have distinct data points representing Successive response measures through time… The other three types of graphs do
Bar graphs
Summarize and compare data for different groups of subjects and/or different conditions.
Used to compare sets of data which are NOT related to one another by a common underlying dimension by which the horizontal axis can be scaled, such as time or distance.
Use of a bar graph
Should not be used to represent the changes in repeated measures across the time
Should not be used to evaluate client progress on a daily, weekly, or monthly basis.
Improper use of bar graphs
A.k.a. semilog six cycle chart
Used in precision teaching
Some behavior analysts think it is the best way of displaying data.
Standard celeration chart
Was developed by Skinner as the primary means of data collection and analysis in EAB laboratory research
Best for behavior as where cumulative responses are important such as saving money or exercise
Cumulative record (or graph)
Best for acquisition targets and setting learning objectives, although they are not generally well received, despite their effectiveness
A.k.a. semilog six cycle chart
Used in precision teaching
Some behavior analysts think it is the best way of displaying data.
Standard celebration charts
A chart used for groups across different conditions
Bar graphs
The primary tool for behavior analysts in almost every setting an application
Equal interval line graph
Usually placed your next data point on the chart as quickly as possible that is as soon as your next unit of time on the X axis has passed
. This means DALY, or at a minimum weekly
The learning curve on the standard celebration chart: three days below the curve and change your teaching strategy
How often to charge your data
Y axis on left side, vertical, has one range, and Y axis on the right side, vertical, has another range.
Can be done on a single celebration
chart
Four different ranges of data
Alternative graph option, double Y axis
Too many dependent variables
Dependent variable’s difficult to see
Charts with units that do not reveal trends
Problems with double Y axis Charting
Stability is the opposite of this
Variability
Nonstandard units
Per class or per session
Whole time units
Per hour, per minute
Represents the relationship between the IV and the DV
Data path
The primary focus of analysis and interpretation
Data paths
can change between phases and condition
Levels of data
Described in terms of increase in the variability and the data around it
Trend
A rough standard of significant change is a
Doubling or halving but only as a guideline
A.k.a. standard behavior chart
Celeration chart
For ABA graphs, each point represents a level or amount of some quantifiable dimension of a target behavior, Measure in relation to some point in time or environmental condition
Data points
Cooper; the value on the vertical axis scale around which a set of behavioral measures converge.
Generally, it’s the mean average value of a set of data points, usually across an entire condition or phase.
But Sometimes look at a subset of data within a phase or condition. (Not typical)
A flat horizontal line drawn through a data set at the average value, a.k.a. the mean value of those data points
Mean level lines are most common
Level
Most common level lines
Mean level lines
Add up all eight data points
Divide that number by the total number of data points.
Draw your line at that number.
Computing the average value of a level line
A systematic form of data examination, characterized by visual inspection of graphical displays of those data.
In ABA it allows for the evaluation of the effects on behavior, of an experimental or clinical manipulation.
Typically, these data are presented as repeated measurements over time.
What is visual analysis?
Pie charts
Area charts
Radar charts
For logarithmic log log graphs, log scale on both the X and Y axis
And many more
Graphic displays not used in ABA
For acquisition targets, no convention exist. It depends a great deal on the specific behavior being charted.
This is what led to the development of the standard Celeration chart, at least in part,. E.g., mands per day can go quickly from one of 200s. This makes a Y axis difficult to arrangemmBut for equal intervals line graphs, with clearly defined learning objectives, extend the Y axis range enough above the learning goal to allow for excellence. Usually 25% to 33% above.
For example, for a target rate of 30 correct responses per minute on single digit multiplication table flashcards, have you arrange go up to 40 or so.
The proper Range: acquisition targets
The standard conventions for the length of the Y axis compared to the length of the X axis are as follows:
Generally, the X axis should be about 1.6 times the length of the Y axis. This is about an 8:5, or more simply a 4:3, ratio.
For graphs stacked up on each other, this ratio could be much greater. See graphs
The comparative Axis Lengths
Between phases and/or conditions, levels of data can change.
Visual inspection of this mean shift in level can allow you to :
Evaluate the effect of the CHANGE in the independent variable (IV)
Shift in level
Trends are also described in terms of
The degree of trend, how rapid is the decrease or increase in the data, and
The extent of variability of data around the trend.
Trend: degree and variability
The direction and degree of trend in a series of graphically displayed data points can be visually represented with a straight line drawn through the data.
Trend lines
Variability is determined around a central reference: the TREND LINE
Variability is not defined by the full range of the data set.
Trend and variability
In a sense, a level can be established with a single data point, but confidence in level increases with an increasing number of data points.
Any judgment on trend or variability requires a bare minimum of three data points.
The more variable the data, the more data points are required to make a decision on trend.
The minimum number of data points needed for visual analysis
When data on dimensional quantities such as weight, duration, I RT, I collected during an equal observation. So, those data must be converted into comparable units, such as per minute or per hour
Converting dimensional quantities to common units
Dimension less quantities such as partial interval, whole interval, momentary time sampling
, are always reported as percentages of recorded intervals during which the criterion on the interval was met. Percentages need no conversion to standard units
Dimensionless quantities need no conversion.
An automated device. When in use, the behavior of the experimental subject create a graph automatically.
It is primarily used in EAB
Each response move the ink stylus one unit, click along its track
When it reaches the end of the track, it reset to zero and begins moving again, one click at a time.
Paper moves under the stylus at a steady rate
RATE is indicated by slope, not Y axis value
Flatline anywhere on the chart equals no responding
The slope of the line represents responses per minute
Cumulative recorder- Skinner
At high rates (slopes above 75 to 80°), major changes in weight can be very difficult to distinguish. Remember, 90° would be an infinite rate.
Local rates, number of responses for any given session on a long-term record, can be difficult to distinguish.
Gradual changes in slope or rate, it can be difficult to distinguish
Some problems with cumulative records.
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