# Graphing

## Why is it important to use a graph?

Once you have collected data from observation sessions, it is important to organize the information in such a way that it is easy to interpret. It can be difficult to see patterns by simply looking at long lists of numbers or reading data collection sheets across different days. Graphs can provide quick and easy visual summaries that allow teachers to determine patterns of behavior, evaluate the results of new teaching strategies, and establish whether or not interventions are having the desired effects. This information can then be used to provide students with feedback on their performance.

## What type of graph should be used?

There are several different types of graphs that can be used to represent data including line graphs, bar graphs, pie charts, or scatter plots. The most common type of graph used to evaluate behavioral data is the line graph. A line graph shows individual data points connected by line, creating a path. Over time, this path can show a visual pattern that helps you evaluate the overall directions of a behavior.

Another common graph used is referred to as a bar graph. A bar graph is often used when portions of a whole are being represented or when reporting a percentage. The bar graph focuses on the height of the data rather than the trend in the data, and is most often used when nonconsecutive data points are being evaluated. This is a particularly useful method when comparing information across individuals, settings, or situations.

Pie charts may be useful when representing portions of a whole. For instance, it might be helpful to create a pie chart indicating the amount of time a student spends actively engaged in activities.

Finally, scatter plots are used when a variety of observations or measures have been taken that are not necessarily collected consecutively. For example, a scatter plot may be used to represent the scores obtained by a class on a standardized achievement test. In this type of graph, each data point is independent. However, depicting the data in this fashion may allow one to see the performance of each person compared to the rest of the group.

Example of a scatter plot showing Mrs. Jones's class grades on a standardized academic achievement test:

## What are the important elements of a line graph?

It is important to know the basic elements of a line graph because it is the most common type of graph used to evaluate behavioral data.

The Horizontal Axis (X-Axis) and Vertical Axis (Y-Axis)

Data are presented in a graph within a boundary containing a horizontal line and a vertical line that are referred to as axes. The horizontal axis is called the x-axis, and the vertical axis is referred to as the y-axis. These two axes meet at the bottom left side of the page. The horizontal axis represents the passage of time. The vertical axis represents the numerical property of the behavior being measured. The numbers on both axes are usually divided into equal intervals. The scale of the y-axis can be an important variable when interpreting graphs. If the scale is set too high or too low, the changes in behavior will look much bigger or smaller in appearance, and this might be misleading. In most graphs, the x-axis (representing time) is longer than the y-axis, especially if repeated observations of the behavior have been made.

Points on a graph

Points are usually plotted on a graph by placing a mark where the lines of the behavior's value (y-axis) and that of the behavior occurrence (x-axis) intersect. Each time an observation is conducted, a point can be plotted on the graph. Points are often connected to each other by lines.

Condition Lines

Each time there is a change that may have an impact on behavior, a vertical line is drawn beginning on the x-axis, passing between the data points represented on the graph. Data points on either side of the condition line are not connected to each other. A condition change line can denote the move from baseline to intervention or from one intervention to another. Condition lines can also be used to denote other changes that may impact the behavior (e.g., sickness, a change in classroom, a change in teacher or supervisor). However, if the changes are temporary (e.g., presence of a substitute teacher, illness, father gone on a trip), arrows rather than condition lines, may be used to mark the beginning and end of these temporary factors.

Condition Labels

Each condition in a graph must be labeled with a short descriptive phrase or word placed at the top of the graph above the data. This descriptive phase or word represents a condition (for instance, the baseline or intervention) that is implemented during the time period represented in the graph.

## How do you use a graph to inspect the data gathered?

A visual analysis of the data in a line graph helps to answer two types of questions:

• Are there meaningful changes in the behavior over time?
• To what extent can that change in behavior be attributed to the teaching strategy or behavioral intervention that was introduced?

Although there are no formal rules for the visual analysis of graphs, there are certain properties that are common to all behavioral data. The properties within and across conditions that are examined visually include variability, level, and trends in the data.

Variability

Variability is the extent to which a behavior changes from one data point to the next. If the behavior does not show much variability, it may not be necessary to collect as much data since the behavior is considered more stable and chances are that the behavior will remain at this level is high. On the other hand, if a behavior shows a lot of variability, additional data should be collected before making any changes. This will allow one to better determine whether or not the changes in behavior are due to the intervention.

Levels of Behavior

The level of a behavior is the increase or decrease in a behavior from the beginning to the end of a condition. The bigger the level of change, the more powerful the effect of the intervention. For instance, the greater the magnitude and direction of change that has occurred from baseline to intervention, the more likely that the intervention is effective. Sometimes a line representing the average of the data points within a condition is drawn on the graph to help show the change in level. This means line can be useful when the data are somewhat variable. In the figure below, the mean level line for the duration of tantrums shows that there isn't much difference between baseline and treatment, indicating that the treatment may not be too effective.

Trend

Trend refers to the direction the data points on a graph are heading. A steep slant upwards shows a strong increasing trend while a slant downward indicates the behavior is decreasing. Looking at the steepness and direction of the data points can also helps you make decisions about the effectiveness of an intervention. Before moving to a new condition, the trend in each phase is evaluated. It is important to make sure that the trend is stable before moving from baseline to intervention or from intervention to a new intervention. For example, if the baseline trend is steadily decreasing or increasing it is considered to be in the process of changing. If the intervention is begun during an increasing or decreasing trend, it is more difficult to know whether the change in behavior is due to the intervention since the behavior was in the process of changing prior to the intervention.