Chapter 3: Graphing Data



Chapter 3: Graphing and Experimental Design

Graphing Data

Basic Elements of a Graph

Axes: Y (vertical), X (horizontal)

Axis Labels: Y (R), X (sessions, days, etc.)

Units (numbers) for Y and X axes

Data points: X-Y plots representing values of R across sessions

Phase-change lines: Vertical lines separating experimental conditions

Phase labels: Descriptions of experimental conditions

Examples of Graphs (see examples on p. 2)

Multiple Plot, More than One Set of Data

Multiple Plot, More than One X Axis

Multiple Plot, Double-Y Axis (Used when data represent different units of measurement)

Bar Graph (Used for Plotting Discontinuous Data)

Frequency Plot versus Cumulative Record

a) Frequency plot: Each data-point value is graphed separately

b) Cumulative record: Each data point-value is added to the previous value

Characteristics of Data Evaluated via Graphical Analysis

Level: Mean (average) value of a set of data

Trend: Systematic change in level across measurements

Variability: Degree of fluctuation in a data set around its mean

Multiple Plot, more than one data set

Multiple plot, more than one X axis

Multiple plot, double Y axis

Bar graph

Frequency plot vs. cumulative record

Experimental Design

Terminology

1. Dependent variable (DV): Variable observed to determine the effects of an experimental manipulation (behavior)

2. Independent variable (IV): Variable manipulated by the experimenter (environmental event or treatment)

3. Confounding variable: Source of influence other than the IV that may produce changes in the DV

4. Experimental design: Rules for applying an IV so as to examine its effects on a DV

5. Functional relation: A relationship in which changes in one variable (DV) are demonstrated to be the result (a function) of changes in another variable (IV)

6. Single subject design: An experimental design in which a functional relationship can be demonstrated with the behavior of only one subject

7. Baseline: Condition in effect prior to introduction of the IV

8. A-B notation system: “A” denotes baseline; subsequent letters (“B”, “C,” etc.) denote different IVs

9. Replication: Duplication of earlier conditions in an experiment

A-B Design

Definition: Single introduction of at least one IV on at least one baseline

Advantage: Repeated measurement under Bl (A) and Rx (B) conditions allows examination of changes in level, trend, and variability

Limitations:

No replication

Therefore, does not rule out the influence of confounding variables

Therefore, no demonstration of a functional relation

Reversal Design

Definition: Introduction and subsequent removal of at least one IV on one BL

Variations: ABAB, ABA, BAB, ABAC, etc.

Advantage: Simple yet powerful demonstration of experimental control

Limitations:

Detrimental effects of reversal: Ethical considerations

Irreversibility: Failure to reproduce effect observed in a previous phase even though conditions are arranged identically

Sequence/Order effect: Influence of a previous manipulation on responding in a later condition (e.g., training ( contingencies)

Multiple Baseline Design

Definition: Sequential introduction of an IV across more than one BL

Variations: Across subjects, behaviors, settings

Advantage: Does not require reversal to show experimental control

Disadvantages:

Stability requirement more cumbersome than with a reversal design

Potential generalization across baselines (more likely with MBL across behaviors or settings)

Multielement Design (aka Alternating Treatments)

Definition: Rapid alternation of BL and IV conditions (or 2 or more IVs) on a single BL

Variations: BL vs. Rx, Rx1 vs. Rx2 (with or without BL), etc.

Advantages:

Does not require baseline (although preferred)

Accommodates trends and instability

Minimizes sequence effects (limited exposure to one condition)

Ideally suited to complex analyses (parametric, component, comparative)

Limitation: Multiple treatment interference

Changing Criterion Design

Definition: Introduction of one IV on a single BL in step-wise fashion, with steps corresponding to progressive changes in either response requirement or value of the IV

Advantage: No reversal and no additional baselines required to show experimental control

Disadvantages:

Requires control over both direction and level of change

Requires careful selection of criterion change

Potential generalization

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