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The Correlation Coefficient – Explained in Three Steps – YouTube

Chapter: 4. Describing Bivariate Data
Section: Restriction of Range Demo
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Range Restriction Demonstration
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Run the Simulation
Instructions Page
Learning Objectives
1. State how range restriction affects the correlation between two
variables
2. State the effect of choosing the upper and lower extremes on the
correlation
Instructions
This demonstration illustrates the effect of restricting the
range of scores on the the correlaton between variables.
When the demonstration begins, the dataset “Strength” is
displayed. The X-axis contains scores on a measure of grip
strength; the Y-axis contains scores on a measure of arm
strength. Notice that there is a strong relationship. Also note
that the two scatterplots are identical and both show that for
Illustrated Instructions
Video Demo
The restriction of range simulation displays data from 1 of 4
datasets. You can change datasets by selecting one from the
drop down menu at the top of the simulation. The top
scatterplot displays all the data from the selected dataset.
Notice the two vertical bars on either side of this graph. You
can “drag” these bars and restrict the range of data from the
dataset that is displayed in the bottom scatterplot. You can
include data on the inside or outside of the bars by selecting
one of the options right above the graph.
For some browsers you will not see the bars
move as you move them. They will move
when you release the mouse button.
the entire dataset of 147 subjects, the correlaton is 0.63. The
two vertical bars on the upper graph can be used to select a
subset of scores to be plotted on the lower graph. If you click
on the left-hand bar and drag it to the right, scores to the left
of the bar will not be included on the lower graph. The
correlaton shown for the lower graph shows only the
correlation for the data in the subset. Similarly, if you drag
the right-hand bar to the left, scores to the right of the bar
will be excluded. If you click the “Data outside bars” button,
the lower graph will, as you might expect, only include scores
to the left of the left-hand bar and to the right of the righthand bar.
The video below shows how to restrict the range by dragging both vertical
bars inward and then changes which data should be included in the bottom
scatterplot. Notice how the statistics change for the second scatterplot based
on which data is included.
Video Demo
EDCO 735
ESSAY: CORRELATION ASSIGNMENT PROMPTS
•
Provide an example of a hypothetical situation in which a Pearson’s r is used. Explain how
the sign and magnitude of r would contribute to a researcher’s understanding of the
relationship between X and Y. Given the assumptions for use of Pearson’s r, what would a
thorough data screening entail to use of (think statistical tests and data visualization)? How
might a researcher attempt to decrease the risk of a Type I error while reporting several
correlations?
•
Discuss the two forms of the regression equation, raw score and z score, and provide
examples of situations in which one would be more useful than the other. Explain how r, R,
and B are related to one another in bivariate regression.

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