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

â€¢

Provide an example of a hypothetical situation in which a Pearsonâ€™s r is used. Explain how

the sign and magnitude of r would contribute to a researcherâ€™s understanding of the

relationship between X and Y. Given the assumptions for use of Pearsonâ€™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?

â€¢

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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