Inferences about Linear Correlation on the TI-83/84/89
Copyright © 2008 by Stan Brown, Oak Road Systems
Copyright © 2008 by Stan Brown, Oak Road Systems
Summary: The TI-83 and TI-84 can’t compute a confidence interval for the linear correlation coefficient ρ. They also can’t do a hypothesis test on ρ unless you first enter all the points. This Web page presents a downloadable TI-83/84 program that adds those capabilities.
See also: Inferences about Linear Correlation gives the statistical concepts with examples of calculation “by hand” and in an Excel workbook.
The flash application, Stats/List Editor, can do a hypothesis test
for ρ ≠ 0; see LinRegTTest. To compute
a confidence interval about ρ, follow the procedure in
Inferences about Linear Correlation.
Your TI-83 or TI-84 has a command, LinRegTTest, to
do a hypothesis test for ρ≠0, but it can’t compute
a confidence interval. Here is a program that computes the p-value
for a hypothesis test and computes a confidence interval for
ρ, the linear correlation coefficient of a population.
There are three methods to get the program into your calculator:
2nd x,T,θ,n makes LINK]
[►] [ENTER], and then on hers press
[2nd x,T,θ,n makes LINK] [3], select the program,
then press [►] [ENTER].To use the program, press [PRGM], select
CORINFER, and press [ENTER] [ENTER].
When prompted, enter the linear correlation coefficient of the sample,
the number of points in the sample, and the desired confidence level,
pressing [ENTER] after each one.
The program uses real variables C, N, R to hold your inputs
and P, T, Z to hold results. If you have values stored in those
variables they will be lost when you run the program. Those six
variables remain in memory at the end of the program; if you want to
recover those few bytes press [2nd + makes MEM] [2] [2].
Example 1: A random sample of 20 (x,y) points has a linear correlation coefficient of 0.49. Estimate the linear correlation of the population that the sample was drawn from; use a 95% confidence level.
Solution: Run the CORINFER program.
Enter .49 for R, 20 for N, and 95 or .95 for C-Level.
In a few moment the answers appear: the confidence interval runs from 0.0606 to 0.7663.
Interpretation: We’re 95% confident that ρ, the linear correlation coefficient of the population, is between 0.0606 and 0.7663. Symbolically,
0.0606 ≤ ρ ≤ 0.763 (95% confidence)
Example 2: In a random sample of 45 points, you find linear correlation of −0.34. Can you say whether there is any linear correlation in the population that this sample was drawn from? Use a 0.05 significance level.
Solution:
| (1) | H0: ρ = 0, there’s no linear correlation in
the population
H1: ρ ≠ 0, there is some linear correlation in the population |
| (2) | α = 0.05 |
| (3–4) | program CORINFER, r = −.34,
n = 45, C-Level=0 for HT.
Results: t = −2.37, df = 43, p-value = 0.0223 |
| (5) | p-value < α. Reject H0 and accept H1. |
| (6) | At the 0.05 significance level, we can say that there is some correlation in the population, and it's negative (ρ<0). |
Remark: As with any two-tailed hypothesis test, if p < α you interpret the result in a one-tailed manner. See p < α in Two-Tailed Test: What Does It Tell You?
Remark: What if an α of 0.01 had been chosen? In that case, p>α and you fail to reject H0. You can’t tell whether there is any correlation in the population or not.
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This page is used in instruction at Tompkins Cortland Community College in Dryden, New York; it’s not an official statement of the College. Please visit www.tc3.edu/instruct/sbrown/ to report errors or ask to copy it.
For updates and new info, go to http://www.tc3.edu/instruct/sbrown/ti83/
