The Chi-Square Test of Independence helps to determine if there is an association between two categorical variables. In this guide, we will explain how to perform this test using a TI-84 calculator. The steps involve entering observed data, calculating expected counts, and interpreting the test results.
2nd
then MATRX (Matrix button).EDIT and press ENTER.[A] and enter the dimensions of your
contingency table. For example, if your data has 3 rows and 4 columns,
input 3 and 4.Example: Suppose your observed data is:
| Below 2000 | 2000-4000 | 4000-6000 | Above 6000 | |
|---|---|---|---|---|
| High-School | 30 | 40 | 20 | 10 |
| Bachelor | 20 | 60 | 50 | 30 |
| Master | 10 | 20 | 30 | 40 |
[A] as 3 x 4.30, 40, 20,
10, 20, 60, 50,
30, 10, 20, 30,
40.Press STAT and scroll over to
TESTS.
Scroll down to C: χ2-Test (Chi-Square Test) and
press ENTER.
Ensure that Observed: is set to
matrix [A]. If it is not, select [A] by
pressing 2nd then MATRX, choosing
[A], and pressing ENTER.
Set the Expected Matrix:
Select an empty matrix (e.g., [B]).
The calculator will automatically calculate and store the expected values in this matrix once you run the test.
Scroll down and highlight Calculate, then press
ENTER. The calculator will display the χ²
statistic, p-value, and degrees of
freedom (df).
Repeat steps 1-4 then select Draw to view a graph of
the Chi-Square distribution, test statistic, and critical
region.
After performing the calculation, the TI-84 will display the following information:
χ² (Chi-Square Statistic): The calculated test statistic.
p-value: Probability associated with the test statistic.
df (degrees of freedom): Calculated as
(rows - 1) × (columns - 1).
Example Output: χ² = 12.34
Compare the p-value to your chosen significance level (e.g., α = 0.05):
If p ≤ α, reject the null hypothesis. This indicates that there is a significant association between the variables.
If p > α, fail to reject the null hypothesis. This indicates no significant association between the variables.
Alternatively, compare the χ² statistic with the critical value from the Chi-Square distribution table at the corresponding degrees of freedom and significance level.
Example Interpretation: - If χ² = 47.36
and the critical value for α = 0.05 and df = 6
is 12.592:
Since 47.36 > 12.592, we reject the null
hypothesis.
Conclusion: There is a significant association between education level and income range.
2nd then MATRX,
select EDIT and choose matrix [B] to view the
expected counts.Make sure the observed data has been entered correctly into
matrix [A].
Verify that the degrees of freedom are accurate: \(df = (r - 1)(c - 1)\), where r
= rows, c = columns.
Ensure that all expected counts are at least 5 to meet the conditions of the Chi-Square test.
[A] do
not match the defined size. Ensure the data matches the size you
specified.[B] for
expected counts before running the test.Using a TI-84 calculator to perform a Chi-Square test of independence is straightforward. By following these steps, you can easily determine whether there is a significant association between two categorical variables based on observed data.
The key steps involve entering your data correctly, performing the test, and interpreting the output. This method is convenient for students, educators, and professionals who need a quick and efficient way to conduct statistical analysis without software.