11.1.3 - Probability Distribution Plots

11.1.3 - Probability Distribution Plots

In previous lessons you have constructed probabilities distribution plots for normal distributions, binomial distributions, and \(t\) distributions. This week you will use the same procedure to construct a probability distribution plot for the chi-square distribution.

Minitab®  – Constructing a Probability Distribution Plot

Chi-square tests of independence are always right-tailed tests. Let's find the area of a chi-square distribution with 1 degree of freedom to the right of \(\chi^2 = 1.75\). In other words, we're looking up the \(p\) value associated with a chi-square test statistic of 1.75.

  1. In Minitab, select Graph > Probability Distribution Plot > View Probability
  2. Choose Chi-Square for the Distribution
  3. For Distribution select Chi-Square
  4. For Degrees of freedom enter 1
  5. Select A specified X value
  6. Select Right tail
  7. For X value enter 1.75
  8. Select OK and OK

This should result in the following output:

Chi-square distribution plot made using Minitab Express; degrees of freedom equal 1; the area to the right of a chi-square value of 1.75 is 0.185877

Example: Area to the Right of Chi-Sq = 6.25, df=3

Construct a chi-square distribution with 3 degrees of freedom to find the area to the right of a chi-square value of 6.25.

  1. In Minitab, select Graph > Probability Distribution Plot > View Probability
  2. Choose Chi-Square for the Distribution
  3. For Distribution select Chi-Square
  4. For Degrees of freedom enter 3
  5. Select A specified X value
  6. Select Right tail
  7. For X value enter 6.25
  8. Select OK and OK
This results in the following output:
Chi-square distribution with the area shaded to the right of 6.25

The area to the right of 6.25 in the chi-square distribution with 3 degrees of freedom is 0.1001.

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