Chi-Square Test of Homogeneity – Learn It 4

  • Complete a chi-square test of homogeneity

Certain conditions and assumptions must be met before using the chi-square distribution to conduct the hypothesis testing.

conditions for a [latex]\chi^2[/latex] test of homogeneity

  1. Appropriate Data and Variables: This is not an official condition, but it is important to make sure that we are dealing with data that give the counts for each value of a categorical variable. That categorical variable should be measured for a sample from each population of interest.
  2. Independence/Randomness Condition: The samples from our populations should be independent, random samples or independent samples that can be considered representative of the respective populations.
  3. Large Sample Sizes Condition: The sample sizes need to be large enough so that the expected count in each cell is at least five.

Recall that we are considering the question of whether the distributions of flight status are the same among the flights of the three airlines.

  On-Time Flights Delayed Flights Canceled Flights Diverted Flights Total
American Airlines 42,600 4,657 296 95 47,648
Delta Airlines 51,620 4,030 150 56 55,856
Southwest Airlines 69,384 9,280 1,782 128 80,574
Total 163,604 17,967 2,228 279 184,078