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[2022] This week, we are looking at hypothesis tests using qualitative variables. All previous hypothesis tests have involved quantitative variables. Specifically, we are going to perform a Chi-Square Goodness of Fit

Week 5 Discussion: Chi-Square Unequal Frequencies

This week, we are looking at hypothesis tests using qualitative variables. All previous hypothesis tests have involved quantitative variables. Specifically, we are going to perform a Chi-Square Goodness of Fit unequal frequencies test. This test is used to compare an expected result to an observed one. This might involve comparing a survey taken 10 years ago to a recent one to see if results have changed. Unequal frequencies could also be used to compare a company’s claim about its product to a sample survey. The null hypothesis will be that the expected equals the observed and the alternative will be the expected is not equal to the observed. You will need to apply this wording to your problem (see the example).

To prepare for this Discussion:

  • Review the Week 5 Discussion resources.
  • Look at the data set that you used in Discussion 1 or 2. In order to do this week’s Discussion, you will need to have data involving qualitative variables. Likely, you will need to modify your data set. You may want to start over with a new data set as shown in the example below.
Last year, I asked 50 nurse colleagues what color scrubs they preferred. 50% said light blue, 20% said black, and 30% said gray.  I want to see if this has changed.
This year, I asked 50 colleague what color scrubs they preferred now and here’s what they said:

  • 35 light blue
  • 5 black
  • 10 gray
Since this fits the requirements for unequal frequencies, I will perform a Chi-Square Goodness-of-Fit Test (Unequal Frequencies).
Null: The distribution of scrub color preferences between last year and this year has not changed.

Alternative: The distribution of scrub color preferences between last year and this year has changed.

Light Blue Black Gray
OBSERVED (this year) 35 5 10
EXPECTED (last year) 25 10 15
  • Review the rubric that will be used for grading.  

With these thoughts in mind:

By Day 4

Post a 1- to 2-paragraph write-up that includes the following:

  1. Describe your scenario and provide your data set.
  2. State your null and alternative hypotheses. Be sure to state your chosen level of significance.
  3. Enter your data into the Sample Editor in Statdisk. Choose Analysis, Goodness of Fit and unequal frequencies.
  4. Perform the test and state your conclusion. Remember the conclusion statement should be of the following format: Since the p-value of # is more/less than the level of significance of #, the null hypothesis is/is not rejected; therefore, the data supports (paraphrase the hypothesis supported). Did you get the results that you expected?

By Day 6

Read a selection of your colleagues’ postings.

Respond to at least two of your colleagues’ postings in one or more of the following ways:

  • Ask a probing question.
  • Share an insight from having read your colleague’s posting.
  • Offer and support an opinion.
  • Validate an idea with your own experience.
  • Expand on your colleague’s posting.

Return to this Discussion in a few days to read the responses to your initial posting. Note what you have learned and/or any insights you have gained because of the comments your colleagues made.

Late Policy: Discussion is an interactive learning environment and all discussion posts must occur within the week within which they are relevant. Posts submitted late but within the week in which they are relevant may be penalized at the instructor’s discretion.

Click on the Reply button below to reveal the textbox for entering your message. Then click on the Submit button to post your message.

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