Chi-square and F Distributions


18 Responses to Chi-square and F Distributions

  1. So helpful website considering the fact that am data analyst trainer.

    • Charles says:

      I am very pleased that you find the website helpful in your work as a data analyst trainer. I plan to add more things to the website so please stay tuned.

  2. Ruxil says:

    Sir, i’d like to ask. I’d like to know how to solve an over-all F-value for two F-value results?

    the two F-values are 0.399 and 0.793? how do i get its over-all F-value?

  3. Maria says:

    Dear Charles,

    I’d be grateful if you could help me with this one.

    Well, let’s say that someone needs to see whether the “type of reasoning” that the respondents use (values: x and y) has something to do with the items (values: flower, bug) about which they are asked in two different scenarios (values: growth scenario, feelings scenario) .

    To be more clear, the participants are asked about “item1-scenario1”, “item1-scenario2”, “item2-scenario 1” , “item2-scenario2”.

    Does the researcher need to proceed with two different 2×2 contigency table in order to separately test “type of reasoning – item” and “type of reasoning – scenario”?

    Or it could ok for them to proceed with one 2×4 contigency table and test “type of reasoning – “question””, where by “question we mean the item and the scenario in which it is integrated at the same time.

    Looking forward to you response.

    Thank you very much for your time,

    • Charles says:


      It really depends on what you are trying to test. You can use a 2 x 4 table with the four categories being “item1-scenario1”, “item1-scenario2”, “item2-scenario 1” , “item2-scenario2”, as you have suggested.

      If you want to model types of reasoning x items x scenarios, then you need a 2 x 2 x 2 contingency table. You can analyze these types of tables using log-linear regression, as described on the webpage
      Log Linear Regression (3-way contingency tables).
      This approach will be more complicated and may not be necessary for your needs.


  4. Iro O. Ada says:

    Hi Dr. Charles,
    Please I’ll like to know what decision to take when the tabular or critical Chi-square value is 12.59 and the calculated value is 11.40. Should I accept or reject the null hypothesis (since the difference is just 1.19)?


    • Charles says:

      At least for the tests shown in the website, the chi-square tests are generally right tail tests. Thus if the test statistic is greater than the critical value, then you reject the null hypothesis (aka a significant result). Otherwise you should retain the null hypothesis (note we don’t use the term accept the null hypothesis). For your situation, you would retain the null hypothesis. The fact that the difference is small or large doesn’t change this.

  5. cameron says:

    Dear Charles,

    I’m sure that you are so busy, but I’d be very grateful if you could help me.
    Is it correct that for a 2 ×2 chi-square table we do not need a post hoc test?
    If it is, so when the results is statistically significant and our cells are:
    a b
    c d
    which cells have relationship with each other?

    • Charles says:

      No post hoc test is necessary.
      Suppose A is the heading for the columns (above a b) and B is the heading for the rows (to the left of a over c), then the relationship you are testing is A with B.

      • cameron says:

        Charles, thank you for your answer, but let me clarify my question. my table is like this:

        single married
        males a=3 b=57
        females c=10 d=50

        And as you said the relationship between gender and marital status was statistically significant. But my question is that can I say that(just by running a 2 ×2 chi square): a<c and d<b (e.g., the frequency of single females was higher than single males and …)
        Is there any another relationship (e.g., between b and c)?
        Kind regards,

        • Charles says:

          I don’t think so, but you can test these sorts of assertions yourself by changing the values of a, b, c and d to see whether you can create counter-examples. E.g. see whether you can create a statistically significant result with a < c and another with c < a. Charles

          • cameron says:

            Charles, could you please say me your opinion about this workbook (page 19):
            (you can download it from google)
            Was my idea correct? (saying that a<c and d<b just by running a 2 ×2 chi square)

          • Charles says:

            Let a, b, c, d take the values 23, 12, 10, 16. Then it is not the case that a < c nor is d < b, but you have a significant result with p = .035. Charles

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