Chi-square and F Distributions

Topics

Reference

Howell, D. C. (2010) Statistical methods for psychology (7th ed.). Wadsworth, Cengage Learning.
https://labs.la.utexas.edu/gilden/files/2016/05/Statistics-Text.pdf

20 thoughts on “Chi-square and F Distributions”

  1. Dear Charles,

    Could you please help me understand how to compare two or three coefficients from different models. I would like to test whether there is a statistically difference between coefficients from different model.

    Thanks

    Harold

    Reply

  2. Hi Charles I need your help

    A researcher is testing the efficacy and tolerability of treatment A and treatment B in a RCT randomised double blind right-left trial. N subjects are given treatment A and treatment B on their right and left arms respectively.
    A severity index (continuous variable) is used to measure the severity of the condition.

    It is found that the severity index reduction is significantly lower (p<0.0001) for treatment A than treatment B.
    What are two possible methods that were used to do the significance test of that severity index score?

    Reply

    • Yusuf,
      You can use a paired t test provided the assumptions are met (primarily normality). Otherwise you can use a Wilcoxon Signed Ranks test.
      You stated that “severity index reduction is significantly lower (p<0.0001) for treatment A than treatment B", and so this is based on some statistical test. Do you know which test was used?
      Charles

      Reply

  3. 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?

    Reply

    • Cameron,
      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.
      Charles

      Reply

      • 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,

        Reply

        • Cameron,
          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

          Reply

          • Charles, could you please say me your opinion about this workbook (page 19):
            4. CHI-SQUARE: INTRODUCING THE
            ‘GOODNESS OF FIT’ TEST AND THE ‘TEST OF
            ASSOCIATION
            (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)
            Respectfully,

          • Cameron,
            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

  4. 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)?

    Regards
    Iro

    Reply

    • Iro,
      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.
      Charles

      Reply

  5. Dear Charles

    It has been 3 years since I started visiting the site, till now 2016 the site is still impressive to me.Bless you

    Reply

  6. 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,
    Maria

    Reply

    • Maria,

      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.

      Charles

      Reply

  7. 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?

    Reply

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