1 / 10

Chi-Square Tests

Chi-Square Tests. Chapter 13. The chi-square test for Goodness of Fit allows us to determine whether a specified population distribution seems valid.

trygg
Download Presentation

Chi-Square Tests

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Chi-Square Tests Chapter 13

  2. The chi-square test for Goodness of Fit allows us to determine whether a specified population distribution seems valid. The Chi-Square ( ) test is an inferential test that shows whether or not a frequency distribution fits an expected or claimed distribution.

  3. The chi-square distribution is NOT symmetric. The shape depends on the degrees of freedom. As the number of df increases, the chi-square distribution becomes more symmetric. Otherwise, each curve is skewed right. All values are non-negative. Chi-Square has df = (number of categories) - 1

  4. 1st: State the hypothesis Ho: Frequency fits a specified distribution (actual equals hypothesized) Ha: Frequency does not fit a specified distribution. (Actual is different from hypothesized). The observed frequency (O), of a category is the frequency (count or value) of the category that is observed in the sample data. The expected frequency (E) of a category is the calculated frequency obtained assuming that the null hypothesis is true. (E=np) n=sample size p=probability

  5. To use the chi-square goodness of fit test, the following conditions must be met: All observed data are obtained using a random sample. All expected frequencies are greater than or equal to 1. No more than 20% of the expected frequencies are less than 5.

  6. O is the observed: Enter into L1 E is the expected: Enter into L2 L3=(L1-L2)^2/L2 For critical values, use Table C (Chi-Square Distribution)

  7. Calculator Commands: Catalog, Sum (L3)---This is your chi-square value. Distribution, cdf(Ans, E99,df)---This is your p-value.

  8. Chi-Squared Test of Independence • A chi-squared two-way table test is a test that determines whether two variables are: Ho: Independent/ have no association. Ha: Dependent/ have an association. Conditions: Same as χ2 GOF test. Data is randomly selected. All expected cell counts are at least 1 and no more than 20% of the expected cell counts are less than 5. df = (r-1)(c-1) r= # of rows, c= # of columns Do not include the “total” row/column.

  9. Expected Cells • E=

  10. Chi-Squared Test of Homogeneity • This tests the claim that several proportions are equal when samples are taken from different populations. Ho: All proportions are equal. Ha: At least one of the proportions is different from the others. df = (r-1)(c-1) Conditions: Same as other Chi-squared tests.

More Related