1 / 9

Chapter 17 Chi-Square and other Nonparametric Tests

Chapter 17 Chi-Square and other Nonparametric Tests. James A. Van Slyke Azusa Pacific University. Distinctions between Parametric and Nonparametric Tests. Parametric tests (e. g. t, z) depend substantially on population characteristics

Download Presentation

Chapter 17 Chi-Square and other Nonparametric 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. Chapter 17 Chi-Square and other Nonparametric Tests James A. Van Slyke Azusa Pacific University

  2. Distinctions between Parametric and Nonparametric Tests • Parametric tests (e. g. t, z) depend substantially on population characteristics • Nonparametric tests depend minimally on population parameters • Fewer requirements • Often referred to as distribution free tests • Advantages for parametric tests • Generally more powerful and versatile • Generally robust to violations of the test assumptions (sampling differences)

  3. Chi-Square (χ2) Single Variable Experiments • Often used with nominal data • Allows one to test if the observed results differ significantly from the results expected if H0 were true

  4. Chi-Square (χ2) Single Variable Experiments • Computational formula

  5. Chi-Square (χ2) Single Variable Experiments • Evaluation of Chi-Square obtained • Family of Curves • Vary with degrees of freedom • k-1 degrees of freedom where k equals the number of groups or categories • The larger the discrepancy between the observed and expected results the larger the value of chi-square, the more unreasonable that H0 is accepted

  6. Chi-Square: Test of independence between two variables • Used to determine whether two variables are related • Contingency table • This is a two-way table showing the contingency between two variables • The variables have been classified into mutually exclusive categories and the cell entries are frequencies

  7. Chi-Square: Test of independence between two variables • Null hypothesis states that the observed frequencies are due to random sampling from a population • This population has proportions in each category of one variable that are the same for each category of the over variable • Alternative hypothesis is that these proportions are different

  8. Chi-Square: Test of independence between two variables • Calculation of chi-squared for contingency tables • fe can be found by multiplying the marginals (i.e. row and column totals lying outside the table) and dividing by N • Sum (fo – fe)2/fe for each cell

  9. Chi-Square: Test of independence between two variables • Evaluation of chi-square • df = number of fo scores that are free to vary • While at the same time keeping the column and row marginals the same • Equation • df = (r – 1)(c – 1) • Where r = number of rows in the contingency table • c = number of columns in the contingency table

More Related