1 / 12

Analysis of Variance (ANOVA)

Analysis of Variance (ANOVA). I231B Quantitative Methods. Syllabus Changes. Thursday April 24 th , Regression April 29: Multivariate Regression May 1: Regression Diagnostics May 6 th : Logistic Regression May 8 th : Display of some advanced topics; Course Review. Analysis of Variance.

cybele
Télécharger la présentation

Analysis of Variance (ANOVA)

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. Analysis of Variance (ANOVA) I231B Quantitative Methods

  2. Syllabus Changes • Thursday April 24th, Regression • April 29: Multivariate Regression • May 1: Regression Diagnostics • May 6th: Logistic Regression • May 8th: Display of some advanced topics; Course Review

  3. Analysis of Variance • In its simplest form, it is used to compare means for three or more categories. • Example: • Income (metric) and Marital Status (many categories) • Relies on the F-distribution • Just like the t-distribution and chi-square distribution, there are several sampling distributions for each possible value of df.

  4. What is ANOVA? • If we have a categorical variable with 3+ categories and a metric/scale variable, we could just run 3 t-tests. • The problem is that the 3 tests would not be independent of each other (i.e., all of the information is known). • A better approach: compare the variability between groups (treatment variance + error) to the variability within the groups (error)

  5. The F-ratio • MS = mean square • bg = between groups • wg = within groups df = # of categories – 1 (k-1)

  6. Interpreting the F-ratio • Generally, an f-ratio is a measure of how different the means are relative to the variability within each sample • Larger values of ‘f’  greater likelihood that the difference between means are not just due to chance alone

  7. Null Hypothesis in ANOVA • If there is no difference between the means, then the between-group sum of squares should = the within-group sum of squares.

  8. Visual ANOVA and f-ratio • http://www.psych.utah.edu/stat/introstats/anovaflash.html

  9. F-distribution • A right-skewed distribution • It is a ratio of two chi-square distributions

  10. F-distribution • F-test is always a one-tailed test. • Why?

  11. Relationship to t-test • Why not just run many t-tests between all possible combinations? • As number of comparisons grow, likelihood of some differences are expected– but do not necessarily indicate an overall difference. • Still, t-tests become important after an ANOVA so that we can find out which pairs are significantly different. • Certain ‘corrections’ can be applied to such post-hoc t-tests so that we account for multiple comparisons (e.g., Bonferroni correction, which divides p-value by the number of comparisons being made)

  12. Logic of the ANOVA • Conceptual Intro to ANOVA • Class Example: anova.do and sm96_compressed.dta

More Related