Lecture 21                      The Chi Square Distribution

The Chi Square Distribution ( х² ) is an inferential statistics technique.  technique that is used when sample data are reported as frequencies (counts).  Chi Square compares these observed frequencies to expected frequencies that are produced by a hypothesis about the population of data.  Only assumptions of random sampling and independence necessary.

The Formula:

х²= Σ [ (0-E)²  /  E ]

A) Goodness of  Fit:  the hypothesis about the population is a theory. If the null hypothesis is retained, the theory is supported b the data.

DF=For one variable:   Number of categories -  1.
       For: two:               (Rows -1) * (Columns-1)

Example: Winthrop wants a more geographic diverse student body. The admissions spend a lot of money on a national media advertising to help with recruiting.  To assess the effect of this campaign, the current year's requests for applications were classified as: five county (565), rest of state (410), and out of state (216).  An analysis of addresses over previous years showed: five-county (51%), rest of state (40%), and out of state (9%).  After the calculation of Chi Square, tell the story that the data supports.

OBS         EXP        (OBS  -  EXP)             (OBS-EXP)²                 (0BS-EXP)²  /  EXP

                                                                                                            х²= Σ [ (0-E)2  /  EXP ]

Phi (size effect)   Ø=   √ X² / n         .1 (small)  .3 (medium .5 (large)

B) Test of Independence:  The hypothesis about the population is that the two variables under consideration are independent. If the null hypothesis is retained, the hypothesis of independence is supported. If the null hypothesis is rejected you can conclude that the two variables are related; they are not independent.  (see work sheet on how to do).