# Chi Square

```
Research report is due Thursday, Dec. 12th.
"For Next Time" is due Friday, Dec. 13th if Eval Conf is Monday or Tuesday.
"For Next Time" is due Monday, Dec. 16th if Eval Conf is Wednesday or Thursday.

Goal: Compute 1 inferential statistic, then close your stat book.
If you've got more than one question, you only have to compute the statistic for one.  Once you've
got one computed, help other people (put your name on the board).  We'll help you with more if
everyone else is this far (later).

Two types of chi square tests that are most common for your projects:
Look at your hypotheses to decide:

(a)  Alternate: There is a difference in the percentages across the categories of
Null: There is no difference in the percentages across the categories of
or
(b) Alternate: There is a difference in the pattern across the categories of
_____ (second variable) for difference categories of _________ (first
variable).
Null: There is no difference in the pattern across the categories of _____
(second variable) for difference categories of _________ (first variable).

```

## Choice (a): X2 for one variable Test for Goodness of Fit

```Choice (a):  X2 for one variable

End:
(from "In the Literature section", p. 557)

Participants showed a significant preference on the question concerning
________, X2(__, n = ___) = ____, p (<, >) .05.

First blank:	name of question
Second blank:	df
Third blank:	n
Fourth blank:	X2
multiple choice:	< or >

How many categories does your variable have?  ______ (A)

Draw a table with (A) ____ rows.
This table will be for your FO's.

Draw another table with the same number of rows.
This table will be for your FE's.
Choice (a):  X2 for one variable
(continued)

Draw a third table with the same number of rows.
This table will be for your differences (FO - FE)'s.

Getting FO's:

Getting FE's:
This comes from your null hypothesis.  It probably says that there will be "no
difference", which usually means "each category will have the same percent of
responses".  If this is right, you can divide 100% into your categories:

100% / (A) ____ = % in each category

For example 100% / 4 categories = 25% in each category.
Multiple 25% (.25) by the total number of responses (surveys, observations) to get
the FE for each cell.   The same number goes in each cell of the table.

Getting your differences (FO - FE)'s:
For each cell in the third table, put the difference between FO and FE.  It doesn't
matter which you subtract from which, just the difference between the two.

X2	=    (fo - fe)2
fe

In your third table, square each number and divide by the number in the FE table for
that cell.

df = (A - 1)

Look at the table on page A-34.  "Proportion in Critical Region" means what?

Now, how about trying a graph.  Goal: graph shows your point. Try a few different
graphs.   In the end you might decide you don't need one, or that a table might be
better, but look at the data in a few different ways first.

```

## Choice (b): X2 for two variables Test for Independence

```
Research report is due Thursday, Dec. 12th.
"For Next Time" is due Friday, Dec. 13th if Eval Conf is Monday or Tuesday.
"For Next Time" is due Monday, Dec. 16th if Eval Conf is Wednesday or Thursday.

Goal: Compute 1 inferential statistic, then close your stat book.
If you've got more than one question, you only have to compute the statistic for one.  Once you've
got one computed, help other people (put your name on the board).  We'll help you with more if
everyone else is this far (later).

End:
(from "In the Literature section")

_______ participants  showed a different pattern of responses  than
_______ participants on the question concerning  ________, X2(__, n =
___) = ____, p (<, >) .05.

First blank:	1st group of your 1st variable
Second blank:	2nd group of your 1st variable
Third blank:	name of question for your 2nd variable
Fourth blank:	df
Fifth blank:	n
Sixth blank:	X2
multiple choice:	< or >

What are your 2 variables?  _______ (1)
_________ (2)
Are they both nominal (do they have categories that can't be put in an order)?
____ Yes
____ No, one can be ordered (go to t-test)
____ No, both can be ordered (go to correlation)
How many categories in first variable?  ____ (A)
How many categories in second variable?  ____ (B)

Draw a table with (A) ____ rows and (B) _____ columns.
This table will be for your FO's.

Draw another table with the same number of rows and columns.
This table will be for your FE's.

Draw a third table with the same number of rows.
This table will be for your differences (FO - FE)'s.

Getting FO's:

Getting FE's:
This comes from your null hypothesis.  It probably says something like "the pattern
of responses for (2)  ____  is the same for all categories of (1) _______."
If so, then see p. 567-568 for good example of how to calculate expected frequencies.
Basically, you need to put in the row and column totals first, then do the cells in the
table.

Getting your differences (FO - FE)'s:
For each cell in the third table, put the difference between FO and FE.  It doesn't
matter which you subtract from which, just the difference between the two.

X2	=    (fo - fe)2
fe
In other words, in your third table, square each number and divide by the number
in the FE table for that cell.

df = (A - 1) * (B - 1)

Look at the table on page A-34.  "Proportion in Critical Region" means what?