## CHI SQUARED TEST - University of Edinburgh

### Chi-squared test for categories of data

We draft our null hypothesis: (well, we already have it…)
Type 3: Three or More Chi-Square
df is calculated by multiplying
(# rows minus 1) by (# columns minus 1)
α is either .05 or .01
use .05
4.

### Chi - Square Goodness of Fit Rejection Region - …

We draft our null hypothesis: (well, we already have it…)
Type 2: Two-Way Chi-Square
The chi-square (x2) value from the table is, once again, your critical “cut-off point”
if your chi-square from the data is less you RETAIN;
if your chi-square from the data is greater you REJECT (it’s in the REJECTION ZONE!)
5.

Set up a data in a summary table to determine chi-square value
Type 1: One-Way Chi-Square
And difference squared
α is either .05 or .01
use .05
6.

## chi-squared distribution when the null hypothesis is true

But in some types of experiment we wish to record how many individuals fall into a particular category, such as blue eyes or brown eyes, motile or non-motile cells, etc. These counts, or enumeration data, are discontinuous (1, 2, 3 etc.) and must be treated differently from continuous data. Often the appropriate test is chi-squared (2), which we use to test whether the number of individuals in different categories fit a null hypothesis (an expectation of some sort).

## Chi-squared equation and null hypothesis help? | …

Now we must compare our X2 value with a 2 (chi squared) value in a with n-1 degrees of freedom (where n is the number of categories, i.e. 2 in our case - males and females). We have only one degree of freedom (n-1). From the 2 table, we find a "critical value of 3.84 for = 0.05.

## Chi-Square test for One Pop. Variance - Homework …

We draft our null hypothesis:
Type 1: One-Way Chi-Square
Is there a tendency to assign certain responses over others?
Type 1: One-Way Chi-Square
Let’s Practice!
5.

## Chi squared rejection region calculator | scholarly search

Calculate critical chi-square value using Table E (page 370)
Type 2: Two-Way Chi-Square
df is calculated by taking the # of categories minus 1
df = k-1
α is either .05 or .01  we tend to use .05
So, once again, we need to know α and df
4.

## Chi squared rejection region calculator ..

Calculate the critical chi-square value using Table E (page 370)
Type 1: One-Way Chi-Square
Difference squared divided by fe
Difference between fo and fe
Expected frequency = fe
Observed frequency = fo
This final total (adding up all the differences squared and divided by fe -- is your chi-square value -- x2
3.

## What is Chi-squared test for goodness of fit? - …

Calculate critical chi-square value using Table E (page 370)
Type 3: Three or More Chi-Square
df is calculated by multiplying
(# rows minus 1) by (# columns minus 1)
Two problems with that.
Assumes normal distribution
Assumes scale measurement
"What about MY abnormally distributed data that is nominal or ordinal?!"
test
There are 3 types:
one-way
two-way
three-or-more
(There are more...)
An example:
Imagine we want to determine whether, in preparing a multiple choice test, an instructor shows a tendency to assign certain responses over others…
How do we determine that?
Imagine this is our data –
This is what we call our
“Observed Frequencies”
The instructor shows no tendency to assign a particular correct response from A to E.

2.