## 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 X^{2} 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.