ChiSquare Goodness of Fit Test
DEFINITIONS
Qualitative variables
are those which classify the units into
categories.
The categories may or may not have a natural ordering to
them.
Qualitative variables are also called categorical variables.
Quantitative variables
have numerical values that are measurements
(length, weight, and so on) or counts (of how many).
Arithmetic
operations on such numerical values do have meaning.
Analysis of Count Data
Three tests
If we have qualitative data on just one variable, a
test of goodness
offit
is used to assess if the qualitative data “fit” or are consistent
with a particular discrete model for the percentages in each
category.
The null hypothesis would state the hypothesized discrete
model.
A
test of homogeneity
is used to assess if two or more populations
are homogeneous or alike with respect to the distribution for some
categorical variable.
The null hypothesis is that the distributions are
the same across the two or more populations.
A
test of independence
determines if two qualitative variables are
related or not for a given population.
The null hypothesis is that the
two variables are independent, that there is no apparent association.
Big Idea for ChiSquare Tests
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
1.
The data consist of
observed counts
—that is, how many of the
items or subjects fall into each category.
2.
We will compute
expected counts
under
H
0
, that is, the counts that
we would expect to see for each category if the corresponding null
hypothesis were true.
3.
We will
compare the observed and expected counts
to each other
via a test statistic
that will be a measure of how close the
observed counts are to the expected counts under
0
H
.
So if this
“distance” is large, we have some support for rejecting
0
H
.
The test statistic that is computed for all three tests is called a
chi
square test statistic
.
THE CHISQUARE STATISTIC
ChiSquare Test Statistic
:
DEFINITIONS
The
observed counts
are the data, the number of observations that
fall into each category or cell.
This is the end of the preview.
Sign up
to
access the rest of the document.
 Summer '11
 KeithEmmert
 ChiSquare Test, Null hypothesis, Statistical hypothesis testing, Chisquare distribution

Click to edit the document details