This preview shows pages 1–3. Sign up to view the full content.
Week Three Lecture – Part I
Introduction
The previous lectures and learning discussed and applied two of the three test
statistics. The z and t test statistics were used in hypothesis testing when there were
large (> 30) and small (</= 30) observations. In these applications, we examined
populations that were interval or ratio data, and assumed that the population was
normal.
We may ask then, can tests be made if the data are nominal and ordinal, and no
assumptions made about the distribution and shape of the parent population?
Remember that nominal data are the lowest type of data. This data can only be
classified into categories such as male and female, Protestant, Roman Catholics,
Jewish, and all others. In ordinal level data, we have seen that this level includes one
category that is ranked higher than another. Notwithstanding the argument about
statistical meaningfulness, let’s assume that rating a product (excellent, good, fair, and
unsatisfactory) is interval. This means that a ranking of excellent is higher than good,
and so forth.
GoodnessofFit Test: Equal Expected Frequencies
Hypothesis tests related to nominal and ordinal levels of measurement are called
nonparametric tests, sometimes referred to as distributionfree tests. Tests that are
distribution free imply that the tests are free from assumptions regarding the distribution
of the parent population. This set of hypothesis testing has several forms of testing. We
will focus on “goodness of fit” testing and use the Chi Square, X
2
as the test statistic, our
third application of test statistics in this course. In this regard, our interest is to
determine how well an observed set of data fits an expected set of nominal or ordinal
data. Moreover, this testing assumes “equal expected frequencies” in the distribution.
Let’s explain this form of testing with an example. Let’s assume an athletic shoe
store plans to sell six new styles of running shoes that are now available on the market.
After one week of sales the store sold the following:
Shoe
Sold
Nike
13
Saucony
33
Adidas
14
New Balance
7
Rebok
36
Zepher
17
Total
120
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document At the end of the first week of sales, can the store conclude the sales of new running
shoes are the same for each brand? Or should the store conclude that the sales are not
the same?
If there were no significant difference between the observed frequencies and the
expected frequencies, we would expect that the observed frequencies would be equal,
or nearly equal. That is we would expect to sell as many Nike shoes as for New
Balance, and so forth. Thus, any discrepancy in the set of observed and expected
frequencies could be attributed to sampling (chance).
Let’s explain expectancy further. Because there are 120 sold running shoes in the
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 10/10/2010 for the course STATS Stats301 taught by Professor Regis during the Spring '10 term at DeVry Irvine.
 Spring '10
 Regis
 Statistics

Click to edit the document details