October 19, 2010
Cross-Tabs and Chi Square
Readings:
Chapter 11 Statistics First Steps (Johnson and Reynolds) (pp. 393-420)
Chapter 7 Tests of Significance and Measures of Association (Pollock) (pp. 145-162)
Chapter 5 Making Controlled Comparisons (Pollock Workbook)
Chapter 7 Chi-Square and Measures of Association (Pollock Workbook)
COURSE LEARNING OBJECTIVES
Students will learn the research methods commonly used in behavioral sciences and will be able to interpret and explain empirical data.
Students will achieve competency in conducting statistical data analysis using the SPSS software program
CROSS-TABULATIONS
Hypothesis Testing With Cross-Tabulations
The purpose of hypothesis testing is to determine whether a relationship exists between two variables.
What is the probability that a particular finding arose by chance?
How strong is the relationship between an independent and a dependent variable?
Types of Hypotheses
The Null Hypothesis- this states that any observed pattern is solely due to chance and that no relationship exists.
The classic case the book uses a good example of innocent until proven guilty.
There is no relationship between my
independent and dependent variable
The Alternate Hypothesis- this is the opposite of the null hypothesis. This says that a relationship does exist between the variables.
We may also call this the research hypothesis.
Always state your Alternate hypothesis clearly and add direction when possible.
A Null Hypothesis can either be:
True- no relationship between the groups, in which case the alternate hypothesis is false---- Nothing is going on!
False- there is a relationship and the alternative hypothesis is correct-- something is going on!
A Type I Error- the incorrect or mistaken rejection of a true null hypothesis (a false alarm)
A Type II Error- failing to reject a null-hypothesis when it should have been rejected. (denial)
The CHI-SQUARE TEST
This is a procedure for evaluating the level of statistical significance attained by a bivariate relationship in a cross-tabulation.
What is Chi-Square
It is a test of significance between two variables.
FOR A CHI SQUARE VALUE TO BE SIGNIFICANT, THERE HAS TO BE A LOT OF VARIATION IN THE TABLE! WE WANT TO SEE THE UNEXPECTED.
How to Tell if we have a significant Chi-Square
Alpha Level (our level of significance)
Degrees of Freedom- (how many cells in our cross-tab)
Critical Chi-Square value- the minimum value
of chi-square needed to demonstrate a significant relationship
if our Chi-Square value from our
test is greater than
or equal to the Critical value from the table, we reject the null
hypothesis- we have a relationship
if our Chi-Square value from our test is less than the Critical Value from the table, we accept the null hypothesis and we have no relationship
Example 1- Church attendance and Sex Ed
Null Hypothesis- There is no
relationship between church attendance and belief in teaching sex ed in the
schools
Alternate Hypothesis- As
religious attendance increases, people are more likely to oppose sex education
in the public schools.
Using the Table
What is the minimum value of chi square necessary for significance.
Based on our Pearson Chi-Square, what do we do with the Null, and why?
Example 2- Gun Ownership and Confidence in Congress
Null Hypothesis- There is no
relationship between gun ownership and Confidence in Congress
Alternate Hypothesis- Gun owners are
less trusting of Congress than non-gun owners.
Example 3- Extra-Marital Sex and Marital Status
Null
Hypothesis- There is no relationship between marital status and support for
extra-marital sex
Alternate Hypothesis- Married people will be more likely to say
that extra-marital sex is always wrong
How to do this in SPSS
Analyze
Descriptive Statistics
Cross-Tabs
Click on the Statistics Tab
Select the Proper Statistic and continue with the cross-tabs!
From the Congress Data Set Here is My alternate Hypothesis: Older Congressmen will have less education because they grew up in a time when Post High-School education was not available or affordable.
What does the Chi-Square Tell us?
What is the Asymp. Sig here?
What do We Do with the null hypothesis?
One To Try Out with the NES 2004
IV= Attend3
DV= Bible
A Chi-Square tests gives us two things
A Chi-Square value - listed below as Pearson Chi-Square
A significance level- listed as Asymp. Sig
The higher our value, the stronger our significance.
The Lower our ASYMP.SIG the stronger our significance
.000 means there is a 1 in 1000 chance of accepting a false null hypothesis.
we accept anything less than .05
Limitations of Chi-Square Values
This page maintained by Brian
William Smith
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