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Sociology
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SOC222H5
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John Kervin
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Sociology

SOC222H5

John Kervin

Fall

Description

SOC 222 -- MEASURING the SOCIAL WORLD
Session #7 -- INF STAT: TABLES
TODAY’S OBJECTIVES
1. Know the difference between confidence intervals and statistical significance
2. Know the difference between a Type I and a Type II error
3. Know the meaning of “expected frequencies” and their role in chi-square
calculations
4. Know the commonly used levels of statistical significance
5. Know how to run a chi-square test on SPSS
6. Know the meaning of “degrees of freedom”
Terms to Know
statistical significance
significance level
research hypothesis
null hypothesis
type I error
type II error
chi-square
expected frequencies
observed frequencies (counts)
degrees of freedom
SITUATION
2 category vars
REFRESHER: THE TWO INFERENTIAL STATISTICS PROCEDURES Procedure #1: confidence intervals
• Question: How much confidence do we have in our estimate of the effect size
in the population?
• Answer: a confidence interval around a population estimate
• Typically 95%
• We’re 95% sure that the population estimate falls within this
interval
• If we drew all possible samples of size N, 95% of them would
give a population estimate within this interval
Procedure #2: statistical significance
• Question: Is there a relationship in the population?
• Answer to this question: statistical significance of the relationship
WHAT IS STATISTICAL SIGNIFICANCE?
Linneman See Kranzler: 108-109
The Logic of Hypothesis Testing
1. Two groups are different
OR
2. Two variables are related
research hypothesis.
With statistics, you can’t show something is true
• It is easier to disprove a statement
SO:
• We create an opposite hypothesis
• And we try to disprove that!
• null hypothesis
Linneman, p. 140
Kranzler, p. 105-106
• Null hypotheses state that nothing is happening:
• In particular, any differences or relationship you find in your sample is
purely by chance If we can disprove the null hypothesis, they we have support for our research
hypothesis
Type I Error
• We find in our sample that X Y
• Could the sample relationship occur just because it’s a non-representative
sample?
We conclude there’s a relationship in the population when there really isn’t.
type I error • We estimate the probability of making a type 1 error
If this probability is low,
• We say the relationship has statistical significance
In most research, we want to minimize type I error
Type II Error
• Concluding no relationship when there really is one
• Normally this is less important Interesting fact: the smaller the chance of a type I error, the larger the chance of a type
II error
STATISTICAL SIGNIFICANCE FROM CHI-SQUARE
What is Chi-Square?
1. Chi-square is a statistic
• Calculated from your sample
2. Chi-square is calculated from crosstabs • The chi-square statistic compares the expected frequencies with the
observed frequencies
3. We know the shape of the sampling distribution for chi-square
• Not symmetrical
• Changes with the size of the crosstab
1. Calculating Expected Frequencies
First step: Calculating expected frequencies
• What would be expected in the population if no relationship
• Based solely on the marginals
• Marginals: the row and column totals in the margins
Male Female
Not working 161
Working 116 112 165

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