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Lecture 7

# SOC222 Lecture 7

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University of Toronto Mississauga

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
2 procedures we can use to make inferences about the relationship
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
We did this last week but with one variable at a time
Procedure #2: statistical significance
• Question: Is there a relationship in the population?
• Answer to this question: statistical significance of the relationship
This question is different from the first procedure – asking if an relationship exist in the
population if we found in the sample – so is the relationship found in the sample is
statistically significant?
WHAT IS STATISTICAL SIGNIFICANCE?
Linneman See Kranzler: 108-109
The Logic of Hypothesis Testing
We start with a theory (below) which leads us to the RH
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 (Carl Pauper)
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 confidence that RH is true; null won’t be on any test
Type I Error
• We find in our sample that X Y (related)
• Could the sample relationship occur just because it’s a non-representative
sample? (could it be sampling error)
We conclude there’s a relationship in the population when there really isn’t. (mistake
that we can make sample misleads us type I error)
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 (opposite mistake)
• 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
Need to find a balance between the two types of error keeping in mind that I is more imp
STATISTICAL SIGNIFICANCE FROM CHI-SQUARE
What is Chi-Square?
1. Chi-square is a statistic
• Calculated from your sample (anything you calculate from your sample is a stat)
2. Chi-square is calculated from crosstabs (Linneman) • The chi-square statistic compares the expected frequencies with the
observed frequencies (less similarity between expected and observed
frequencies = bigger value of chi-square)
3. We know the shape of the sampling distribution for chi-square
- Has its own curve: chi-curve
• Not symmetrical
• Changes with the size of the crosstab (columns and rows degrees of
freedom)
1. Calculating Expected Frequencies
First step: Calculating expected frequencies
• What would be expected in the population if no relationship
• Based solely on the marginals (sums we find)
• Marginals: the row and column totals in the margins
Male Female
Not working 161
Working 116

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