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University of Toronto Mississauga
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Sociology
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SOC222H5
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John Kervin
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Lecture 6

Department

Sociology

Course Code

SOC222H5

Professor

John Kervin

Description

1
SOC 222 -- MEASURING the SOCIAL WORLD
Session #6 INFERENTIAL STATS II: SIGNIFICANCE & CONFID. INTERVALS
Linneman: ch. 5
Kranzler: chs. 6, 7
WHERE WE ARE
samples
populations
standard error
sampling error
sampling distribution
Today
Today’s Objectives: Know…
1. The difference between statistical significance and confidence intervals
2. The logic of hypothesis testing and null hypotheses
3. The difference between Type I and Type II errors
4. How Type I error is calculated
5. The role of the normal distribution in calculating Type I errors
6. The five conventional significance levels
7. How confidence intervals are calculated
8. how sample size is related to statistical significance and confidence intervals
9. The SPSS procedures for getting statistical significance and confidence intervals
for single variables
Terms to Know
confidence interval
mu (μ)
t-curve
normal curve
statistical significance
significance level
research hypothesis
null hypothesis
type I error
type II error
degrees of freedom 2
USING the STANDARD ERROR
STATISTICAL SIGNIFICANCE
• Could the population characteristic actually be zero?
• Cat-cat: the percentage difference is really zero
• Cat-rat: the difference in means is really zero
• Rat-rat: the correlation coefficient “r” is really zero
the slope “b” is really zero
the coefficient of determination “R ” is really zero
Does not say or ask anything about size or strength of a relationship
HYPOTHESIS TESTING
1. A research question:
• Do students who study more hours achieve higher grades?
2. A research hypothesis:
• Hypothesis: students who study more hours achieve higher grades.
The Problem of “Truth”
Logically, it is very difficult to show something is true- cant test all swans in the world(all
swans are white)
So instead its easier to prove the opposite- no swans are not white
Disprove reverse hypothesis
Null Hypotheses
null hypothesis: the opposite
EG:
• Research hypothesis: students who study more hours achieve higher grades.
• X and Y are related
• Null hypothesis: students who study more hours do not achieve higher grades
• X and Y are not related
NOTE:
• Disproving a null hypothesis does not prove the research hypothesis
It just supports the research hypothesis, hypothesis are never proven true, theyre just
supported
Null Hypotheses, Samples, and Populations
• sampling error- what you found in sample was a mistake, there is
nothing going on in population. 3
we try to disprove that null hypothesis- then we have support and we can test null
hypothesis reputedly . We keep on disproving null, then belief in research gets stronger
INFERENCE ERRORS
Population Reality (unknown)
Sample Results: Relationship No Relationship
Relationship OK Type I Error
No relationship Type II Error OK
Type I Error
We can never know if we make a type 1 error
Say there’s relationship but there really isn’t
We estimate the probability of making a type 1 error
The statistical significance of an X-Y relationship is related to
• Probability of a Type I error
Standard Error and Chance of a Type I Error
Bad samples are found in tail of distribution, more spread out the more the chance of
bad sample
• The more spread out the sampling distribution, the more chance of a bad sample
• The more chance of a bad sample, the higher the chance of a type I error
• IE, the more spread in the sampling distribution, the higher the chance of a type I
error
• Statistical significance is the chance of a type I error.
Calculating Chance of a Type I Error
We can never REALLY know if we made a type 1 error
To do this, we need to know the shape of the sampling distribution curve
1. The mean of the sampling distribution statistic
2. The standard error of the sampling distribution statistic
3. The overall shape of the sampling distribution curve
Estimate of standard error comes from what we can calculate from standard deviation
There are different distribution curves (4 in this class)
The Normal Distribution
This is a bell-shaped curve.
• The statistic is said to be normally distributed
• The sampling distribution of means is normally distributed 4
• Distance from the mean is in terms of SEs from the mean
• These are the Z scores
• The size of the area under the curve corresponds to the number of possible
samples in particular part of the curve
-3 -2 -1 0 1 2 3
Standard Errors from the Mean
sample
mean
Our null hypothesis: the population mean is zero- there’s nothing going on
Our sample finding: a mean with a Z score of 1.25 5
-3 -2 -1 0 1 2 3
Standard Errors from the Mean
sample
mean
Probability of a type I error
= Proportion of samples with Z scores of 1.25 or more
= 6/36
So chance of a type I error is 1/6,

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