Transcript Chapter 11: Bivariate Statistics and Statistical Inference

“Figures don’t lie, but liars figure.”
Chapter 11: Bivariate Statistics
and Statistical Inference
Key Concepts: Statistical
Inference
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Making Inferences
 We calculate the odds…
 Crossing a busy street and not getting hit?
 The movie will be good?
 A child will be safe if left with parents in which
there was previous child abuse?
 Probability (the odds, chances of)
 The chances of an event based on the ratio of
favorable outcomes to total outcomes.
 Getting heads on a coin flip 1/2 = .5 (50%)
 Getting an Ace from cards: 4/52 = 7.7%
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What are the odds (con’t.)
 Average height: male – 5’9”; female 5’5”
 Which groups are all male and all female?
 Is the sample representative of the population?
 How certain are you of your answer?
 Could all 3 groups be the same sex?
Group 1: 5’8, 5’6, 5’4, 5’2, 5’4, 5’5, 5’6, 5’1
Group 2: 5’9, 6’1, 5’8, 5’7, 5’8, 5’9, 6’2, 5’6
Group 3: 5’6, 5’8, 6’0, 5’2, 5’7, 5’5, 5’7, 5’6
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Statistical Inference
 Variation – differences in behavior,
attitudes, values, characteristics, etc.
 There is variation in the population
 e.g., some people like chocolate, others like vanilla.
 A sample is picked from the population.
 We study the sample to make inferences about the
population.
 To do so, the sample must reflect the population in
the characteristics under study.
 If 30% prefer chocolate in the sample, we’d like to
conclude that 30% prefer chocolate in the
population.
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Statistical Inference (con’t.)
 BUT, sometimes the sample does not reflect the
population – the extent to which it doesn’t is
SAMPLE ERROR.
 We can calculate the chances that the relationship
between variables in the sample is due to sample
error.
 Influences on sample error
 Luck – someone wins the lottery even if the odds are
40 million to 1.
 Sample size – smaller samples will have more
chances of error.
 Homogeneity – less variation in the population yields
smaller sample error.
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Hypothesis Testing
 Testing the relationship between two or more
variables.
 Statistical tests are used to find the probability
that the relationship between variables is due
to sampling error or to chance.
Type
Example
Null hypothesis (Ho) – No relationship There is no relationship between
income and mental health.
Two-tailed hypothesis (H1) – There is
a relationship
There is a relationship between income
and mental health.
One-tailed hypothesis (H1) –
Directional relationship
The greater the income the greater the
mental health.
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Statistical Inference (con.)
 p-value
 The probability that a relationship between
variables or a mean difference found in a sample
is a result of sample error.
 p =.05 means there is a 5% chance that the
relationship found in the sample is a result of
sample error.
 p =.05 means there is a 95% that the relationship
is NOT due to sample error, and actually reflects
the differences in the population.
 Rejection level: If the p value is <.05, we reject
the null hypothesis and accept the alternative
hypothesis. (Why .05? – Convention).
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