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University of Guelph
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Psychology
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PSYC 2360
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Mark Fenske
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Chapter 8

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Psychology

PSYC 2360

Mark Fenske

Winter

Description

Chapter 8:
Hypothesis Testing and Inferential Statistics
Probability and Inferential Statistics
- any pattern of data that might have been caused by a true relationship between
variables might instead have been caused by chance
- why research never actually “proves” hypothesis or theory
- Hypothesis Testing Flow Chart:
Develop Research Hypothesis
Set alpha (Usually α=.05)
Calculate power to determine
sample size that is needed
Collect Data
Calculate statistic and p-value
Compare p-value to alpha(.05)
p < .05 p > .05
Reject Fail to Reject
Null Hypothesis Null Hypothesis - Those previous procedures involve
- use of probability
- statistical analysis
- Inferential Statistics -- statistical procedures that use sample data to draw inferences
- about true state of affaires
Sampling Distributions and Hypothesis Testing
- directly testing whether a research hypothesis is correct or incorrect NOT achievable
goal
- not possible to specify what observed data would look like if hypothesis was
true
- possible to specify in statistical sense, what observed data would look like if
hypothesis was not true
- Sampling Distribution -- distribution of all the possible values of a statistic
- each statistic has associated sampling distribution
- there is a sampling distribution for:
- mean
- standard deviation
- correlation coefﬁcient
- Binomial Distribution -- distribution of correct and incorrect guesses
- as sample size ↑, extreme values are less likely to be observed
- as sample size ↑, distribution becomes narrower
- Null Hypothesis
- Null Hypothesis (H ) 0- assumption that the observed data reﬂects only what
- would be expected under the sampling distribution
- speciﬁes the least-interesting possible outcome
- the hope in an experiment is to REJECT the null hypothesis
- to be able to conclude that observed data was caused by something
other than chance
- Testing for Statistical Signiﬁcance
- Setting Alpha
- observed data must deviate substantially from what is to be expected in
order to reject null hypothesis
- Signiﬁcance Level (alpha) -- standard that the observed data must
- meet
- alpha normally = 0.05
- rejecting null hypothesis if observed data = so unusual that they
would have occurred by chance at max. 5% of the time
- as alpha ↓, ↑ stringent the standard
- Comparing p-value to Alpha
- Probability Value (p-value) -- shows likelihood of an observed statistic
- occurring on basis of sampling distribution
- indicates how extreme data scores are
in terms of caused by chance
- Statistically Signiﬁcant -- if the p-value is less than alpha (p < .05)
- REJECT null hypothesis - Statistically Nonsigniﬁcant -- if the p-value is greater than alpha
- (p > .05)
- FAIL TO REJECT null hypothesis
- p-value for given outcome is found through examination of sampling
distribution of statistic
- Using One- and Two-Sided p-values
- One-sided p-values -- unusual outcomes occur in only one way
- Two-sided p-values -- unusual outcome occur in more than one way
- p-value is always 2x bigger than one-way p-
value
- because binomial distribution is
symmetrical
- provide more conservative statistical test
- allow us to interpret statistically signiﬁcant
relationships
- even if differences are not in direction
originally predicted in hypothesis
Reduction of Inferential Errors
REJECT FAIL TO REJECT
Null Hypothesis Null Hypothesis
Null Hypothesis is Type 1 Error Correct Decision
TRUE Probability = α
Probability = 1 - α
Null Hypothesis is Correct Decision Type 2 Error
FALSE Probability = 1- β Probability = β
**POWER**
- Type 1 Errors
- Type 1 Error -- reject null hypothesis when it was actually true
- should have failed to reject null hypothesis
- we know we will make a Type 1 error no more than 5% of the time (if α = .05)
- you never know for sure whether or not you make a Type 1 error
- it is possible that data that interpreted as rejecting null hypothesis are cause by
random error and that the null hypothesis is really true
- by setting alpha, it allows us to assure that a Type 1 error has not been made
- Type 2 Errors
- Type 2 Error -- fail to reject null hypothesis when it was actually false - should have rejected null hypothesis
▯ - missing true relationship
- Statistical Power
- Power -- probability that the research will reject the null hypothesis given that
- the null hypothesis is actually false
- correctly rejecting null hypothesis
- Power = 1 - β
- depends in part of how big the relationship being searched
for actually is
- bigger it is, easier to detect
- Effect Size
- beta can only be estimated
- Effect Size -- size of relationship between variables
- indicated by a statistic
- indicates the magnitude of relationship
- 0 = no relationship between variables
- large & positive = strong relationship between variables
- because researcher can never know ahead of time the exact effect size
of relationship
- cannot exactly calculate power

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