Chapter%208:%20Hypothesis%20Testing%20and%20Inferential%20Statistics

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Chapter 8 Hypothesis Testing and Inferential
Statistics

• What are inferential statistics, and how are
  they used to test
• a research hypothesis?
• What is the null hypothesis?
• What is alpha?
• What is the p-value, used in most hypothesis
  test?
• What are Type 1 and Type 2 errors, and what is
  the relationships
• between them
• What is beta, and how does beta relate to the
  power of a statistical
• test?
• What is the effect size statistic, and how is it
  used?

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Sampling Distribution
Sampling Distribution
The distribution of all of the possible values of
a statistic.
Example. To examine your friends ESP aptitude,
you ask your friend to guess on ten coin flips
(heads and tails)
nCr
210 1024
10C5
252
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Binomial distribution
See Figure 8.2 on page 132...
nCr
10C5


24.6

Task 1. Calculate the other possibilities and
their distribution.
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The null hypothesis
The assumption in which the variable A is not
statistically differ from the variable B.
H0
Example 1. The coin guessing experiment H0 is
that the probability of a correct guess is chance
level ( .5)
Example 2. A correlational design H0 is that
there is no correlation between the two measured
variables (r 0). (the correlation between SAT
and College GPA.)
Example 3. An experimental design H0 is that the
mean score on the dependent variable is the same
in all experimental group (helping behavior
between men and women)
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Reject null hypothesis and fail to reject null
hypothesis
Reject null hypothesis There is a significant
statistical difference
between A and B.
Example 1. Observed data is statistically differ
from the chance level
Example 2. Variable A is statistically correlate
with Variable B.
Fail to reject null hypothesis there is no
significant statistical
difference between A and B
Example 1. Observed data is not differ from the
chance level.
Example 2. Variable A is no correlation to
Variable B
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Testing for Statistical Significance
Significance Level (alpha ?)
Who decides the level?
The level in which we are allowed to reject the
null hypothesis.
The researcher
By convention, alpha is normally set to ? .05
Probability value (p value)
The likelihood of an observed statistic
occurring on the basis of the sampling
distribution.
Statistically Significant
If P value is less than alpha (p lt .05)
Reject null hypothesis
Statistically nonsignificant
If P value is greater than alpha (p gt .05)
Fail to reject null hypothesis
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Comparing the P-value to Alpha
Example. The coin guessing experiment (Take a
look at Figure 8.2!)
P value for 10 correct guesses .001 P value for
9 and 10 correct guesses .01 . 001 .011 P
value for 8, 9, and 10 correct guesses .044
.01 .001 .055 P value for 7, 8, 9, and 10
correct guesses .117 .044 .01 .001 .172
P lt .05
P lt .05
P gt .05
P gt .05
Two-sided p-value
P value for number of guesses as extreme as 10 P
value for number of guesses as extreme as 9 P
value for number of guesses as extreme as 8 P
value for number of guesses as extreme as 7
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Type 1 Error Type 2 Error
Scientists Decision Reject null hypothesis
Fail to reject null hypothesis
Type 1 Error Correct Decision probability
? Probability 1- ? Correct decision Type 2
Error probability 1 - ? probability ?
Null hypothesis is true Null hypothesis is false
Type 1 Error
Type 2 Error
?
?
Cases in which you reject null hypothesis when it
is really true
Cases in which you fail to reject null hypothesis
when it is false
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Statistical Significance and the Effect Size
Statistical Significance Effect Size (ES) X
Sample Size
ES
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Hypothesis Testing Flow Chart
Develop research hypothesis null hypothesis
Set alpha (usually .05)
Calculate power to determine the sample size
Collect data calculate statistic and p
Compare p to alpha (.05)
P lt .05
P gt .05
Reject null hypothesis
Fail to reject null hypothesis