Transcript Lecture9 - University of Idaho

PSYC512: Research Methods
Lecture 9
Brian P. Dyre
University of Idaho
PSYC512: Research Methods
Lecture 8 Outline
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Exam Next Week
 Will cover all lecture material, all material in Howell Chapters 15, broad concepts assumptions from Howell Chapters 6-11
 What do I mean by “broad concepts?”
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which tests are associated with which types of scaling properties of
variables?
What variants of the tests exist and why?
What assumptions underlie the test?
Questions about material covered in Lecture 8
 Describing Data
The Normal Distribution
Testing Hypotheses
Inferential Statistics
PSYC512: Research Methods
Review: The Normal
Distribution
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What is the difference between a normal
distribution and a standard normal distribution?
What is the difference between a raw score and
a standardized score?
What are confidence intervals?
PSYC512: Research Methods
Testing Hypotheses
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Hypothesis testing is the process by which
hypothetical relationships between intervening
variables are assessed
Hypotheses are always tested relative to oneanother or to a “null” hypothesis
Examples
 Comparing groups
 Assessing performance interventions
 Assessing relationships between variables
PSYC512: Research Methods
Null-Hypothesis Testing and
Inferential Statistics
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2 possible realities
 Relationship between your variables does not exist—a
null relationship (Ho, the null hypothesis)
 Relationship between the two variables in question
actually exists (H1, the experimental or alternative
hypothesis)
2 possible decisions when looking at the data
 Conclude that a relationship exists (reject the null
hypothesis, Ho  DISCONFIRMATION!)
 Conclude that no relationship exists (do not reject the
null hypothesis  CONFIRMATION? NO!)
PSYC512: Research Methods
Null-Hypothesis Testing and
Inferential Statistics
2 realities by
2 decisions
form a 2 x 2
matrix of 4
possibilites
Decision
True State of the World
Ho True
Reject Ho
Type I
(conclude there is error
an effect)
(false
alarm)
Do not Reject Correct
Ho (conclude Decision
there is NOT an
effect)
PSYC512: Research Methods
Ho False
Correct
Decision
Type II
error (miss)
Null-Hypothesis Testing and
Inferential Statistics
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Frequency
Why might we observe a
difference between two
groups if no difference
actually exists (null is
true; samples are drawn
from the same
population)?
Each sample may have a
unique mean due to
sampling error
0.04
y ( x)
1.48710
7
 50
m
x
2 samples
Frequency
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1 Population
0.04
y ( x)
7
0.04
y ( x)
7
1.4871.487
10 10
 50  50
X1 X 2
PSYC512: Research Methods
x
x
50
50
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How does this change if
a difference actually
exists between my
groups?
Each sample has a
unique mean that
represents both
sampling error and the
differences between the
2 populations
0.04
y ( x)
2 Populations
0.04
y ( x)
7
1.48710
1.48710
 50
7
m1  50m2 x
Frequency
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Frequency
Null-Hypothesis Testing and Inferential
Statistics
0.04
y ( x)
1.48710
7
0.04
y ( x)
1.48710
 50
X1
PSYC512: Research Methods
x
7
 50
x
X2
x 50
50
Hypothesis Testing:
Probability and Statistics
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Problem: How do we distinguish real differences or relationships
from measurement noise?
Probability and statistics may be used to assess (descriptive
statistics) or compare (inferential statistics) the relative magnitude
of different types of variability
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Effect (treatment) Variance
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Variability due to relationship between variables or effect of
different levels of independent variable (treatments)
“Good” variance that we want to maximize
Error Variance
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Variability in measure due to factors other than the
treatment
“Bad” variance that we want to minimize
PSYC512: Research Methods
Hypothesis Testing: Inferential
Statistics
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All inferential statistics are evaluating this ratio:
Test statistic =
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Effect (good) Variance
-------------------------------------Error (bad) Variance
Example test statistics: Chi-square, t, F
These test statistics have known distributions that then
allow us to estimate p, the probability of a Type I error
(inappropriately rejecting the null hypothesis)
Decision to reject null is made by comparing p to some
generally accepted criterion for Type I error probability, a
= .05
PSYC512: Research Methods
How is the probability of a Type I
error, p, calculated? It depends on…
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Scaling properties of your dependent variable (DV)
 DV is interval or ratio parametric tests
 DV is nominal or ordinal non-parametric tests
Research design
 Experimental – test differences on measure
between conditions or groups  t-test, ANOVA,
sign test, Mann-Whitney
 Correlational – test relations between different
measures  Pearson product-moment correlation,
point-biserial correlation, etc.
Manner in which you phrase your hypotheses
 One tailed vs. two-tailed tests
PSYC512: Research Methods
Examples?
PSYC512: Research Methods
Next Time…
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Topic: Review of broad concepts related to
power, Chi-square, t-tests, and correlation
Be sure to:
 Review Howell chapters 6-10
 Bring questions!
 Continue searching and reading the scientific
literature for your proposal
PSYC512: Research Methods