Transcript Statistics for the Social Sciences - the Department of Psychology at

Statistics for the Social Sciences
Psychology 340
Fall 2006
Review For Exam 1
Outline
Statistics for the
Social Sciences
• Review
• Statistical Power Analysis Revisited
Review
Statistics for the
Social Sciences
• Basic research methods and design
– Experiments, correlational methods, variables, decision tree,
samples & populations, etc.
• Describing distributions
– With graphs (histograms, freq. dist. tables, skew, and numbers (e.g.,
mean, median, std dev, etc.)
• Z-scores, standardized distributions, standard error, and the
Normal distribution
• Hypothesis testing
– Basic logic, types of errors, effect sizes, statistical power
Things to watch for
Statistics for the
Social Sciences
• Show all of your work, write out your assumptions, and the
formulas that you are using
• Keep track of your distributions - samples, distribution of
sample means, or population
• Write out your hypotheses, don’t forget to interpret your
conclusions (e.g., “reject H0” isn’t enough)
• 1-tailed or 2-tailed, and the impact of this on your critical
comparison values
• Understand what the numbers are on the Unit Normal Table
The exam
Statistics for the
Social Sciences
• The first one is closed book
• Has 5 questions (each with subparts)
• I’ve provided some of the formulas
– You need to know formulas for standard deviation and
mean
Statistical Power
Statistics for the
Social Sciences
Real world (‘truth’)
H0 is
correct
H0 is
wrong
Real world (‘truth’) H0: is true (is no treatment effect)
Type I
error

The original (null) distribution
Type
II error

 = 0.05
Reject H0
Fail to reject H0
Statistical Power
Statistics for the
Social Sciences
Real world (‘truth’)
H0 is
correct
H0 is
wrong
Real world (‘truth’) H0: is false (is a treatment effect)
Type I
error

Type
II error

The new (treatment) distribution
The original (null) distribution
 = 0.05
Reject H0
Fail to reject H0
Statistical Power
Statistics for the
Social Sciences
Real world (‘truth’)
H0 is
correct
H0 is
wrong
Real world (‘truth’) H0: is false (is a treatment effect)
Type I
error

Type
II error

The new (treatment) distribution
 = 0.05
Reject H0
The original (null) distribution
 = probability
of a Type II
error
Fail to reject H0
Failing to
Reject H0, even
though there is
a treatment effect
Statistical Power
Statistics for the
Social Sciences
Real world (‘truth’)
H0 is
correct
H0 is
wrong
Real world (‘truth’) H0: is false (is a treatment effect)
Type I
error

Type
II error

The new (treatment) distribution
 = 0.05
Power = 1 - 
Probability of
(correctly)
Rejecting H0
Reject H0
The original (null) distribution
 = probability
of a Type II
error
Fail to reject H0
Failing to
Reject H0, even
though there is
a treatment effect
Statistical Power
Statistics for the
Social Sciences
• Steps for figuring power
1) Gather the needed information: mean and standard error of the
Null Population and the predicted mean of the Treatment
Population
1  60;  X  2.5
2  55;  X  2.5
2
1
Statistical Power
Statistics for the
Social Sciences
• Steps for figuring power
2) Figure the raw-score cutoff point on the comparison distribution
to reject the null hypothesis
1  60;  X  2.5
From the unit normal  = 0.05
table: Z = -1.645
Transform this z-score to a
raw score
1
raw score  1   X (Z X ) 60  (2.5)(1.645)  55.89
Statistical Power
Statistics for the
Social Sciences
• Steps for figuring power
3) Figure the Z score for this same point, but on the distribution
of means for treatment Population
2  55;  X  2.5
Remember to use the
properties of the
treatment population!
 0.355
X   55.88  55
Z

X
2.5
Transform this raw score to
a z-score
55.89
Statistical Power
Statistics for the
Social Sciences
• Steps for figuring power
4) Use the normal curve table to figure the probability of getting
a score more extreme than that Z score
 = probability
of a Type II
error
From the unit normal table:
Z(0.355) = 0.3594
 0.355
Power = 1 - 
Power  1  0.3594  0.64
55.89
The probability of detecting this an effect of this size from these
populations is 64%
Statistical Power
Statistics for the
Social Sciences
Factors that affect Power:
 -level
– Sample size
– Population standard deviation 
– Effect size
– 1-tail vs. 2-tailed