Theories - the Department of Psychology at Illinois State University
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Transcript Theories - the Department of Psychology at Illinois State University
Using Statistics in Research
Psych 231: Research
Methods in Psychology
Final Drafts of class experiment due in
labs the week after Thanksgiving
Don’t forget to look over the grading checklist
in the PIP packet
Announcements
Purpose: To make claims about populations
based on data collected from samples
What’s the big deal?
Example Experiment:
Group A - gets treatment to improve memory
Group B - gets no treatment (control)
After treatment period test both groups for memory
Results:
Group A’s average memory score is 80%
Group B’s is 76%
Is the 4% difference a “real” difference (statistically
significant) or is it just sampling error?
Inferential Statistics
Step 1: State your hypotheses
Step 2: Set your decision criteria
Step 3: Collect your data from your sample(s)
Step 4: Compute your test statistics
Step 5: Make a decision about your null hypothesis
“Reject H0”
“Fail to reject H0”
Testing Hypotheses
Step 1: State your hypotheses
Null hypothesis (H0)
• “There are no differences (effects)”
Alternative hypothesis(ses)
This is the
hypothesis
that you are
testing
• Generally, “not all groups are equal”
You aren’t out to prove the alternative hypothesis
(although it feels like this is what you want to do)
If you reject the null hypothesis, then you’re left
with support for the alternative(s) (NOT proof!)
Testing Hypotheses
Step 1: State your hypotheses
In our memory example experiment
Null
H0: mean of Group A = mean of Group B
Alternative HA: mean of Group A ≠ mean of Group B
(Or more precisely: Group A > Group B)
It seems like our theory is that the treatment should
improve memory.
That’s the alternative hypothesis. That’s NOT the
one the we’ll test with inferential statistics.
Instead, we test the H0
Testing Hypotheses
Step 1: State your hypotheses
Step 2: Set your decision criteria
Your alpha level will be your guide for when to:
• “reject the null hypothesis”
• “fail to reject the null hypothesis”
This could be correct conclusion or the incorrect conclusion
• Two different ways to go wrong
• Type I error: saying that there is a difference when there really
isn’t one (probability of making this error is “alpha level”)
• Type II error: saying that there is not a difference when there
really is one
Testing Hypotheses
Real world (‘truth’)
H0 is
correct
Reject
H0
Experimenter’s
conclusions
Fail to
Reject
H0
Error types
H0 is
wrong
Type I
error
Type II
error
Real world (‘truth’)
Defendant
is innocent
Defendant
is guilty
Type I error
Jury’s decision
Find
guilty
Type II error
Find not
guilty
Error types: Courtroom analogy
Type I error: concluding that there is an effect (a difference
between groups) when there really isn’t.
Sometimes called “significance level”
We try to minimize this (keep it low)
Pick a low level of alpha
Psychology: 0.05 and 0.01 most common
Type II error: concluding that there isn’t an effect, when there really
is.
Related to the Statistical Power of a test 1
How likely are you able to detect a difference if it is there
Error types
Step 1: State your hypotheses
Step 2: Set your decision criteria
Step 3: Collect your data from your sample(s)
Step 4: Compute your test statistics
Descriptive statistics (means, standard deviations, etc.)
Inferential statistics (t-tests, ANOVAs, etc.)
Step 5: Make a decision about your null hypothesis
Reject H0
Fail to reject H0
“statistically significant differences”
“not statistically significant differences”
Testing Hypotheses
“Statistically significant differences”
When you “reject your null hypothesis”
• Essentially this means that the observed difference is
above what you’d expect by chance
• “Chance” is determined by estimating how much
sampling error there is
• Factors affecting “chance”
• Sample size
• Population variability
Statistical significance
Population mean
Population
Distribution
x
n=1
Sampling error
(Pop mean - sample mean)
Sampling error
Population mean
Population
Distribution
Sample mean
x
n=2
x
Sampling error
(Pop mean - sample mean)
Sampling error
Generally,
as the
sample
Population
mean
size increases, the sampling
error decreases
Sample mean
Population
Distribution
x
x
n = 10
x
x
x x
x
x xx
Sampling error
(Pop mean - sample mean)
Sampling error
Typically the narrower the population distribution, the
narrower the range of possible samples, and the smaller the
“chance”
Small population variability
Sampling error
Large population variability
These two factors combine to impact the distribution of
sample means.
The distribution of sample means is a distribution of all possible
sample means of a particular sample size that can be drawn
from the population
Population
Distribution of
sample means
Samples
of size = n
XA XB XC XD
“chance”
Sampling error
Avg. Sampling
error
“A statistically significant difference” means:
the researcher is concluding that there is a difference above
and beyond chance
with the probability of making a type I error at 5% (assuming an
alpha level = 0.05)
Note “statistical significance” is not the same thing as
theoretical significance.
Only means that there is a statistical difference
Doesn’t mean that it is an important difference
Significance
Failing to reject the null hypothesis
Generally, not interested in “accepting the null hypothesis”
(remember we can’t prove things only disprove them)
Usually check to see if you made a Type II error (failed to
detect a difference that is really there)
• Check the statistical power of your test
• Sample size is too small
• Effects that you’re looking for are really small
• Check your controls, maybe too much variability
Non-Significance
Different statistical tests
“Generic test”
T-test
Analysis of Variance (ANOVA)
Have a great Thanksgiving break
Next time: Inferential Statistical Tests