Download Theories - the Department of Psychology at Illinois State University

Using Statistics in Research
Psych 231: Research
Methods in Psychology
From Correlation to Regression

Last time we “imagined” a line through the
points
Y
6
5
4
3
2
1
1
2
3
4
5
6 X
From Correlation to Regression

Compute the equation for the line that best
fits the data points
Y
6
5
Y = (X)(slope) + (intercept)
4
3
2
1
0.5
Change in Y
1
2
3
4
5
6 X
Change in X
2.0
= slope
Regression

4.5
Can make specific predictions about Y
based on X
Y
6
5
X=5
Y = (X)(.5) + (2.0)
Y=?
Y = (5)(.5) + (2.0)
Y = 2.5 + 2 = 4.5
4
3
2
1
1
2
3
4
5
6 X
Regression

Also need a measure of error
Y = X(.5) + (2.0) + error
Y = X(.5) + (2.0) + error
• Same line, but different relationships (strength difference)
Y
6
5
Y
6
5
4
3
2
1
4
3
2
1
1
2
3
4
5
6 X
1
2
3
4
5
6 X
Cautions with correlation & regression



Don’t make causal claims
Don’t extrapolate
Extreme scores (outliers) can strongly
influence the calculated relationship
Inferential Statistics

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?
Testing Hypotheses





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
Error types
Real world (‘truth’)
H0 is
correct
Reject
H0
Experimenter’s
conclusions
Fail to
Reject
H0
H0 is
wrong
Type I
error

Type II
error

Error types: Courtroom analogy
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

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
How likely are you able to detect a difference if it is there
1
Testing Hypotheses




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”
Statistical significance

“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
Sampling error
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
x x
x
x xx
x
x
n = 10
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
Large population variability
Sampling error

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”
Avg. Sampling
error
Significance

“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
Non-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
Next time: Inferential Statistical Tests

Different statistical tests



“Generic test”
T-test
Analysis of Variance (ANOVA)