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PSY 395 Lab #8 – Data Analysis
Three basic data analysis approaches for many
research questions:
(1) Correlation
(2) Regression
(3) Independent Samples t-test
What is it?
Hypothesis Testing
When do you use it?
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Method 1: Correlation
What is it?
Numerical index that reflects the degree of linear
relationship between two variables
 The correlation is also called the Pearson
product-moment correlation.
 Measures a linear relationship between 2
variables (usually continuous)
 Represented as r
Characteristics
1. Direction: The sign specifies the direction of
the relationship (positive = direct relationship,
negative = inverse relationship).
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2. Form: typically used for linear relationships
linear 
not linear! 
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3. Magnitude or strength:
 degree to which the relationship between
the two variables fits the form (typically
a straight line)
 a perfect correlation has a value of +1 or
–1 (so a correlation of -.78 is stronger
than a correlation of .23 even though -.78
is negative)
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A correlation is a ratio between the degree that 2
variables vary together and the degree that the 2
variables vary in different ways.
r = degree that X and Y vary together/degree that X and Y vary separately
or in mathematical terms:
r
cov( x, y )
var( x) var( y)
where cov = covariance and var = variance
A perfect correlation is +1 or -1 which would mean
that for every z-score change in the value of X there
is an equivalent corresponding z-score change in the
value of Y (+1 means change is in the same direction;
-1 means the change is in the opposite direction).
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Hypothesis Testing
Sample statistic: r
Population parameter: population correlation 
(rho)
Step 1: Hypotheses & 
The question of interest is whether the
relationship obtained in the sample will hold in
the population.
Two-tailed:
Ho:  = 0
We will use =.05.
H1:   0
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Step 2: Critical region
Use the table of critical values for the
correlation.
Need to know:
 1 or 2 tailed test

 df
Example: rcrit = .805.
To reject Ho, we need to obtain r > +.805.
Step 3: Test statistic.
The obtained sample correlation is r = +.90.
Step 4: Evaluate Ho.
We reject the null hypothesis because r > +.805.
We can conclude there is a significant
correlation.
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When do you use it?
Interested in assessing the strength of
association between two variables
Sometimes there is no obvious distinction
between independent variable and dependent
variable
Examples:
What is the relationship between self-esteem and
extraversion?
Is level of reading readiness related to
intelligence in children?
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Method 2: Regression
What is it?
Linear regression fits a line to a set of data and
uses the equation for this line to predict future
values on the variables.
The relationship can also be represented by the
following general equation:
Y  b0  b1 X
b0 : Y-intercept
b1 : slope
Regression is like correlation in that positive
correlations mean positive regression slopes
(and negative correlations mean negative
regression slopes). However regression is used
for predicting scores. Regression can be used to
predict values of Y.
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If the relationship between the # of hours of TV
watched per week (X) and GPA (Y) is
Y  .07 X  4.0 , you would predict a person who
watches 10 hours per week has a GPA of
Y  .07(10)  4.0  3.3
In order to find the regression line that best fits
the data, we solve the following equation:
Ŷ = b0  b1 X
Ŷ: predicted value of Y
There will be some error of prediction between
Ŷ and the actual value of Y, represented as the
difference between actual and predicted values:
Y–Ŷ
To estimate the total error, it is necessary to
square the discrepancies and sum them to
calculate the total squared error:
(Y – Ŷ)2
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We need to find the linear equation that
minimizes the total squared error.
This equation is the least-squares error
solution.
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Hypothesis Testing
Sample statistics:
b0
b1
Population parameters:
0
1
Step 1: Hypotheses & 
The question of interest often is focused on
slope.
Two-tailed:
Ho:  1 = 0
We will use =.05.
H1:  1  0
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Step 2: Calculate t statistic
t = sample statistic–hypothesized population parameter
estimated standard error
t  b1 S  1
b1
Step 3: Critical region
Use the table for t statistic.
Need to know:
 1 or 2 tailed test

 df
Example: t-critical = 2.04
Step 4: Test statistic.
The obtained t-value is t = 3.36.
Step 5: Evaluate Ho.
We reject the null hypothesis because t > 2.04.
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When do you use it?
Related to correlation in that both are concerned
with assessing the relationship between sets of
paired data.
Regression is often used when there is a clearer
distinction between what the independent and
dependent variable are (i.e., when you know Y,
what is being predicted [the DV] and X, what is
predicting it [the IV]).
Also correlation tends to be used when the
primary interest is in assessing the strength of
relationship, regression is used when primary
interest is in prediction.
Regression is also often used when we have
more than one independent variable.
Example: We’re interested in predicting
extroversion from self-esteem scores.
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Method 3: Independent Samples t-test
What is it?
Independent samples t-test is used when we’re
interested in the mean difference between two
sets of data
Used when we have an independent-groups
design: study uses separate samples for each
treatment condition (also known as a betweensubjects or between-groups design)
Want to know if the sample data support
rejecting equal means between groups in the
population. If this support is obtained, then we
can conclude that the mean of one group is
significantly different from the mean of another
group.
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Hypothesis Testing
Sample statistic:
X1  X2
Population parameter:
1 – 2
Step 1: Hypotheses & 
Ho: 1 – 2 = 0
(no difference between population means)
H1: 1 – 2  0
OR equivalently
H1: 1  2
(there is a mean difference between groups)
 = .05 and a two-tailed test will be used.
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Step 2: Set decision criteria and locate critical
regions.
Example: To reject Ho, the obtained t-statistic
must be < -2.101 or > +2.101.
Step 3: Collect sample data and calculate the tstatistic.
The independent measures t-statistic has the
same basic structure as before.
t = sample statistic–hypothesized population parameter
estimated standard error
t = ( X 1  X 2 ) – ( 1  2 )
sX 1  X 2
Step 4: Evaluate Ho.
Example: The obtained t-statistic is greater than
+2.101.
We reject Ho.
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When do you use it?
You have a study with a dependent variable, and
you are interested in the mean difference on that
variable for two independent groups.
Examples:
Do people who jog have fewer heart attacks than
those who don’t?
What is the effect of caffeine vs. no caffeine on
test performance? (note: this is a t-test if you had
2 groups, 1 who had a cup of coffee vs. 1 group
who had a glass of water; how could you make
this a correlational study instead, correlating
caffeine intake with test scores?)
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Homework for Lab 8
1. Which of the three methods would likely be most appropriate for
the following situations? Explain why?
a. An organization wants to evaluate whether there are
differences between African Americans vs. Caucasians
regarding whether an employment test is fair.
b. Research designed to assess the relationship between gender
and approval ratings of President Bush.
c. The Michigan Highway Safety Commission wants to know
whether the “Click It or Ticket” billboards are effective.
d. Research designed to examine the extent to which higher
levels of education lead to higher levels of money given to
charities.
2. Consider your final project:
(2a) At the construct level what is the general relationship you
are interested in (remember focus only on two variables)?
Which might be considered the IV or predictor, and which the
DV or criterion?
(2b) Now look at each variable. List three different ways you
could measure each variable. Be specific (e.g., don’t just say
“look at their behavior,” say “count the number of times an
individual opens a door for another person in a day”).
(2c) What would you say to convince a granting agency that
your study is important and worth funding (2-3 sentences max)?