CHAPTER 4
CORRELATION
Discovering Statistics Using SPSS
© Andy Field 2005
Summary of the last two lectures
• Simple statistical models
• SPSS environment
• Exploring Data – checking whether it is
“normal”
Discovering Statistics Using SPSS
© Andy Field 2005
Simple statistical models: Variance
•
•
•
•
Mean = The sum
SS = Sum of squared errors
Variance = SS/N-1
Then……
• Standard deviation = square root of the variance
• The bigger the number of the SD, the more to show that
the mean is not an accurate model.
Discovering Statistics Using SPSS
© Andy Field 2005
The Standard Error
• It is the standard deviation of sample means.
• ### A large standard error (relative to the sample mean)
means that there is a lot of variability between the means
of different samples and so the sample we have might
not be representative of the population.
• ### A small standard error indicates that most sample
means are similar to the population means and so our
sample is likely to be an accurate reflection of the
population.
Discovering Statistics Using SPSS
© Andy Field 2005
Normal Distribution and Z-score
http://www.youtube.com/watch?v=1xhCL5m
4nI0&feature=related
Discovering Statistics Using SPSS
© Andy Field 2005
Assumption of Parametric
date
1. Normally distributed data
2. Homogeneity of variance – each of the group you
tested should have the same variance
3. Interval data – the distance between points of your
scale should be equal at all parts along the scale
4. Independency – data from different subjects are
independent, which means that the behavior of one
participant does not influence the behavior of another.
Discovering Statistics Using SPSS
© Andy Field 2005
We need to check the “normality’ of the data by
doing this:
• Analyze>Descriptive Statistics>Frequencies…
• Analyze>Descriptive Statistics>Explore…
• Graphs>Bar…
– http://www.uk.sagepub.com/field3e/SPSSstudentmovies8.htm
Discovering Statistics Using SPSS
© Andy Field 2005
RELATIONSHIP BETWEEN
VARIABLES
Discovering Statistics Using SPSS
© Andy Field 2005
Correlation
Discovering Statistics Using SPSS
© Andy Field 2005
Correlation is…
• A measure of the linear relationship
between variables
• Three relationships can exist between X &
Y
– + (positive)
– - (negative)
– No relationship
Discovering Statistics Using SPSS
© Andy Field 2005
Covariance
• The simplest way to look at whether two
variables are associated is to look at
whether they COVARY
• In other words – whether changes in one
variable are met with similar changes in
the other variable.
• If one deviates from the mean, (if they are
related), another variable will also move
Discovering Statistics Using SPSS
© Andy Field 2005
Variance = SS/N-1
• When there are two variables, rather than
squaring each difference, we can multiply
the difference for one variable by the
corresponding difference for the second
variable.
Discovering Statistics Using SPSS
© Andy Field 2005
Covariance
• A positive covariance indicates that as one
variable deviates from the mean, the other
variable deviates in the SAME direction.
• A negative covariance indicates that as
one variable deviates from the mean, the
other deviates from the mean in the
opposite direction.
Discovering Statistics Using SPSS
© Andy Field 2005
Standardization
• The standardized covariance value is
known as a correlation coefficient = r
• Always lies between -1 (perfectly negative)
and +1 (perfectly positive)
Discovering Statistics Using SPSS
© Andy Field 2005
Figure 4.1
Discovering Statistics Using SPSS
© Andy Field 2005
Before calculating the r
• Use a scatterplot to have a “feel” of the
relationship between the two or more
variables
• Why? It helps us to see whether there
seems to be a relationship between the
variables, what kind of relationship it is
and whether any cases are markedly
different from the others.
Discovering Statistics Using SPSS
© Andy Field 2005
Simple Scatterplot
Discovering Statistics Using SPSS
© Andy Field 2005
3D Scatterplot
Discovering Statistics Using SPSS
© Andy Field 2005
Overlay Scatterplot
Discovering Statistics Using SPSS
© Andy Field 2005
Matrix Scatterplot
Discovering Statistics Using SPSS
© Andy Field 2005
Calculation
There are two types of correlation:
1. Bivariate (two variables)
2. Partial (two variables while controlling the
effect of one or more additional variables)
http://www.uk.sagepub.com/field3e/SPSSstu
dentmovies.htm
Discovering Statistics Using SPSS
© Andy Field 2005
If any of the variables is a categorical variable,
the….
• Biserial and Point-Biserial Correlations
Discovering Statistics Using SPSS
© Andy Field 2005
Partial Correlation
Discovering Statistics Using SPSS
© Andy Field 2005
Partial Correlation
Discovering Statistics Using SPSS
© Andy Field 2005
Discovering Statistics Using SPSS
© Andy Field 2005