in statistical analysis we compute correlations to determine how one or
more variables are tied to each other if there is a relationship between one or
two and I really like this cartoon which is about the debate about correlation
and causation and then you may see correlation but it's not approved for
causation there's a correlation between drownings and ice-cream sales but ice
cream sales don't cause drowning suggested ice cream sales and drownings
increase during summertime so correlation even with this caveat is an
important statistical tool for us to analyze how variables behave in each
other's presence for categorical variables we can use cross tabulations
and the test associated with it is chi-square test and for continuous
variables one way of looking at the correlation between two continuous
variables is to draw a scatterplot and see if there is a trend you can also
estimate a correlation coefficient is they are continuous variables we can use
Pearson correlation and if there are categorical variables we can use
tetrachord correlation here is the mathematical notation on how to compute
correlations my advice would be to consult your stats book on these details
when you're using statistical software they can readily compute these numbers
but essentially you're looking at the deviations from mean for both variables
in the multiplication both and then you take the sum of it and divide it by the
number of observations and that's your covariance and then when you take the
covariance and divide by standard deviation for each variable that is the correlation
more important than the mathematical notation is to understand what
correlation means let's say you have two variables x and y and they are
positively correlated and we computed the correlation coefficient it's
0.74 to visualize that if two variables have a positive correlation of
0.74 this is the trend you would see that is when one increases so does the other
if they have a negative correlation see this small negative sign here you would
see a downward sloping curve that as one increases the other one declines and
when there is no correlation between the two variables you see this
random bedrooms so in our data set of beauty and evaluation we we plotted
these results and fit the regression line and it's very weak correlation this
is a the r square value which we will discuss later but you could see that
there is a positive trend that has beauty increases so does the teaching
evaluation but it's not that clear-cut proof there so if you were to compute
the bivariate correlation the correlation coefficient which is called
a pearson correlation coefficient its point one eight nine and that's the
correlation between beauty and evaluation or beauty score and evaluate
teaching evaluation it's the same here in sort of a matrix so is it
statistically significant yes again we will not discuss the statistics behind
it or the math behind it this is for hypothesis testing later but to
demonstrate that if you have a variable and the variable has a positive
correlation it may not even appear as a positive correlation just by looking at
it but when you compute the correlation coefficient its point one eight nine and
based on this statistical theory we can see there's a statistical significant
correlation we'll discuss that later how do you create a scatter plot and compute
the correlation coefficient in SPSS we click on graphs chart builder select the
scatterplot drag this here and click on normalize beautiful score bring it on
x-axis teaching evaluation score goes on y-axis and that's pretty much it we
click OK and the output comes in here and now we fit a regression line to it
so we double click on this output and click here it says do you want to fit a
linear regression line i'm not going to attach the label so i deselect this you
can see this is a dialog box and reapply and say close here and there's the
regression line then for correlation you click on analyze then on correlate
bivariate pick the two variables which are the beauty
score and the teaching evaluations click on ok