This is a summary of all the calculations for the course Introduction to Statistical Analysis. It includes how to do the calculations, how to do them in SPSS, and additional useful information.
Exam Grade: 9,9
Final Course Grade: 9,8
(How to do a crosstab in SPSS is included in Chi-square TFI)
, Pearson’s r
How can I calculate this?
Hand calculations and SPSS
When/why do I calculate this?
When you want to know the relationship/correlation between two variables
What is the level of measurement for the variables?
Both are interval/ratio
Calculation:
Step 1: draw a scatterplot if this helps you visualize the correlation.
Step 2: calculate the covariance
First, calculate the mean of the values in variable X and the mean of the values in variable Y.
Then, create a table like this:
X Y (X – Mx) (X – Mx) (X – Mx) x (X – Mx)
Fill in the table for each value.
After this, sum up all the values under (X – M x) x (X – Mx)
Divide this sum by n – 1 (the amount of samples – 1), and the result is your covariance
The formula for covariance is thus: covxy =
∑ ( X−Mx )( Y −My)
n−1
Step 3: calculate the standard deviations for X and Y
Create a table like this:
X Y (X – Mx) (Y – My) (X – Mx)2 (Y – My)2
Fill in the table for each value (of course you don’t have to since you already have most values from
the previous table, but it could make it easier to visualize)
After this, sum up all the values under (X – Mx) 2
Divide this sum by n – 1 and then take the root of that number
So the formula for the standard deviation is: SDx=
(Y – My) 2
√ ∑ ( X− Mx )2 Do the same for the values under
n−1
Step 4: calculate Pearson’s r
With the known covariance and standard deviations for X and Y, we can simply calculate Pearson’s r
by dividing the covariance by the multiplication of the two standard deviations
covxy
Thus, the formula looks like this: r =
SDx × SDy
Step 5: conclusion
The answer of this last calculation is (if you did it correctly) somewhere between -1 and 1.
This is important for the conclusion. If the number has the minus symbol (-), it shows that the
correlation is negative, and if the number has no symbol (+), it shows that the correlation is positive.
You can check this in your scatterplot if you drew one.
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