Covariance and correlation. Dr David Field. Summary. Correlation is covered in Chapter 6 of Andy Field, 3 rd Edition, Discovering statistics using SPSS Assessing the co-variation of two variables Scatter plots
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Dr David Field
Sum right hand column and divide by number of participants -1 to find the “population” covariance
-786 / 9 = -87.3
The bar on top refers to the mean of the variable
Sigma (the sum of)
N - 1
Under what circumstances would cov(x,y) equal approximately zero?
SDx * SDy
This means divide by the total variation in both variables
What is the biggest value r could take?
10.58 * 9.37
The scatter plot with 0 correlation provides a null hypothesis and null distribution for calculating an inferential statistic.
The correlation coefficient between two variables is itself a descriptive statistic, analogous to the effect size of the difference between two sample means.
We can also calculate the p value of an observed correlation (data) being obtained by random sampling from the null scatter plot.
Venn diagrams showing proportion of variance shared between X and Y
Strong (but not perfect) correlation
r = 0.9 – 81% shared variance
r = 0.5 – 25% shared variance
r = 0.3 – 9% shared variance