1. Stats Club Marnie Brennan
Correlation
Stats Club
Marnie Brennan

2. Have you used correlation before?

3. References
Petrie and Sabin - Medical Statistics at a Glance: Chapter 26 Good
Petrie and Watson - Statistics for Veterinary and Animal Science: Chapter 10 & 12 (12.7) Good
Kirkwood and Sterne – Essential Medical Statistics: Chapter 10 & 30
Thrusfield – Veterinary Epidemiology: Chapter 14 (pges )

4. Other reads
Mathematics Learning Support Centre – Statistics: Correlation - Good
Bewick, V, Cheek, L and Ball, J (2003) Statistics review 7: Correlation and regression. Critical Care, Vol. 7,
Swinscow, TDV (1976) Statistics at square one: XVIII – Correlation. British Medical Journal, Vol. 2,
Swinscow, TDV (1976) Statistics at square one: XIX – Correlation (continued). British Medical Journal, Vol. 2,
Swinscow, TDV (1976) Statistics at square one: XIX – Correlation (concluded). British Medical Journal, Vol. 2,

6. What is correlation?
Use it to look at the relationship between two continuous (numerical) variables
To see if you have a linear relationship between them
If you interchanged the x and y axes, you would still have the same relationship
To measure the degree of the relationship

7. How does it differ from other calculations?
T-tests and ANOVAs
These measure the differences between subsets within your data/between groups
Regression (this will be covered in a later session)
This describes the linear relationship between two variables
Describes how one variable (independent) predicts the other (dependent)
You cannot interchange the variables between the x and y axes

8. When would you use correlation?
To see if there is a relationship between two variables, and how strong it is
As a prequel to linear regression
If variables are highly correlated (or collinear), this will effect how they interact in a linear regression calculation
Therefore, you need to know whether variables are correlated or not before you do a linear regression
Other reasons??

9. When wouldn’t you use correlation!
To compare two different methods of measurement on the same thing (reliability)
E.g. How many neutrophils are in a blood sample? Compare using an IDEXX machine versus counting on a blood smear
To compare the same method of measurement but used multiple times (reproducibility)
E.g. How many neutrophils are in a blood sample? Preparing two blood smears from the same sample, and comparing the results
Kappa (and associated) analysis – covered in a previous session
Categorical data

10. First step – descriptive stats
Scatter plot
What does the relationship look like?

11. Shape and what does it mean?
Does it increase or decrease as the values get higher?
Does the relationship look linear?
How ‘steep’ is the slope of the shape?
Are there any outliers?
Taken from Petrie and Sabin

12. Scatter plot examples

13. Demonstration if required….

14. Demonstration if required….
GenStat
Graphics, 2D Scatter Plot (Y variate, X variate)
Run

15. Measurement for correlation
Correlation coefficient
Numerical representation of the degree of association between the variables
Between -1 and +1
Positive – the relationship is increasing with increasing values
Negative – the relationship is decreasing with decreasing values
It is dimensionless (spooky….)
No units of measurement

16. What are the assumptions that have to be satisfied?
There is a linear relationship between the variables
There are no outliers present
There are no subgroups within the data that affect the relationship e.g. sex
Multiple data from the same subjects
Taken from Petrie and Sabin

17. Represented as r (rho) Calculation of correlation coefficient
Pearson’s coefficient – r
If our null hypothesis is that there is no relationship e.g. the correlation coefficient is zero
At least one variable has to be normally distributed
Taken from Petrie and Sabin

18. P-values and confidence intervals
As standard with p-values (you can calculate confidence intervals – not normally included)
You state your cut off e.g. if p<0.05, reject the null hypothesis and conclude that there is a relationship
A significant result is not necessarily CAUSAL
There is an ASSOCIATION

19. Minitab

20. Minitab – Pearsons

21. SPSS

22. SPSS - Pearsons

23. GenStat
GenStat
Stat, summary, correlations

24. What if our assumptions cannot be met?
Use Spearman’s rank correlation coefficient (or Kendall’s coefficient)
Rank your variables from lowest to highest, and then calculate the correlation coefficient
Still between -1 and 1
Remove outliers
Rule of thumb – if the outliers are outside +/-2 standard deviations away from the group mean, you can remove them
Transform data into a linear relationship????

25. Minitab – Spearman’s

26. Minitab – Spearman’s

27. SPSS – Spearman’s

28. SPSS – Spearman’s

29. GenStat
GenStat
Stat, summary, correlations
Rank??

30. How does this fit with what you do or have seen/experienced?

31. Summary Make sure you are using correlation in the correct way
Eyeball first with a scatter plot – look for strength, slope, relationship, outliers
If it doesn’t fit the assumptions, use a non-parametric equivalent e.g. Spearman’s

32. Next time…
Linear regression……