Properties of Correlation
Video from https://www.youtube.com/watch?v=BBPOr8uf-94
Overview:
Correlation is used when you want to determine the strength of the linear association between two quantitative variables. To obtain this information you must construct a scatterplot that uses two quantitative variables.
Conditions
Properties
- The sign of a correlation coefficient gives the direction of association
- Correlation treats x and y symmetrically
- Correlation is always between -1 and +1
- Correlation has no units
- Correlation is not affected by changes in the center or scale of wither variable
- Correlation is sensitive to outliers
Correlation does not mean Causation
Scatterplots and correlation coefficients never prove causation. It is tempting to state that there is a cause and effect, but scatterplots and correlations can only reveal an association between two variables.
TI Tip
Hit 2nd CATALOG, and scroll down until you find DiagnoticOn. Hit Enter. After checking the conditions, go to the STAT CALC menu and select 8: LinReg (a+bx) and hit ENTER. Now specify x and y by importing the names of your variables from the LIST NAMES menu. First name your x-variable followed by a comma, then your y-variable, for example LinReg(a+bx) L1, L2. A list of numbers will be given, the one we want is “r” which is the correlation.
Final Reminders:
Changing units on the scatterplot will not change the correlation because correlation is based on standardized values.
Example 1:
We found a correlation of r = -0.879 between hurricane speeds in knots and their central pressures in millibars. Suppose we wanted to consider the wind speeds in miles per hour (1 mile per hour = 0.869 knots) and central pressures in inches of mercury ( 1 inch of mercury = 33.86 millbars). How would that conversion affect the conditions, the value of r, and our interpretation of the correlation coefficient?
Solution: Not at all! Correlation is based on standardized values (z-scores), so the condition, the value of r, and the interpretation are all unaffected by change in units!
Correlation is used when you want to determine the strength of the linear association between two quantitative variables. To obtain this information you must construct a scatterplot that uses two quantitative variables.
Conditions
- Quantitative Variables Condition: If the variables aren’t quantitative, you cannot apply correlation to them.
- Straight Enough Condition: You must be able to judge that the scatterplot has a linear association. This is mostly a personal judgment call.
- Outlier Condition: The outliers can change a correlation dramatically, so it is best to report the correlation with and without the outlier.
Properties
- The sign of a correlation coefficient gives the direction of association
- Correlation treats x and y symmetrically
- Correlation is always between -1 and +1
- Correlation has no units
- Correlation is not affected by changes in the center or scale of wither variable
- Correlation is sensitive to outliers
Correlation does not mean Causation
Scatterplots and correlation coefficients never prove causation. It is tempting to state that there is a cause and effect, but scatterplots and correlations can only reveal an association between two variables.
TI Tip
Hit 2nd CATALOG, and scroll down until you find DiagnoticOn. Hit Enter. After checking the conditions, go to the STAT CALC menu and select 8: LinReg (a+bx) and hit ENTER. Now specify x and y by importing the names of your variables from the LIST NAMES menu. First name your x-variable followed by a comma, then your y-variable, for example LinReg(a+bx) L1, L2. A list of numbers will be given, the one we want is “r” which is the correlation.
Final Reminders:
Changing units on the scatterplot will not change the correlation because correlation is based on standardized values.
Example 1:
We found a correlation of r = -0.879 between hurricane speeds in knots and their central pressures in millibars. Suppose we wanted to consider the wind speeds in miles per hour (1 mile per hour = 0.869 knots) and central pressures in inches of mercury ( 1 inch of mercury = 33.86 millbars). How would that conversion affect the conditions, the value of r, and our interpretation of the correlation coefficient?
Solution: Not at all! Correlation is based on standardized values (z-scores), so the condition, the value of r, and the interpretation are all unaffected by change in units!