# Statistics- Correlations

• Created by: Jadepw
• Created on: 08-03-15 10:43
• Correlations
• Correlation  Vs Causation
• Just because two variables are highly correlated does not mean that one has caused the other.
• CORRELATION DOES NOT IMPLY CAUSATION
• Responses
• Common response- Both X and Y respond to changes in some unobserved variable.   •Ice cream sales and shark attacks both increase during summer.
• Causation-  Changes in X cause changes in Y. For example, football weekends cause heavier traffic
• •Ice cream sales and the number of shark attacks on swimmers are correlated.
• CORRELATION DOES NOT IMPLY CAUSATION
• Confounding- The effect of X on Y is hopelessly mixed up with the effects of other explanatory variables
• Pearsons (r)
• This measures the strength of the linear relationship between two variables
• Pearsons r is always between -1 (\) and 1 (/) r=0
• when there seems to be no relationship between x and y to create a linear line, r=0
• explanation of correlations
• •It is called “product-moment” because it is calculated by multiplying the z-scores of two variables by one another to get their “product” and then calculating the mean value, which is called a “moment” of these products. –However, the Pearson’s r is rarely computed this way
• When should Pearsons r be used ?
• measures the relationship between any two variables on an interval or ratio scale
• What is a correlation ?
• •Scatterplots are made up of paired X and Y values.
• it  expresses quantitatively the magnitude and direction of a relationship
• To describe the relationship with a straight line (linear correlation),
• Spearman (rs)
• A statistic that shows the degree of relationship between 2 variables that are arranged in rank order
• measured on an ordinal scale
• Interpreting Coefficient Magnitude
• We have discovered the different ways correlation can be expressed numerically.
• Often 1/-1 is described as a strong coreelation with the closer the number is to zero being described as a weaker correlation
• This is not the case as the context must be taken into consideration before this assumption is made.