Practical Statistics Correlation

There are six statistics that will answer 90% of all questions! 1. Descriptive 2. Chi-square 3. Z-tests 4. t-tests 5. Correlation 6. Regression

Correlation tests the degree of association between measures if you have interval and ratio measures.

Darwin Galton Karl Pearson

Correlation is based on a very simple idea that Karl Pearson saw….

If you take two measures of the same person or object, multiple them, and then add the products across person or objects… such as: Person M1 M2Product Sum = 55

The largest possible sum will occur if M1 and M2 are in perfect ordinal order. Person M1 M2Product Sum = 54 Note what happens when only pair is out of order.

The smallest possible sum will occur if M1 and M2 are in perfect inverse order. Person M1 M2Product Sum = 35

But Pearson wanted an Index of Association, not just a measure of association that would change with every n and scale value.

The “normal score” is equal to:

Converting the measures to Z scores… Person M1 M2Product Sum = 5.0

Converting the measures to Z scores… And arranging for perfect inverse order: Person M1 M2Product Sum = -5.0

So: When X and Y are in ranked order.

Then X = Y, and : This is called “the sum of the cross products”

When M1 and M2 are in perfect ordinal order: In perfect order, this value will always = n - 1

The average of the sum of cross products is the correlation.

How to do this on Excel:

The correlation can be graphically shown by using a scatter plot:

The correlation is related to the shape of the scatter plot:

The correlation is an INDEX of association. It contains three pieces of information: 1.How much association is present? 2.Is that a “significant” association? 3.And, what is the magnitude of that association?

The correlation is an INDEX of association. It contains three pieces of information: The correlation is r….. R-squared is the amount of variation accounted for in Y by knowing X.

The correlation is an INDEX of association. It contains three pieces of information: R-squared is the amount of variation accounted for in Y by knowing X.

Be careful!! The correlation does not tell you that X is the cause of Y. It is a necessary condition for cause, but it does not prove cause…

Correlation proves causation: Is a logical fallacy by which two events that occur together are claimed to have a cause-and-effect relationship. The fallacy is also known as cum hoc ergo propter hoc ( Latin for "with this, therefore because of this ")

Since the 1950s, both the atmospheric CO 2 level and crime levels have increased sharply.CO 2 Hence, atmospheric CO 2 causes crime.

Young children who sleep with the light on are much more likely to develop myopia in later life.myopia

Service Encounter Are the summative measures of the service encounter related to each other?

Service Encounter Are the summative measures of the service encounter related to each other?

Service Encounter Are the summative measures of the service encounter related to personality?