The correlation coefficient between the two variables was found to be -0.90, which means:
Pearson CorrelationOne of the most common errors found in the media is the confusion between correlation and causation in scientific and health-related studies. In theory, these are easy to distinguish — an action or occurrence can cause another (such as smoking causes lung cancer), or it can correlate with another (such as smoking is correlated with alcoholism). If one action causes another, then they are most certainly correlated. But just because two things occur together does not mean that one caused the other, even if it seems to make sense. Show
One way to get a general idea about whether or not two variables are related is to plot them on a “scatter plot”. If the dots on the scatter plot tend to go from the lower left to the upper right it means that as one variable goes up the other variable tends to go up also. This is a called a “direct (or positive) relationship.” On the other hand, if the dots on the scatter plot tend to go from the upper left corner to the lower right corner of the scatter plot, it means that as values on one variable go up values on the other variable go down. This is called an “indirect (or negative) relationship."
A really smart guy named Karl Pearson figured out how to calculate a summary number that allows you to answer the question “How strong is the relationship of a correlation?” In honor of his genius, the statistic was named after him. It is called Pearson’s Correlation Coefficient (r).
Calculating Pearson Correlation Coefficient
Step By Step Directions for Calculating a Pearson's r1. Create a table like this one and fill in your values for each variable. One of the variables is designated as X and the other is designated as Y.
2. Calculate and fill in the X2 and Y2 values 3. Multiply each X score by its paired Y score which will give you the cross-products of X and Y. 4. Fill in the last row of the table which contains all of you “Sum Of” statements. In other words, just add up all of the X scores to get the ΣX, all of the X2 scores to get the Σ X2 and etc. 5. Enter the numbers you have calculated in the spaces where they should go in the formula. 6. Multiply the (ΣX)( ΣY) in the numerator (the top part of the formula) and do the squaring to (ΣX)2 and (ΣY)2in the denominator (the bottom part of the formula). 7. Do the division by n parts in the formula. 8. Do the subtraction parts of the formula 9. Multiply the numbers in the denominator. 10.Take the square root of the denominator. Important Things Correlation Coefficients Tell You It Tells You The Direction Of A Relationship: Correlation Coefficients Always Fall Between -1.00 and +1.00: Larger Correlation Coefficients Mean Stronger Relationships
Making Statistical Inferences from Pearson’s r:How do you determine whether or not a correlation is simply a chance occurrence or if it really is true of the population? There is a additional step you can do to determine the "significance" of your correlation coefficient. Just like other statistical tests, the significance of a correlation tests two hypotheses:
You will need three things in order to determine whether you can infer that the relationship you found in your sample is significant (in other words, “is generalizable” in the larger population):
Draw your conclusion by comparing the calculated and critical r values:
Using Excel 2016 to calculate the Correlation Coefficient
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