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# Statistics: correlation and causation

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What is correlation?

How is correlation used to understand the relationship between two variables?
What is the difference between positive and negative (inverse) correlation?

What is the correlation coefficient (r-value)?

What values can the correlation coefficient (r-value) have and what do these values reveal about the relationship they describe?

How is SPSS used to calculate the correlation (also called the Pearson Correlation)?

How do you identify the dependent and independent variables in a correlation analysis?

Does correlation imply causation?

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Statistical measure

What is correlation?

Correlation is a statistical measure that indicates the extent to which two or more variables fluctuate together.

How is correlation used to understand the relationship between two variables?

What is the difference between positive and negative (inverse) correlation?

A positive correlation indicates the extent to which those variables increase or decrease in parallel; a negative correlation indicates the extent to which one variable increases as the other decreases.

When the fluctuation of one variable reliably predicts a similar fluctuation in another variable, there's often a tendency to think that means that the change in one causes the change in the other.

What is the correlation coefficient (r-value)?

The quantity r, called the linear correlation coefficient, measures the strength and the direction of a linear relationship between two variables.

What values can the correlation coefficient (r-value) have and what do these values reveal about the relationship they describe?

The correlation coefficient (r-value) is a number between -1 and 1, which shows us the relationship between the two-variables. If r takes a positive value, we say that the variables are positively correlated. That means, they fluctuate in parallel, as we mentioned before. Otherwise, if r is negative, we say that the two variables fluctuate contrarily: if one increases, the other one decreases and vice versa.

If r is close to +1, then we say that there is a strong relationship between the two variables. If r is close to -1, there is a strong negative relationship between the two variables. If r is 0, or very close to 0, we say that the two variables are not correlated.

How is SPSS used to calculate the correlation (also called the Pearson Correlation)?

To calculate a correlation coefficient in SPSS, click on the "Analyze" drop-down menu, highlight "Correlate", and then click "Bivariate", as pictured below. Then we highlight the two variables we want to correlate. Then we click "OK" and navigate to the Output window to find your results. The output will generate a correlation matrix from which we get the correlation coefficient between the two selected variables.

How do you identify the dependent and independent variables in a correlation analysis?

In a correlation analysis, the independent variable is the exogenous variable, while the dependent variable is the endogenous variable. The causation of the dependent variable is implied by the independent variable.
For example, if we make a study regarding the final grade of a student in a Statistics Class and numbers of hours he is studying for this class, the independent variable must be the number of hours of study, while the dependent variable should be the final grade. That is because the final grade is influenced ( caused) by the numbers of studying hours.

Does correlation imply causation?

Correlation does not imply causation. There may be, for example, an unknown factor that influences both variables similarly.

Here's one example: A number of studies report a positive correlation between the amount of television children watch and the likelihood that they will become bullies. Media coverage often cites such studies to suggest that watching a lot of television causes children to become bullies. However, the studies only report a correlation, not causation. It is likely that some other factor - such as a lack of parental supervision - may be the influential factor.

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