Statistic work

Review-The Correlation Coefficient (r)

• A coefficient that tells us about the strength and direction of a relationship

• Always ranges from -1 to 1

• Direction: • Positive numbers indicate a positive relationship

• Negative numbers indicate a negative relationship

• Strength:

-1 Perfect Neg. Correlation

1 Perfect Pos. Correlation

-.6 Strong Neg. Correlation

.6 Strong Pos. Correlation

-.3 Moderate Neg. Correlation

.3 Moderate Pos. Correlation

-.1 Weak Neg. Correlation

.1 Weak Pos. Correlation

No Correlation 0

Review- The Computational Formula for r

The Potential Problem of Correlation

• Correlation measures the strength and the direction of a relationship between TWO variables • But what about other variables that may affect this relationship?

• Considering another variable may change the observed strength and/or direction of the relationship between the original two variables

The Potential Problems of Correlation- Example

The Potential Problems of Correlation- Example

Possibilities

Genuine Relationship Conditional Relationship Spurious Relationship Changed Relationship

Partial Correlation

Find the Partial Correlation Coefficient- Specific Steps

Find the Partial Correlation Coefficient- Specific Steps

• Calculate the degrees of freedom • N – 3

• Look up the critical value in the Table H • alpha = .05

• Compare the calculated correlation to the critical value • If the calculated value is > critical value we reject the null hypothesis

• If the calculated value is < critical value we fail to reject the null hypothesis

Partial Correlation- Example

• Suppose we have the following correlation matrix between X, Y, and Z:

• What is the partial correlation between X and Y controlling for Z?

X Y Z

X 1.00 .60 .20

Y .60 1.00 .30

Z .20 .30 1.00

Partial Correlation- Example

• Suppose we have the following correlation matrix between X, Y, and Z:

• What is the partial correlation between X and Y controlling for Z?

X Y Z

X 1.00 .846 .821

Y .846 1.00 .988

Z .821 .988 1.00

Requirements Assumptions for Using Correlation

• Linear relationship between X and Y • Can check for this with a scatterplot!

• Interval level data

• Random sampling

• Characteristics normally distributed OR sample size is over 30

Correlation does NOT equal Causation

Next Class

• Introduction to Regression