Correlations FSE 200

What You Will Learn in Chapter 5 All about correlation coefficients… What they are How to compute them How to interpret them Using the CORREL function Data Analysis Toolpak Other types of correlations and when to use them

What Correlations Are About… Examines the relationship between variables How the value of one variable changes in relation to changes in another variable Range between -1 and 1 Bivariate correlation (2 variables) Pearson product-moment correlation Karl Pearson

Types of Correlation Coefficients Positive correlation Direction correlation When variables change in the same direction Negative correlation Indirect correlation When variables change in opposite directions rXY = correlation between X and Y

Relationships Between Variables Types of Correlations and Relationships

Computing Simple Correlations Pearson product-moment… What do these symbols represent?

Steps in Computation List the two values for each participant Compute the sum of X values, and compute the sum of Y values Square the X values, and square the Y values Find the sum of the XY products Now plug these values into the formula

CORREL Function Data for computing the correlation coefficient

CORREL Function Computing the correlation coefficient

Scatterplot A simple scatterplot

Scatterplot A perfect direct or positive correlation

Strong Positive Relationship A strong positive correlation

Strong Negative Relationship A strong indirect relationship

Correlation Matrix Income Education Attitude Vote 1.00 0.35 -0.19 0.51 -0.21 0.43 0.55

Data Analysis Toolpak The correlation dialog box

Data Analysis Toolpak Entering the input range information

Data Analysis Toolpak A correlation matrix

Interpreting Correlation Coefficients Size of the Correlation Coefficient Interpretation   .8 to 1.0 Very strong relationship .6 to .8 Strong relationship .4 to .6 Moderate relationship .2 to .4 Weak relationship .0 to .2 Weak or no relationship

Variance Explained Coefficient of determination rxy = .70 .702 = .49 or 49% Coefficient of alienation .702 = .49 1.00 – .49 = .51 or 51%

How Variables Share Variance Remember: Association, not Causation

Types of Correlations

Summary Showing how things are related to one another and what they have in common is a powerful idea and a very useful descriptive statistic. Correlations express a relationship that is only associative. This statistic gives us valuable information about relationships and how variables change or remain the same.

Acknowledgement The majority of the content of these slides were from the Sage Instructor Resources Website