Bit More About Correlation

Now that you’ve mastered one variable, let’s add another. Everything up to now has been based on observing one dependent variable (one criterion). All we have done is to observe; we haven’t manipulated, stapled or mutilated anything; just observed.

With correlations we are going to continue that practice, we’re only observing, but we’re going to look at two variable and see how they are related to each other. When one variable changes, we want to know what happens to the other variable. In a perfect correlation, the two variable with move together. When there is no correlation, the variables will act independently of each other.

To use this simple and yet powerful method of description, we must collect two pieces of information on every person. These are paired observations. They can’t be separated. If we are measuring height and weight, it’s not fair to use one person’s height and another person’s weight. The data pairs must remain linked.

That means that you can’t reorganize one variable (how highest to lowest, for example) without reorganizing the other variable. The pairs must stay together.

Sign & Magnitude

A correlation has both sign and magnitude. The sign (+ or -) tells you the direction of the relationship. If one variable is getting larger (2, 4, 5, 7, 9) and the other variable is headed in the same direction (2, 3, 6, 8, 11), the correlation’s sign is positive. In a negative correlation, while the first variable is getting larger (2, 4, 5, 7, 9), the second variable is getting smaller (11, 8, 6, 3, 2).

The magnitude of a correlation is found in the size of the number. Correlation coefficients can’t be bigger than 1. If someone says they found a correlation of 2.48, they did something wrong in the calculation. Since the sign can be positive or negative, a correlation must be between -1 and +1.

The closer the coefficient is to 1 (either + or -), the stronger the relationship. Weak correlations (such as .13 or -.08) are close to zero. Strong correlations (such as .78 or -.89) are close to 1. Consequently, a coefficient of -.92 is a very strong correlation. And +.25 indicates a fairly weak positive correlation.

Magnitude is how close the coefficient is to 1; sign is whether the relationship is positive (headed the same same) or negative (inverse).

NOW YOU CHOOSE:
    Day 5: Correlation
    Bit More About Correlation
    Even More About Correlation
    Calculate Correlation
    Practice Problems
    More Practice Problems
    Word Problems
        Sim1            Sim2             Sim3
        Sim4            Sim5             Sim6
        Sim7            Sim8             Sim9
    Basic Facts About Correlation
    Vocabulary
    Formulas
    Quiz 5
    Summary