OK, I’ve Signed Up For Statistics. Now What

In a normal (“bell shaped”) distribution, the mean, median and mode will be smack in the middle of the curve, with 50% to the left and 50% to the right. The mean of a Z score distribution will be 0, and the standard deviation will be 1

linear regression calculates an equation that allows us to make an “educated guess” at a person's score on some measure, given their scores on other measures. For instance, we might want to predict a person's GPA in college, given their GPA in high school.

Bivariate correlation involves two variables, and (not surprisingly) multiple correlation involves more than two variables. The former is calculated using the Pearson correlation statistic (r), while multiple correlation is calculated using the multiple correlation coefficient, R. Correlations of 0 indicate no linear relationship, while correlations of 1 indicate perfect linear relationship.

Measures of Association usually involve some form of correlation. Correlations look at if two (or more) variables are related in some way. One common example might be eye color and hair color.

Measures of Central Tendency are statistics that try to capture the average, or typical aspect of a distribution.

Factor Analysis—This method has many similarities to components analysis, and is often discussed in the same chapter. There are some mathematical differences between the two, but both seek to reduce the number of observed variables into a much smaller subset of factors. Unlike components, factors are more involved in the search for theoretical meaning of the data, rather than a description of the relationships themselves.

Chi Square Analysis—This is a fairly simple procedure that many undergraduate courses teach. The idea is that there may be a relationship between two categorical variables. For example, is there a relationship between political party (Democrat, Republican, Independent) and pet ownership (Dog, Cat, Bird, Other, None)?

Multiple Regression and Correlation (R)—Similar to the above, but with more than one predictor variable. Multiple regression involves two or more predictor variables, combined, to generate a predicted value on the criterion variable. Most often we are interested in 1) how well the model (the predictors) account for the observed data (R squared), as well as how each individual predictor, independent of the others, correctly predicts the outcome measures

The correlation is a derived value that will always be between -1 and +1. The closer the value is to either of its limits, the stronger the relationship is. Conversely, the closer to zero, the weaker the relationship. Correlations are not to be inferred as causal; Variable A does not cause Variable B to occur. Rather, Variables A and B are related to one another with a certain level of strength. Even if two variables are perfectly correlated, we cannot legitimately infer any causal connection.

Correlation refers to both the degree (magnitude) of the relationship, and the direction (positive, negative, or zero)