Lab #9 Preview
Correlation and Regression
Purpose
Scenario for this lab: a memory experiment – participants study a list of words and then try to recall them
Variables to be analyzed:
- age = age of participant
- studtime = amount of time spent studying the words (sec)
- resptime = amount of time spent recalling the words (sec)
- score = number of words correctly recalled
Null Hypothesis: There is no relationship between the variables
Alternative Hypothesis: There is a relationship between the variables
A scatterplot is a graphical representation used to visualize the relationship between two variables. One variable is represented on the X-axis, the other variable on the Y-axis. Each point (X, Y) on the scatterplot represents the two scores for a single individual.
Pearson correlation coefficient (r): measures the direction (positive or negative) and strength (weak, moderate, or strong) of the relationship between the two variables.
The correlation test is a test of the null hypothesis. Based on test results, we either:
- Reject the null hypothesis (and conclude the alternative is likely true), or
- Fail to reject the null hypothesis (and conclude there is no relationship between the variables)
Regression line: can be used to predict the value of one variable (Y), given the value of the other variable (X).
APA Style
Results of correlation tests are reported with a statement about how the given variables are related, followed by an “r-statement”. The written sentence should indicate the strength and direction of the relationship (if the variables are related) or a statement that they are not related. The r-statement would include the letter r, the degrees of freedom in parentheses, the calculated r value, and the p-value. Degrees of freedom for a correlation is not directly given in the output in SPSS but it is easy to calculate: it is N – 2 (where N is the sample size). See the following for examples:
- High school GPA and college GPA were strongly positively correlated, r(123) = .68, p = .009.
- Ratings of happiness and intelligence test scores were not significantly correlated, r(46) = .11, p > .05.
- There was a moderate negative correlation between hours spent playing video games and GPA, r(145) = -.32, p = .041.