Explanatory and response variables Displaying relationships: scatterplots Interpreting scatterplots Adding categorical variables to scatterplots Measuring linear association: correlation Facts about correlation
A study of 21 children finds that children who start to speak when very young are more likely to have high Gesell test scores than children who start to speak at an average age, while children who start to speak the oldest have the lowest Gesell test scores. What has been measured? Is this an ironclad rule? What other variables are lurking in the background?
strength of correlation is not related to its sign (+ or -) correlation of 0.7 is as strong as correlation of - 0.7
Correlation coefficient only tells you about the strength of a linear association
Example: Anscombe data Anscombe (1974) invented four data sets to illustrate the importance of investigating data using scatter plots and not relying totally on the correlation coefficient. *** data r = 0.816 and = 3.0 + 0.5 x
To study relationships between variables, we must measure the variables on the same group of individuals. A scatterplot displays the relationship between two quantitative variables measured on the same individuals. Look for an overall pattern showing the direction, form and strength of the relationship, and then for outliers or other deviations from this pattern. The correlation measures the strength and direction of the linear association between two quantitative variables.