Correlation, Regression, Chi Square

• Correlation is a measure of the relationship between variables
• Pearson product-moment correlation coefficient (r) is a measure of the strength of the linear relationship between two sets of data.
• Pearson-product moment correlation coefficient (r) is the most common correlation coefficient, ranges from -1 to +1
• On a scatterplot, the predictor (IV) goes on the x-axis and the criterion (DV) goes on y-axis.
• If it’s unclear which is predictor and criterion then axis doesn’t matter
• Perfect Positive Correlation

  
• High Positive Correlation

  
• Low Positive Correlation

  
• No Correlation

  
• Low Negative Correlation

  
• High Negative Correlation

  
• Perfect Negative Correlation

  
• Perfect correlation: if X is 1, Y should be 1
• Positive correlation: if X goes up, Y goes up
• r = 0: no correlation
• r = 1: perfect positive correlation
• r = -1: perfect negative correlation
• negative correlation: if X goes up, Y goes down
• correlation coefficient (r): measures the strength/direction of relationship between two variables
• If regression line rises from left to right the correlation coefficient is positive
• If regression line falls from left to right the correlation coefficient is negative
• Strength: The closer the data points are to the regression line the stronger correlation
• Strength: the closer the correlation coefficient is +1 or -1, the stronger the correlation. The closer the coefficient is to 0, the weaker the correlation
• .09 or .69: which is the stronger correlation?

  .69
• -.78 or .42: which is the stronger correlation?

  -.78
• -.45 or .45: which is the stringer correlation?

  both
• can you infer causation from correlation?

  no
• 0 to +- .25 = weak correlation
• +- .25 to +- .75 = moderate correlation
• +- .75 to +- 1 = strong correlation
• It’s possible to have a weak correlation that is statistically significant if the sample size is large enough
• It’s possible to have a strong correlation that is not statistically significant if sample size is small enough
• APA format: There is a significant positive correlation between variable 1 and 2 r(4)=.99, p < .001. Specifically, as variable 1 increases, variable 2 increases.
• r(df) = (n-2)
• Spearman’s r is the correlation between ranked (ordered) variables
• APA format: There is a significant positive correlation between variable 1 and 2, r(4)=.89, p = .02. Specifically, as variable increases, variable 2 increases.
• point biserial correlation is correlation between one continuous variable and one dichotomous variable
• dichotomous variable is a variable that can only take two values, such as male or female, yes or no, high or low
• Dichotomous variables are coded with a number, the number is nominal (a label) and not quantitive. Such as 1 for female and 2 for male
• Point biserial correlation