Week 3: Correlations

correlation

-focus on relationship between variables → no manipulation or clear IV or DV

-relationship between two continuous or two categorical variables

Pearson’s correlation

-relationship between two continuous variables

scatterplots

-each dot resembles one person

-each person has a score on the x-variable and a score on the y-variable

-the correlation looks at the pattern of all the people together

conclusions we can draw from correlation results

• X has caused Y → variation in scores on Y can be explained by the differences in scores on X

• Y has caused X → variation in scores on X can be explained by the differences in scores on Y

• relationship between X and Y can be explained by a third variable Z

• relationship visible is purely by chance

correlation vs causality

-correlation does not infer causality

-could be third variable

positive relationship (direction of relationship)

-when the score on variable A increases, the score on variable B increases as well

negative relationship (direction of relationship)

-when the score on variable A increases, the score on variable B decreases

strength of relationship

-the more the data resembles a straight line, the stronger the correlation will be

correlation coefficient (r)

-indicates the strength of the relationship

-indicated with a value between 0 (no relationship) and 1 (perfect relationship)

combining direction and strength in correlation coefficient

-can have a positive or a negative correlation

-can have a number value between 0-1 to indicate the strength

very strong relationship

r = 0.70 - 0.99

strong relationship

r = 0.40 - 0.69

moderate relationship

r = 0.20 - 0.39

weak relationship

r = 0.01 - 0.19

H₀

r = 0 (no linear relationship between variables in population)

H₁

r ≠ 0 (a linear relationship between variables in population)

Pearson’s correlation output

-table of all variables and how they correlate with each other (including how a variable correlates with itself)

assumptions that must be met in order to use Pearson’s correlation

• no clear outliers

• assumption of linearity

no clear outliers (assumptions that must be met in order to use Pearson’s correlation)

-outliers on a scatterplot can drive a correlation to seem significant while there actually is no linear relationship

assumption of linearity (assumptions that must be met in order to use Pearson’s correlation)

-that there actually is a linear relationship between the two variables

-look for obvious violations of linearity

-if we used correlation analysis on non-linear relationships (even if there is a relationship e.g., U-curve), then we would have concluded that there is no association → even though there may have been a non-linear relationship

degrees of freedom

-comparing two variables

-calculation of each variable’s mean has N-1 degrees of freedom

• df = total sample size - 2

descriptive statistics (reporting results of Pearson’s r)

-which variable did you compare

-direction and strength of relationship → only if significant

inferential statistics (reporting results of Pearson’s r)

-relationship significant or not

-r(df) = [r value], p = [p value]

interpretation of results (reporting results of Pearson’s r)

-make sure to link it back to the terms in the research question

Spearman’s rho

-non-parametric alternative to Pearson’s r

-uses ranked scores

-used when assumptions for Pearson’s r have not been met

Spearman’s rho SPSS

-rank variables from lowest to highest

-compare the ranks (ignore original scores)

Spearman’s correlation coefficient

rₛ

descriptive statistics (reporting results of Spearman’s Rho)

-which variable did you investigate

-direction and strength of relationship → only if significant

inferential statistics (reporting results of Spearman’s Rho)

-relationship significant or not

-rₛ = [rₛ value], p = [p value]

interpretation of results (reporting results of Spearman’s Rho)

-link back to terms in research question