Correlation

Research final pt 4

Correlation coefficient ( r )

measures strength and direction of linear relationship between two numerical variables (linear relationships only).

• values range from -1.00 to +1.00, sign only indicates direction of relationship, but when looking at strength, use absolute value - closer to 1 is stronger

• report by giving size of relationship and its associated significance. give value to 2 decimal places

• it acts as its own effect size, so you don’t have to give a separate value

correlation coefficient primary goal

to assess how the value of one variable changes in relation to change in another. Useful as both a descriptive and inferential statistic

scatterplot

used to represent the relationship between a set of scores on separate axes. The general shape of the data points indicate if correlation is direct (+) or indirect (-)

• data points follow a straight line shows the strength of the relationship

curvilinear relationships

correlation coefficient can’t describe this accurately because while there’s a clear relationship, it is not linear. This is why scatter plots are necessary - by number alone, this may not have a strong relationship, but on a graph it’s obvious

Pearson Correlation Coefficient

used to compare 2 continuous variable in a parametric test

• no more than 2 variables

• interval or ratio level data

• parametric

• population parameter

population parameter

rho = 0 is null hypothesis and the opposite is alternative hypothesis

Pearson Correlation Coefficient assumptions

random and independently sampling

variables being correlated are normally and equally distributed

level of data is appropriate to measure of association (ratio/interval)

two variables have a linear relationship

Size of the correlation

• >.80 = very strong relationship

• .50-.80 = strong relationship

• 0.3-0.5 = medium relationship

• .1-.3 = low relationship

• 0-.1 = no relationship

variance and correlation

• we look at overlap between two variables. we want a lot of overlap for them to be correlated

• coefficient of determination

• coefficient of non-determination/alienation is the opposite, the amount of unexplained variance

coefficient of determination (r²)

the percentage of variance in one variable that is accounted for by the variance in the other variable. stronger the correlation, more variance can be explained

• coefficient of non-determination/alienation

you subtract r from 1

• always remember to present this value to show how much variability is shared/accounted for. report without leading zero, and use two decimal places. give exact p-value

Other options of correlation

confounding variable

this can come into play that we don’t notice, making it look like causation when it’s really just correlation. Ice cream doesn’t increase crime rates

partial correlation

can eliminate the impact by looking at this.

you chart out Venn diagrams of each of the variables in the relationship; it’ll go three ways and you’ll see what the “left over” value not touched by the confounding variable actually is. There are ways to control for the third variable mathematically