Module 7 - Correlational Designs Flashcards
If you wanted to see whether there was a relationship between two continuously valued variables, what design would you use?
Correlational
What is a “median split”?
When you take one variable and divide it into two equally sized groups around the median, then use a t-test or similar test. (This is generally a bad idea, more Type II errors are common.)
Explain Pearson’s r.
r is the correlation coefficient, a measure of the strength and relationship between two continuous variables. it ranges from -1 to +1, with r=1.00 indicating a perfect positive correlations, 4=0.00 indicating no correlation, and r=-1.00 indicating a perfect negative correlation.
what is the formula for r?
Σ ZxZy
r = ———–
N-1
Explain how to calculate r.
transform both variables into Z-scores, find the product of each pair of z scores, add all of the products together, then divide that total by N-1.
If p > .05…
reject the null hypothesis, and consider the relationship between your variables to be statistically significant.
If p = .05 or p < .05…
retain the null hypothesis – you haven’t found evidence for a relationship.
What does it mean if we reject Ho?
Our correlation is statistically significant, this doesn’t mean the correlation is large, strong, or important, it just means we’ve found a pattern in our data that is unlikely to occur randomly.
What are the rough guidelines for interpreting r?
If the magnitude of Pearson’s r is .10-.29 the effect size is weak. If the magnitude of Pearson’s r is .30-.49 the effect size is moderate. If the magnitude of Pearson’s r is .50+ the effect size is strong.
What is a statistical model?
a mathematical abstraction that lets you make guesses about a data set.
What is the coefficient of determination?
The proportion of variance explained by the relationship between two variables as expressed by r^2.
What are the assumptions for use of Pearson’s r?
The relationship between the variables isn’t curvilinear, the data are interval or ratio scaled, and there aren’t any major outliers.
Explain linear vs curvilinear relationships, and how they are relevant to Pearson’s r.
linear relationships go in a straight line, curvilinear is a relationship that is rounded or otherwise not a straight line, for Pearson’s r tests, the data must be linear, it cannot detect curvilinear relationships, even if they are very obvious, such as a U shape.
What is the most common non-parametric equivalent of Pearson’s r?
Spearman’s Rho.
Why not always use Spearman’s Rho.
Spearman’s Rho works by transforming the data into ranks and then correlating the ranks with one another. In transforming the data into ranks information is lost.
Explain subgroups.
if our sample consists mainly of two subgroups, we might see an illusory correlation.
What does a scatterplot show?
scores on one varied plot against scores on a second varied plot.
The correlation between two variables A and B is .12 with a significance of p < .01. What can we conclude?
There is a small relationship between A and B.
A correlation of .5 would produce a scatterplot in which the slope is…
upwards (from the bottom left corner to the top right corner of the graph).
How much greater is the shared variance between two variables if the Pearson correlation coefficient between them is –.4 than if it is .2?
four times as great.
If two variables are significantly correlated, r = .67, then:…
They share variance.
If a correlation coefficient has an associated probability value of .02 then…
We should accept the null hypothesis.
