exam Flashcards
What is an ‘association’?
Two variables have an association if change in values of one variable coincide with a pattern of change in the other variable.
Give an example of a positive association.
As a person’s height increases, so does their weight.
Give an example of a negative association.
As water temperature increases, dissolved oxygen concentration decreases.
What data is needed for studying associations?
One sample of randomly chosen individuals from the population of interest with measurements for two variables of interest.
What does each row in a dataset for associations represent?
Each row contains the measurements for X and Y made on a single individual.
What is correlation analysis used for?
To determine if an association is positive or negative and to assess if it is strong or weak.
What are the null and alternative hypotheses in correlation analysis?
H0 ∶ ρ = 0, Ha ∶ ρ ≠ 0.
What does a scatterplot with a strong positive association look like?
Scatterplot dots tend to fall in a tight cluster about the linear pattern.
What does a correlation coefficient quantify?
The direction and strength of an association.
What does a correlation coefficient value close to 0 indicate?
A weak association.
What is Pearson’s correlation coefficient formula?
r = (sum of cross products) / (σx^2 - σx^2)(σy^2 - σy^2).
What does a correlation coefficient value near -1 or +1 indicate?
A strong association.
What does a correlation coefficient of r = +0.98 indicate?
A very strong positive association.
What does a correlation coefficient of r = +0.04 indicate?
No significant association.
What are the assumptions for Pearson’s correlation analysis?
- The sample is a random sample from a population
- Population distribution for both X and Y variables is Normal
- True association between X and Y is linear.
What does it mean when we say ρ = 0?
There really is NO correlation between X and Y.
What is the purpose of a correlation matrix?
To quickly assess associations among many variables.
What is Spearman’s rank correlation?
A non-parametric test that converts data values to ranks to eliminate outliers and skewness.
True or False: Spearman’s correlation can fix all non-linear data.
False.
What is a characteristic of monotonic non-linear relationships?
They constantly change slope but remain non-linear.
What is an example of a non-linear relationship that is still considered monotonic?
A consistently increasing or decreasing trend without reversal.
What happens to the correlation when data is converted to ranks?
It eliminates outliers and skewness.
What is the implication of a scatterplot with equal numbers of dots in all four quadrants?
Indicates NO association.
What is the interpretation of r = 0.20, p < 0.001?
Evidence of a weak association.
