statistics: 3.1 CORRELATION ANALYSIS

what is a correlation? 1 pt

the degree to which two variables move in coordination with one another; statisitcal measure of the linear relationship between two variables

why is a correlation useful? 1 pt

because it tells us about the relationship between variables

how do we visually represent the relationship between two variables together? 1 pt

using scatterplots

Y axis- dependent variable
X axis- independent variable

what is a linear relationship? 1 pt

a statistical term that we use when the relationship between two variables follows a straight line

positive vs negative linear relationship? 2 pts

1. positive- as the values of one variable increases so do the values of the other

2. negative- as the values of one variable increases the values of the other decreases

how to measure a correlation between two variables? 2 pts

1. covariance- statistical measure of how X and Y vary together

2. pearson correlation coefficient- a measure of the linear relationship between two variables measured at least at the interval or ratio level (scale) and results are always a number ranging from -1 to 1

how to calculate covariance? 5 pts

1. For each participant/observation, calculate the differential score of x > x-mean of x

2. For each participant/observation, calculate the differential score of y> y – mean of y

3. For each participant/observation, multiply the differential scores > (x-mean of x) (y-mean of y)

4. Sum the result of the multiplications across all participants/observations

5. Divide the result of the sum by the sample size minus 1

what is the problem with covariance? 3 pts

1. it cannot always be directly interpreted because it can take on very large numbers

2. has no known bounds and can take on any value

3. makes it hard to interpret because each variable has its own scale and defined unit

(solution = pearsons r)

how to calculate pearsons r? 10 pts

1. calculate the mean of x and the mean of y

2. for each participant observation calculate x-mean of x and y-mean of y

3. multiply (x-mean of x) and (y-mean of y) for each participant

4. sum all the products to get the numerator

5. for each participant square the x and y deviation scores (x-mean of x)2 and (y-mean of y)2

6. sum all the products of the squared deviations

7. multiply the two sums of squared x deviation and squared y deviation

8. take the square root of this result to form the denominator

9. divide the numerator from the denominator

10. result is pearson’s r

(pearsons r= covariance/(standaard deviation of X x standard deviation of Y)

interpreting Pearsons r? 4 pts

1. r<0.3 → no relationship/ very weak relationship

2. 0.3< r <0.5 → weak relationship

3. 0.5< r <0.7 → moderate relationship

4. r>0.7 → strong relationship

when can i perform a pearson’s correlation? 4 pts

1. when your two variables are quantitative

2. when you assume there is a linear relationship between the two variables; confirm the assumed relationship by creating a scatterplot and visually inspecting if the relationship is linear or not

3. there should be no significant outliers as pearson’s correlation is sensitive to them and they should be kept at a minimum

4. variables should be normally distributed; confirm with density plots for each variable separately and observe the shape of the graph or use shapiro-wilk test of normality

what is an outlier? 1 pt

a point that does not follow the usual pattern of the graph (extremities)