Correlation & Partial correlation (W8)✅

Question 1

What is meant by bivariate linear correlation?

Answer 1

Examines the relationship between two variables

Relationships vary in:

1. Form
   * Linear
   * Curvilinear
2. Direction
   * Positive
   * Negative
3. Magnitude/strength
   * r = - 1 (perfect negative relationship)
   * r = +1 (perfect positive relationship)
   * r = 0 (no relationship)

Question 2

What is the hypothesis testing in linear correlation?

Answer 2

• Measure the relationship between two variables in a sample
  => use sample statistics to estimate the population parameters
• Always assume null hypothesis is true: there is no relationship between the population variables.
• Once we’ve determined the relationship in our sample, inferential analyses allow us to determine: the CHANCE of measuring a relationship of that magnitude when the null hypothesis is true
  -> if p < 0.05 then can reject null hypothesis

Question 3

What are the main 4 parametric assumption of correlational studies (and 1 thing to look out for)?

Answer 3

1. Both continuous variables
   -> if one or both is ordinal, use non-parametric alternative
2. Related pairs: Each participant should have a pair of values (x, y)
3. Absence of outliers (can skew correlation if present)
4. Linearity: scatterplot should be best explained with a straight line -> NOT curved line

Note: sensitive to range restrictions

=> If seriously violated these assumptions: use non-parametric equivalent (Spearman’s rho)

Question 4

What is Pearson’s correlation coefficient (r)?

Answer 4

• Long name – Pearson product-moment correlation coefficient (PPMCC)
• Correlation coefficient (r) is a measure of the strength of
  association between the two quantitative, continuous variables

Question 5

What is the relationship between covariance and correlation coefficient (r)?

Answer 5

• Covarience (cov): measure of the variance shared between x and y variables
  1. For each datapoint, calculate the difference from the mean of x and y (e.g. xi - xm AND yi - ym)
  2. Multiply the difference
  3. Sum the multiplied differences
  4. Divide by N-1
• Correlation coefficient (r): the ratio of covariance to separate variance (multiply SDs of x and y)
  -> r = cov(x,y) / (Sx*Sy)
• r reflects how well a straight line fits the datapoint (strength of correlation)
  -> If datapoints cluster closely around the line, r is FURTHER from 0 (STRONGER)

Question 6

What is sampling error in correlational studies?

Answer 6

Difference in r-values if we recruit another sample from the population and measure the correlation strength of it.

r-distribution have a 95% confidence interval
-> there is a 5% chance that the population’s r falls above/below the 95% CI limit

Question 7

What is meant by shared variance? (r^2)

Answer 7

r^2: expresses the proportion of the separate variances that is shared

NOTE! r = .8 ix 4x as strong as r = .4 (power of squared)

r is another useful measure of effect size -> squared to give a measure of shared variance (similar to partial eta squared)
=> Tell how much the variance in y can be ‘explained by’ x

Question 8

What is meant by partial correlation?

Answer 8

• Allows us to examine the relationship between two variables, while removing the influence of 3rd variable
• we can control for [3rd variable] by statistical means

Question 9

How to interpret partial correlation: change in r when control for the 3rd variable?

Answer 9

1. If r-value decreases AND is not significant -> suggest the relationship between V1 and V2 may be explained by the influence of V3 on both 1&2.
2. If the r-value decreased but remained significant -> suggest that the relationship was partially explained by V3
3. If the r-value not decreased & remained significant -> suggest that the relationship was not influenced by V3.