Pearson's parametric test

Question 1

When do we use a Pearson’s test?

Answer 1

• Both variables use continuous data
• two data points from each observation
• relationship is linear
• Each pair of scores in your dataset must belong to one individual/unit, and those scores must not influence or depend on the scores from any other individual/unit.
• normally distributed residuals
• Homoscedasticity = the variability (or spread) of one variable remains constant across the range of another variable
• absence of outliers

Question 2

What do we use to check for linearity? and what are we looking for?

Answer 2

• We use the residuals vs fitted plot (residuals = x, fitted = y)
• looking for = roughly flat horizontal red line

Question 3

How can we check for normality of residuals? what are we looking for?

Answer 3

Use the Q-Q plot of residuals
Looking for majority of values falling on or close to diagonal reference line

Question 4

How do we check for Homoscedasticity? what are we looking for?

Answer 4

• The scale-location plot
• looking out for a roughly random spread of points as we move from one end of x-axis to other
• red line should be roughly flat and horizontal

Question 5

What does a scatterplot help with?

Answer 5

Helps to visualize the relationship:
- regression line shows direction
- how clustered shows strength

Question 6

When do we accept the hypothesis

Answer 6

If the p-value is < (less than) the decimal (e.g. p < 0.001), then reject null hypothesis

Question 7

What does the r mean

Answer 7

r = Pearson’s correlation coefficient, also effect size

Question 8

calculation for df?

Answer 8

n - 2

Question 9

What is the CI?

Answer 9

Confidence interval, shows the precision around the effect size

Question 10

How would you write it up?

Answer 10

1. State both hypothesis
2. State relationship (p <>=…)
3. write something like this:
   We hypothesised that there would be a statistically significant relationship between study hours and test scores. A Pearson correlation revealed a strong, positive, statistically significant relationship between study hours and test scores, r(198) = .73, p < .001, 95% CI = [.66, .79], suggesting that higher study hours are associated with higher test scores.