Statistics Probability

• What does bivariate data mean?


  Data with two variables
• What is the range of correlation values?

  • 1 to +1
• What does Pearson’s product moment correlation coefficient measure?

  Linear correlation for non-linear data
• What is the notation for Pearson’s product moment correlation coefficient?


  r
• What does Spearman’s rank correlation coefficient measure?

  Association between rank orders of two variables
• What is the notation for Spearman’s rank correlation coefficient?

  rs
• How does Spearman’s handle tied ranks?

  Uses tied ranks for equal values
• What must be included when interpreting a correlation value?

  Strength, direction, and context
• What does correlation NOT imply?

  Causation
• How does scaling data affect correlation?

  It does not change the correlation
• What does a pmcc value of r indicate?

  Changing units does not change r
• What does r = 1 indicate?

  A perfect straight line with positive values
• What does a Spearman’s value of $r_s =$$1$ indicate?


  A perfectly increasing relationship
• What can significantly change the value of the correlation coefficient?

  Outliers
• What is the process to calculate the product moment correlation coefficient?

  1. Collect bivariate data
  2. Calculate means and standard deviations
  3. Compute covariance
  4. Divide covariance by product of standard deviations
  5. Interpret the correlation value
• What does an r value of 0.701 indicate in the context of blood pressure and age?

  Moderate positive correlation
• What was the claim made by the journalist regarding football teams?

  More shots at goal lead to more goals
• What is the Spearman’s rank correlation coefficient for the football teams data?

  $r_s =$$0.562$
• What does an $r_s =$$0.562$ indicate in the context of football teams?


  Moderate positive association
• What are the key differences between Pearson’s and Spearman’s correlation coefficients?


  • Pearson’s: Measures linear correlation
  • Spearman’s: Measures association of ranks
  • Pearson’s uses raw data, Spearman’s uses ranks
  • Pearson’s sensitive to outliers, Spearman’s less so