Week 8

• Counterbalancing with multiple conditions

  USE FACTORIALS

  5 conditions = 120 possible orders (5! = 5 x 4 x 3 x 2 x 1 = 120)

  6 conditions = 720 possible orders (6! = 720).
• Other type of counterbalancing

  partial counterbalancing = use a mixture of orders but not every order possible.

  This differs from full counterbalancing, which uses all possible orders equally often
• How to set partial counterbalancing

  Latin square

  
• Limitations of Latin square

  some carry-over effects may remain

  • Condition A directly follows B in two out of the four orders (P2 and P4). This means A would get more ‘carry-over’ than other conditions.
  • Imagine that there was something about condition B that means it affects the condition immediately after it.
  • condition A would be more affected by this carry-over effect than other conditions

  
• Solution

  balanced Latin square:

  • each element appear once in every row and column
  • each element follows the other elements only once across rows.
• Correlation


  • extent to which two variables are related
  • measures pattern of responses across variables
  • pattern can then be quantified
• Small +ve relationship between variables

  Line indicates relationship

  
• +ve relationship

  • both variables rise together

  
• -ve relationship


  • as one rises, the other falls

  
• Measuring relationships


  • whether as one variable increases, does the other variable increase, decrease, or stay the same
  • calculate covariance
  • looks at how much each score deviates from the mean
  • if both variables deviate from mean by the same amount = they are likely to be related
• Covariance

  • tells us how much scores on TWO variables differ from their RESPECTIVE MEANS

  
• Variance formula

  
• Covariance formula


  Calculate the error of variable 1 (x)

  Calculate the error of variable 2 (y)

  Multiply

  Divide by N - 1

  * need to have same number of datapoints for both variables, if not, remove from both so same number of datapoints

  
• Covariance EXAMPLE

  
• Limitations of covariance


  • depends on units of measurement
  • SOLUTION: standardize it (divide by SD for both)
  • the standardised version of covariance = correlation coefficient
  • unaffected by units of measurement
• Calculating correlation coefficient (r)

  Divide covariance by SD of both

  
• Correlation coefficient (r) EXAMPLE

  
• Reporting correlations

  
• Correlation notes

  
• Solving inequalities

  • -ve number changes direction of inequality sign

  
• Inequalities with 3 terms

  
• Notation and boundary values

  
• The notation with ONE boundary

  
• Quadratic inequalities

  
• Bivariate correlation

  Correlation between two variables

  • partial correlation considers more variables