Proportional reduction of error (PRE)
Assesses the relationship between two variables by determining the extent to which knowing about one variable reduces our error in predicting the value of the other variable
What are the 3 (sometimes 4) things PRE can tell us about the relationship between two variables?
1) Its strength
2) How accurately we can predict it
3) What % of variation in the DV can be explained by the IV
4) Its directionality (ONLY SOMETIMES, ONLY WITH GAMMA)
Measure of association (MOA)
A single number that summarizes the strength of a relationship by assessing the PRE of the IV and DV
What is lambda and what are its characteristics?
1) MOA used for nominal variables
2) Cannot indicate directionality (only strength of relationship)
3) Value can range from 0 - 1 (no negatives)
What does E1 represent in lambda?
The number of predictive errors made when the IV is ignored (how many times we were wrong)
What does E2 represent in lambda?
The number of predictive errors made when the IV is taken into account (The sum of how many times we were wrong when taking the IV into account)
What are the steps for doing a lambda test?
1. Find E1 by subtracting the largest row total from the total sample
2. Find E2 by subtracting the largest cell value from its column total for EACH column, then add together
3. Plug into the lambda formula
4. INTERPRET the results (strength)
What is gamma and what are its characteristics?
1) MOA used for ordinal variables
2) Used for predicting the order of 'pairs of cases' (if one case will have a higher or lower score than another)
3) Value can range from - 1 - 1, meaning it CAN indicate directionality
What does Ns represent in gamma?
The number of same ordered pairs (high/high or low/low)
What does Nd represent in gamma?
The number of differently (or inverse) ordered pairs
What are the steps for doing a gamma test?
1. Find Ns by multiplying the upper left cell with the lower right cell
2. Find Nd by multiplying the upper right cell with the lower left cell
3. Plug into the gamma formula
4. INTERPRET the results (strength and direction)
What are 4 ways you could interpret lambda results?
1) Having information on (the IV) decreases our error in predicting (the DV) by xx%
2) Having information on (the IV) increases our ability in predicting (the DV) by xx%
3) We are xx% more accurate in predicting (the DV) if we know (the IV)
4) Strength of relationship ranging from 1.0 = very strong 0.0 = no relationship
What are 4 ways you could interpret gamma results?
1) Having information on (the IV) decreases our error in predicting (the DV) by xx%
2) Having information on (the IV) increases our ability in predicting (the DV) by xx%
3) We are xx% more accurate in predicting (the DV) if we know (the IV)
4) Strength AND direction of relationship ranging from -1.0 = strong negative 0.0 = no relationship 1.0 = strong positive