Methods Week 7 - Associations & Predictions (2/2)

Pearson correlation

Measures the linear relationship between two continuous variables (e.g., height vs. weight)

what is a limitation of correlations?

1. type 1 error

2. non-hierarchical: only examine the association between one predictor and one outcome variable

regression analyses (WILL SEE REGRESSION TABLE ON FINAL)

examine the association between several variables at the same time

can make predictions based on correlations and a bunch of other variables to make correct assumptions

• can be used to control for covariates, examine moderators, and/or test for mediating effects

ex. can ask to assume weight based on correlation of weight and hight, SES, hours stationary ect.

predictor

independent variable

criterion

dependent variable or outcome variable

advantages of a regression

1. decrease type 1 error because your doing one analysis vs. several correlations

2. look at relationships between variables and separate their influences (separating correlations to reduce confound influence)

• can see the effects of weight and tv watching without height, or can find the effect of weight and height without tv watching

simultaneous regression

put all variables (IV and DV) all at the same time

hierarchical regression

inputting your variables one at a time to see how they effect your data separately 

standardized beta coefficient

between -1 and 1; relationship between two variables based on their SD

interpret the same way as r value but only for regressions

curvilinear patterns

fitting prediction lines when the data is non-linear can bias predictions

• only run a regression when your data is linear

outliers

extreme cases can “pull” the effects towards more (or less) extreme conclusions

restriction of range

sampling too narrow of a range of data can bias the conclusions

• regression cannot predict anything above or below the given range

extrapolating beyond the data

inferring beyond the data can bias conclusions

covariates

variables that you think are potential confounds and you cannot control for the confounds, so you put it in a regression that can take out the confound for.

reflect the demographic characteristics, pretest scores, context variables, and/or confounding variables that a researcher wishes to control for

moderators

reflect the variables that the researcher thinks will interact with the key predictor variables to explain when or with whom an effect is most likely to occur

• influences the strength or direction of the relationship between the primary IV and the DV. moderator modifies the effect of the IV on the DV

• ex. depending on your age, you will gain more or less muscle when you work out

mediators

reflects the variables that a researcher believes can explain how or why a predictor is related to a criterion variable

ex. why people who play an instrument have higher grades, mediator is the SES 

what is the difference between moderation and interaction

they are the same, but moderation is used in the context of regression and interaction is used in the context of ANOVA’s

difference between mediator and moderator 

• Mediator = mechanism → explains how or why.

  • why or how X affects Y

• Moderator = context → explains when or for whom.

  • X → Y depends on Moderator Z to occur

unstandardized beta coefficients (b)

reflect ‘raw’ beta-coefficient in the original unit of measurement

ex. for every inch you gain in height, you gain 5lbs of weight

why are standardized beta coefficients better than unstandardized

want to compare apples to apples and not apples to oranges, this is why we use z-scores.

coefficient of determination (R²)

the overall size of the effect (ie. the % of variance explained) based on all the variables in that step of the model (combine all Beta scores and see how much of all the variables introduced ACTUALLY impact your DV

what does it mean if you have a 0.024 R²

it means the influence of the combined variables only explains 2.4% of relationship between the IV and the DV

what is delta R²

seeing the change in R² from your first step (without multiple variables) to your second step (with multiple variables) to see if your % relationship went up or down.