Analysis of Relationships Flashcards
What is a Correlation?
Linear relationship between 2 variables
Concept of covariance (i.e., 2 variables vary in similar patterns)
What is a partial correlation?
Relationship between 2 variables with the effects of a 3rd held constant (removing its effect)
What are assumptions related to the correlation? (3)
- Linear relationship
- Adequate variability in both scores to get a correlation
- Homoscedasticity
What is Homoscedasticity?
- Homogeneity of variance but multivariate
- For each variable, on various points of the variable, the other variable has equal variability
What does it mean to have adequate variability in both scores to get a correlation?
No floor or ceiling effects: these will give low correlations
How do you interpret relationships? (5)
Direction
Strength
Variance shared
Significance
Confidence intervals
What are 2 ways to visually interpret relationship?
- Scattergram
Plot showing relationship between two variables
Dot for each participant’s score on both variables - Line of best fit
What is the difference between positive and negative relationships?
- Positive relationship
Both variables more in the same direction
Slope up to the right - Negative relationship
Variables move in opposite directions
Slope down to the right
What is strength of relationship?
Visually, how close the dots are to the line of best fit
What is the strength of the relationship (quantitatively)?
- Correlation coefficients (i.e., ‘r’)
- Statement of strength of relationship
Range between 0.00 & ±1.00 - Affected by sample size, measuring error, type of variables
What is ‘‘Shared variance’’?
- Practical/Clinical significance: How much variance is accounted for
- Coefficient of determination - r2
Some effect sizes based on
variance explained - eta squared (ɳ2 )
& omega squared (ω2)
How do you establish significance of relationships?
- Statistical testing of strength
All correlations test the null
H0 = no relationship exists between the variables
r = 0
Get p value, if at or below alpha level, reject H0 and conclude that the two variables are related
How are CI important in the interpretation of relationships? (4)
- Represent range in which ‘true’ score lies
- Set degree of confidence require – often 95%
- Range of scores given
- Larger the sample size, the smaller the confidence interval
What are the parametric tests of the correlations?
- Pearson Product Moment Correlation - r
- Same assumptions as other parametric tests
What is important rule to remember when interpreting correlation coefficients?
- Correlation ≠ causality
Any observed relationship could be caused by intermediary variable(s)
e.g., A significant positive
When can you generalize correlations? (3)
- Generalize only within the tested range
- Impossible to know what would happen before or after that range
- Restricted range of scores may not reflect true relationship
Important to measure over full range
What is Bivariate Regression?
- Uses the correlation between one independent predictor variable (X) and one dependent variable (Y) to predict Y
E.g., reading predicted by phonemic awareness
*Bivariate analysis looks at two paired data sets (one independent predictor variable (X) and one dependent variable (Y)) to see if a relationship exists between them (predict Y)
- A “line of best fit” is calculated i.e., the regression line
What are effects of outliers in bivariate regressions?
Outliers can have a dramatic effect upon correlations and the calculation of regression lines, particularly if N is small
