Week 12 & 13 Flashcards
Correlation
2 variables related to each other
Correlation Coefficient
- Statistics used when looking for association between variables in 1 sample
- Used in combination with p-value
Correlation Assumptions
Sample subjects should be indep & randomly selected
Pearson’s R
- Both variables should have normal distribution & homoscedasticity
- Must be interval/ratio
- Magnitude between -1 to 1
- Positive or negative direction
Chi-Square/Gamma
Nominal or ordinal
Spearman’s R
Ordinal or interval/ratio
Homoscedasticity
Having the same variance
Correlation Analysis
- Measure strength of association (linear relationship) between 2 variables
- No casual effect is implied
Direction of Relationship
- Linear association: straight line
- Either positive or negative
Positive Correlation
1 variable increases & other variable increases as well
Negative Correlation
- 1 variable increases & other decreases
- R is negative
Strength of Relationship
- Determined by absolute value of r
- Closer to +/- 1 = 1 stronger relationship
- Closer to 0 = weaker relationship
- 0 = no relationship
Direction of Relationship
- Determined by sign (+/-)
- -1 = perfect negative relationship
- +1 = 1 perfect positive relationship
- 0 = no relationship
Strength of Correlation
- Weaker relationship requires larger sample size to detect
- Sample size helps verify relationship strength
Key Requirements to Infer a Casual Relationship
- Time order (IV to DV)
- Statistical association
- No confounding variables that can influence IV & DV
Correlation vs Causation
- Correlation only describes mathematical relationship between 2 variables
- Correlation is not sufficient condition for determining causality
P-Value Significance
- P > alpha = not significant
- P < alpha = significant
Coefficient of Determination (R2)
- Values between 0 and 1
- R2 multiplied by 100 gives % of variance
% Variance
Amount of variance in DV that is explained by IV
Correlation Coefficient Clinical Importance
Any value r > 0.3 (explains 9%+) often clinically important
Regression Analysis
Predict value of DV based on value of at least 1 IV
Simple Linear Regression Model
- 1 IV (x)
- Relationship between x & y is described by a linear function
- Changes in y assumed to be caused by changes in x
Simple Linear Regression
Predicting 1 DV from 1 IV
Multiple Regression
- Predicting 1 DV from multiple IVs
- Considering multiple control variables simultaneously
Regression Coefficient
- How much DV is expected to increase, when IV increases by 1
- Holding all other IVs constant
Bivariate Analysis
- Compares 2 variables simultaneously
- Looks at their association
- Assess strength of their association
Limits of Chi-Square
- Sensitive to sample size
- Can’t indicate strength of the association
% Difference
- Provides 1 weak indicator of strength of relationship
- Larger difference = stronger relationship
Gamma
- Nominal & ordinal variable only
- Statistic that varies between 0 and +/-1
- 0= (no association)
- 1 = perfect association
Multivariate Analysis
- Analysis of 2+ variables simultaneously
- Can be discrete, continuous or both
Zero-Order
- Original relationship between indep & dep variables
- Zero variables controlled
First-Order
1 control variable included in the model
Partial
Association of indep & dep variables for a subset of observations
Elaboration Model
- Introduces 3rd (control) variable into analysis
- Enhance/elaborate understanding of bivariate relationship
- Helps explain relationship between 2 original variables
- Control variable held constant
Antecendent Control Variable
- Non-spurious: occurs directly before IV only
- Spurious: occurs directly before both IV & DV
Intervening Control Variable
Occurs between IV & DV
Confounding Control Variable
Influences relationship of IV & DV
Elaboration Model Purpose
- Understanding relationship between 2 variables by controlling effects of a third
- Illustrates the fundamental logic of multivariate & casual analysis
Replication Pattern
- Partial relationships are same as original relationship
- 3rd variable does not change the original relationship
- 3rd variable unrelated to original relationship
- Partials remain unchanged/change insignificantly
Explanation Pattern - Antecedent
- Original relationship shown to be false through introduction of controlled variable
- 3rd variable explains away original relationship
- Original relationship no longer related
- First-order partials are significantly less than zero-order relationship
Explanation Pattern Conditions
- Control variable must be antecedent to both IV & DV
- First- order partials are significantly less than zero-order relationship
Interpretation Pattern - Intervening
- Control variable mediates effect of IV &DV
- 3rd variable intervenes in original relationship
- Original relationship no longer related
- First- order partials are significantly less than zero-order relationship
Specification Pattern
- Partial relationship differ from one another
- 3rd variable specifies conditions under which the original relationship varies
- Original relationship in at least 1 partial increase/decrease/disappears but not in others
Suppressor Variable
- Concealing the relationship
- Creates illusion of independence between IV & DV
- Control variable increases association between DV & IV
- Control variable associates pos with 1 variable and neg with other
Distorter
- Distorting the relationship
- Reverse true direction of relationship between IV & DV
Limits to Elaboration Model
- Doesn’t fit every situation
- Doesn’t specify statistical significance
