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