Bivariate Analysis: Correlation/Association Flashcards
What is Correlation?
Describes the degree to which the change in value of one variable corresponds to a change in value of a second variable
What is the Pearson Correlation Coefficient?
Measure of the linear relationship between two continuous variables
What is the parameter and range for the Pearson Correlation Coefficient?
Rho
-1 to +1
0 < r < 1 Indicates what in the Pearson Correlation Coefficient?
Positive correlation, as one variable increases the second variable increases
0 > r > 1 Indicates what in the Pearson Correlation Coefficient?
Negative correlation, as one variable increases the second variable decreases
r = 0 Indicates what in the Pearson Correlation Coefficient?
No Linear Relationship
A positive correlation is seen with what line tilt in a Pearson Correlation Coefficient?
With the higher end of the line pointed towards the positive numbers
What type of data is used in Pearson Correlation Coefficient?
Continuous data, a mean must be calculated BUT it does NOT need to be on the same scale
What is the hypothesis for Pearson’s Correlation Coefficient?
Ho = p=0
p is rho, the population parameter for r
The larger the what, = a larger t-statistic and a greater chance to be significant
- r
- N
What is the Spearman Rho Coefficient?
Used with ORDINAL/RANKED data, or continuous data that are not normally distributed
-Continuous data can be transformed into ranks then used to calculate Spearman Rs
Values of Rs can vary between what for Spearman Rho Coefficient?
-1 and +1
Pearson and Spearman are very similar, how so?
- Both have values that range between -1 and +1
- Values close to 1, indicate greater correlation; positive or negative signs indicate positive or negative correlation
When can Spearman Rs be used?
- Continuous data is not available
- Continuous data is skewed
What is the Phi Coefficient?
Estimates the extent/strength of the relationship between 2 dichotomous variable
What is the range for the Phi Coefficient?
-1 to +1
How is the Phi Coefficient related to Chi Square?
Chi Square is equal to the pho coefficient squared
If variables are POSITIVELY associated, the data falls along what cells?
DIAGONAL: a and d
If variables are NEGATIVELY associated, the data falls along what cells?
NON-DIAGONGAL: b and c
What are the ranges of relationship for Phi Coefficient?
- Weak or NO Relationship: -0.3 to +0.3
- Moderate Relationship: +/- 0.3 to +/- 0.7
- Strong Relationship: +/- 0.7 to +/- 1
How do you find the test statistic with Chi Square and Phi Coefficient?
X2 test stat = (sample size)(phi coefficient^2)
What is the Kappa Coefficient?
Examine inter-rater agreement
Only covers 2x2
What is the range for Kappa Coefficient?
0 to 1
No such thing as a negative
What does 0 mean in Kappa Coefficient?
No more agreement between two raters as can be expected on the basis of chance aka CHANCE
What does 1 mean in Kappa Coefficient?
Perfect agreement, all observations on the diagonal
What are the ranges of relationship for Kappa Coefficient?
- Poor Agreement lower than 0.4
- Fair to Good Agreement 0.4-0.75
- Excellent Agreement greater than 0.75
Correlation does NOT indicate Causality, it what?
Indicated if the value of one variable increases or decreases while a second variable increases or decreases
Variables with casual relation will be correlated but
Variables that are correlated do not have to have a causal relationship
