Lesson 13 Flashcards
How variable is related to some other variable
Measures of Association and correlation
- Answers the question “Is there some sort of relationship?”
- Also called bivariate tables/RxC tables
Contingency Table
Elements of Contingency Table
- Title (variables, year, source)
- Column variables
- Row variables
- Column marginals - subtotals
- Row marginals - subtotals of row variables
- Grand total
- Source
Values of ___? variables can be explained by the variables of independent variables
Dependent
For ____? variables, the order of categories depends on personal preference
Nominal
Modelling Relationships between 2 Variables
- One-Way Direct Relationship
- Two-Way Direct Relationship
The variable is “controlled for” when we take into account its effect on variables in the bivariate relationship
Control Variable
If there’s a change in direction between the relationship of 2 variables, there exist a different type of variable (T or F)
T
Possible conclusions when a 3rd variable is introduced?
- A direct relationship still exist (the third effect has no effect
- A spurious or intervening relationship exists
- A condition relationship exists
Types of Relationship
- Direct Relationship
- Spurious Relationship
- Intervening Relationship
- Conditional Relationship
Type of relationship where when we introduce a variable, there is no direct relationship between IV and DV
Spurious Relationship
Type of relationship where we cannot directly explain the other variable and must be defined first
Conditional Relationship
Summary measure that reflects the strength of the relationship between two variables (how strong the relationship between two variables)
Measures of Association
The closer the measure to 1, the ??? the association
Stronger
If measures equals 0, there is ??? between the two variables
No relationship
The sign of the measure indicates whether the relationship is positive or negative.
Direction
Types of Measures of Association where the value of the measure is the same regardless of which variable is the IV or DV
Symmetric Measure
Types of Measures of Association where the value of the measure may vary depending on which variable is assigned as the IV or the DV
Asymmetric Measure
Different Methods of Association for Nominal Variables
- Phi
- Cramer’s V
- Lambda
- T^2
- Contingency Coefficient, C
- Tetrachoric Correlation, rtet
- Rank Biserial Correlation, rrb
- Used to measure association between nominal variables in 2x2 Contingency Tables.
- Adjusts the chi-square statistic by the sample size
- Both IV and DV have 2 categories
- For 2x2 tables, the Value ranges from 0 (No association) to 1 (Perfect Association)
- For larger tables, the generated value exceeds 1, making it harder to interpret
Phi
- Appropriate for testing the relationship between nominal variables in table of any size
- Easy to derive once the x^2 test statistic has already been computed
- Has an upper limit of 1, regardless of the size of the table
- Has a major issue like Phi where there is no meaningful interpretation for values between the extreme values of 0 and 1.
- Not sensitive to sample size
Cramer’s V
Different Methods of Association for Ordinal Variables
- Spearman’s Rho
- Gamma
- Somer’s d
- Kendall’s tau (tau-b)
- Appropriate for ordinal variables that are continuous in form and have a broad range of different scores and few ties between cases on either variables.
- Shows the level of agreement or consistency in the rankings between the two variables.
Spearman’s Rho
Property of Spearman’s Rho that states there are no disagreement in ranks between the two variables (Rs = +1)
Perfect Positive Association
Property of Spearman’s Rho that states there are perfect disagreement in ranks between the two variables (Rs = -1)
Perfect Negative Association
Rs^2 indicates the ___? of prediction when predicting the rank of one variable based on the range of another variable
Proportional Reduction in Errors
Use this method when the level of measurement is nominal and have two dichotomous variables
Phi
Use this method when the level of measurement is nominal and have two variables with any number of categories
Cramer’s V
Use this method when the level of measurement is nominal and have two variables with any number of categories (but IV and DV must be specified)
Lambda
Use this method when the level of measurement is ordinal and have ranked data (If one is inherently ordinal and the other is interval/ratio, both must be expressed into ranks prior to the computation)
Spearman’s Rho
Use this method when the level of measurement is ordinal and have data with several tied observations
Gamma
Use this method when the level of measurement is ordinal and have IV and DV that have equal number of categories
Kendall’s Tau
Use this method when the level of measurement is interval/ratio (both scales are interval/ratio)
Pearson’s R
Refer to categorical/nominal variables or ordinal (shows the strength or if related)
Measures of Association
Use of measures to evaluate whether variables are contemporaneous, covary, or coexist in space/ or time.
Correlation
Correlation = Causation (T or F)
F whahaha
Cases obtaining high scores on one variable tend to obtain high scores on the second variable (High-High)
Positive Relationship
Cases obtaining high scores on one variable tend to obtain low scores on the second variable (High-Low)
Negative Relationship
___? Correlation does not indicate a cause and effect relationship between variables
High
Failure to find relationship between the variables may be due to:
- The variables are in fact, not related
- The variables are related but in a non-linear manner
- The range of values is one or both variables is restricted (truncated)
