Measures of Association

These flashcards cover essential vocabulary and concepts related to statistical measures of association discussed in the lecture.

Measures of Association

Statistics summarizing the strength of the relationship between two variables.

Chi-squared Test

A statistical test assessing whether observed frequencies differ significantly from expected frequencies.

Cramer’s V

A measure of association for nominal variables that ranges from 0 to 1.

Effect Size

A quantitative measure of the magnitude of the difference between groups.

Lambda (λ)

A proportional reduction in error statistic that quantifies how much prediction error decreases using an independent variable.

Cell Frequencies

The count of observations in each cell of a contingency table.

Column Percentages

The percentage of the total for each category in a column, used to analyze relationships in crosstabs.

Dependent Variable

The variable being tested and measured in an experiment.

Independent Variable

The variable that is manipulated to observe its effect on the dependent variable.

Ordinal Variables

Variables that represent categories with a meaningful order but no specific difference between categories.

Statistical Independence

A condition where two events are independent if the occurrence of one does not affect the probability of the other.

Proportional Reduction in Error (PRE)

A concept used in statistics to measure the improvement in prediction accuracy when using a model.

Pearson’s Chi-squared Test

A test used to determine if there is a significant association between categorical variables.

Null Hypothesis

The default assumption stating there is no association between variables.

Sample Size

The number of observations in a dataset, impacting statistical tests.

Expected Outcomes

The predicted frequencies in a statistical test based on the null hypothesis.

Effect Size Interpretation

Qualitative assessment of the size of the effect indicated by statistical measures.

Statistical Significance

A measure of whether observed results are likely due to chance alone.

Column Observation Weighting

Adjusting calculations to account for the differing total counts in column categories.

Statistical Significance Level

The threshold at which the results of a test are considered statistically significant.

Categorical Variables

Variables that represent distinct categories and can be nominal or ordinal.

Chi-squared Formula

The formula used to calculate the chi-squared statistic from observed and expected frequencies.

Degrees of Freedom

A parameter that quantifies the number of values in a statistical calculation that are free to vary.

Crosstabulation

A method to present the relationship between multiple categorical variables.

Strength of Relationship

The extent to which changes in one variable are associated with changes in another variable.

Cramer’s V Calculation

The method of deriving Cramer’s V using chi-squared and sample size.

Interpretation of Cramer’s V

Cramer’s V values are interpreted as follows: 0 means no association; 1 means perfect association.

Residual Analysis

Evaluating the differences between observed and predicted values to understand relationships.

Cross-Tabulation Analysis

A technique to investigate the relationship between categorical variables by creating contingency tables.

Confidence Intervals

A range that estimates the degree of uncertainty surrounding a sample statistic.

Statistical Packages in R

Software libraries used for statistical analysis, such as DescTools and descr.

Directional Measures of Association

Statistics that account for the direction (positive/negative) of relationships between variables.

Ordinal Crosstab Analysis

Analysis of crosstabs where variables are ordinal, which involves specific measures like gamma or tau.

Gamma (γ)

An ordinal measure of association assessing the strength and direction of a relationship.

Tau-b and Tau-c

Measures of association that account for tied pairs in ordinal data.

Lambda Interpretation

Lambda values express the proportional decrease in prediction error from using an independent variable.

Tied Pairs in Data

Observations where two categories have the same rank in either the independent or dependent variable.

R Function for Lambda

Function used to calculate lambda values in R for two categorical variables.

Interpreting Lambda

A lambda value indicates the percentage decrease in guessing error using the independent variable.

ASSOCIATION STRENGTH RANGES

Guidelines indicating how to interpret the strength of relationships based on effect size measures.

Gender Gap in Survey Analysis

Examining differences in responses between genders in survey data.

Statistical Power

The likelihood that a study will detect an effect when there is an effect to be detected.

Residual Analysis Purpose

To enhance understanding of how well a statistical model describes observed data.

Data Visualization Techniques in R

Methods to graphically represent data for better interpretation of relationships.

Proportions Calculation in Crosstabs

The arithmetic process of determining the fraction of a total represented by individual parts.

Regression Analysis

A statistical method for modeling the relationship between a dependent variable and one or more independent variables.

Confirming Statistical Results

The process of validating statistical findings through repeated analysis and testing.

Null Hypothesis Rejection

The conclusion that a significant difference exists between groups in hypothesis testing.