Chapter 14: Correlation and Scatterplots

These flashcards cover key terms and definitions related to correlation and scatterplots as discussed in Chapter 14 of the lecture notes.

Correlation

A statistical measure that expresses the extent to which two variables are linearly related.

Scatterplot

A graph that displays values for two variables for a set of data, using points to represent individual data points.

Independent Variable

The variable that is manipulated or controlled to test its effects on the dependent variable.

Dependent Variable

The variable that is being tested and measured in an experiment.

Negative Relationship

A relationship in which one variable increases as the other decreases.

Positive Relationship

A relationship in which both variables increase or decrease together.

Mean

The average value of a set of numbers.

Median

The middle value in a data set when the numbers are arranged in order.

Skewness

A measure of the asymmetry of the probability distribution of a real-valued random variable.

Crosstab

A table that displays the frequency distribution of variables.

Histogram

A graphical representation of the distribution of numerical data.

Fertility Rate

The average number of children a woman would have during her lifetime.

Life Expectancy

The average period that a person may expect to live.

Ratio-level Variables

Variables that can be ordered and have a true zero point.

Descriptive Statistics

Statistics that summarize data sets, providing simple summaries about the sample and the measures.

Pearson's r

A measure of the linear correlation between two variables, ranging from -1 to 1.

Lambda

A measure of association that represents the proportional reduction in error when predicting a dependent variable.

Cramer’s V

A measure of association between two nominal variables, giving a value between 0 and 1.

Kendall's Tau-b

A measure of correlation that assesses the strength and direction of association between two variables.

Correlation Matrix

A table showing correlation coefficients between variables.

Scatterplot Matrix

A grid of scatterplots that visually display relationships among multiple variables.

Proportional Reduction in Error (PRE)

A statistic that quantifies how much knowing the value of the independent variable reduces the error in predicting the dependent variable.

Partial Correlation Coefficient

A measure of the relationship between two variables while controlling for the effect of one or more additional variables.

Null Hypothesis (H0)

The hypothesis that states there is no effect or no difference.

Alternative Hypothesis (H1)

The hypothesis that states there is a significant effect or difference.

Significant Relationship

A relationship in which the observed effect is unlikely to have occurred by chance.

Visual Patterns in Data

Observable trends in data represented in graphs or plots.

Random Sampling

A sampling method that ensures every member of a population has an equal chance of being selected.

Explanatory Variables

The variables used to explain variances in the dependent variable.

Covariation

The degree to which two variables change together.

Data Analysis

The process of inspecting, cleansing, transforming, and modeling data to discover useful information.

Statistical Significance

A determination that results are unlikely to be due to chance.

Computational Statistics

A field of statistics that uses computational approaches to analyze data.

T-test

A statistical test used to compare the means of two groups.

p-value

A value that helps determine the significance of the results.

Bivariate Analysis

An analysis that involves two variables.

Multivariate Analysis

An analysis that involves more than two variables.

Error Reduction

The process of making predictions with less variance from the actual results.

Log Transformation

A mathematical technique where logarithmic values are used to minimize the influence of extreme values.

R Packages

Collections of R functions, data, and documentation designed to work for specific tasks.

Hmisc

An R package that provides various statistical functions.

DescTools

An R package that offers various descriptions and statistical analysis tools.

scatterplots

Visual tools to represent the relationship between two continuous variables.

data distributions

The way values are spread across different ranges in the dataset.

Cumulative Distribution Function

A function that shows the probability that a variable takes a value less than or equal to a certain number.

Statistical Models

Mathematical representations of observed data used for analysis.

Quantitative Research

Research that relies on measurable data to formulate facts.

Data Interpretation

The practice of examining and explaining data to extract meaningful conclusions.

Outliers

Data points that differ significantly from other observations in a dataset.