Hypothesis Testing with Multiple Groups

These flashcards cover key terms and definitions relevant to hypothesis testing with multiple groups, focusing particularly on ANOVA and its applications.

Hypothesis Testing

A statistical method used to make inferences or draw conclusions about population parameters based on sample data.

Mean Difference

The difference in the average values of a particular variable between two or more groups.

Dependent Variable

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

Independent Variable

The variable that is changed or controlled in a scientific experiment.

ANOVA

Analysis of Variance, a statistical method used to compare means among three or more groups.

Null Hypothesis (H0)

A statement asserting that there is no effect or difference, used as a starting point for statistical testing.

Alternative Hypothesis (H1)

A statement indicating the presence of an effect or difference, contrary to the null hypothesis.

F-Ratio

A statistic used in ANOVA to compare the variance between groups to the variance within groups.

Cohen's D

A measure of effect size that indicates the standardized difference between two means.

Eta-squared (η²)

A measure of effect size that indicates the proportion of variance explained by an independent variable.

T-test

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

Box Plot

A graphical representation of data that shows the distribution's median, quartiles, and outliers.

Histogram

A graphical representation of the distribution of numerical data, where the data is divided into bins.

Descriptive Statistics

Statistics that summarize or describe the characteristics of a dataset.

Sample Size (N)

The number of observations or data points used in a statistical analysis.

Mean

The average value calculated by summing all observations and dividing by the number of observations.

Median

The middle value in a dataset when the numbers are arranged in ascending order.

Skewness

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

Standard Deviation

A measure of the amount of variation or dispersion in a set of values.

Sum of Squares Total (SST)

The total variation in the dependent variable, calculated as the sum of the squared deviations from the mean.

Sum of Squares Between (SSB)

The variation in the dependent variable between groups, measuring how much group means differ from the overall mean.

Sum of Squares Within (SSW)

The variation in the dependent variable within groups, measuring how much observations differ from their group means.

Degrees of Freedom (df)

The number of independent values or quantities which can be assigned to a statistical distribution.

Mean Square Error (MSE)

An estimate of the variance within groups in ANOVA, calculated as SSW divided by its degrees of freedom.

Mean Square Between (MSB)

An estimate of the variance between groups in ANOVA, calculated as SSB divided by its degrees of freedom.

F-Distribution

The probability distribution of the F-ratio under the null hypothesis.

Critical Value

A threshold that determines the boundary for the rejection of the null hypothesis.

Post-hoc Test

A statistical analysis conducted after an ANOVA to find which specific groups' means are different.

Tukey's HSD

A post-hoc test used to determine which means are significantly different after an ANOVA.

Quartile

A type of quantile that divides a dataset into four equal parts.

GDP per Capita

A measure of a country's economic output that accounts for its number of people.

Internet Access

The ability of individuals or households to connect to the internet.

Descriptive Statistics for Group Means

Statistics that summarize the mean, median, and standard deviation for each group in analysis.

Histogram Interpretation

Assessing the shape and distribution characteristics of a dataset through a histogram.

Variance

A measure of how much values in a dataset differ from the mean value.

Research Question

A precise question about a phenomenon that guides a scientific investigation.

Effect Size Interpretation

Understanding the practical significance of a statistical result based on its effect size.

Population Size

The total number of individuals within a defined area or group being studied.

Regional Differences

Variations in characteristics due to geographical factors among distinct areas.

Statistical Significance

A determination that results are unlikely to have occurred by chance, often assessed with a p-value.

p-Value

The probability of obtaining results at least as extreme as the observed results of a statistical hypothesis test.

Cut2 Function

A command used in R to categorize a continuous variable into discrete groups.

Compmeans Function

A command in R that computes mean values across categories of a grouping variable.

Hist Function

A command in R to create a histogram for visualizing the distribution of data.

Subset Analysis

Analyzing a specific group or category within a larger dataset.

Missing Data Handling

Approaches to deal with incomplete or unavailable data points in a dataset.

Plotmeans Function

A command in R to visualize mean values with confidence intervals across groups.

R Libraries

Packages in R that enhance its base functionalities for statistical analysis.

Significance Codes

Symbols used to indicate the level of statistical significance in results output.

Exploratory Data Analysis

An approach to analyzing data sets to summarize their main characteristics, often using visual methods.

Computational Statistics

The field of statistics that uses algorithms and numerical methods to analyze data.

Mean Differences Visualization

Graphical methods to display and compare the means of different groups.

Null Hypothesis Rejection

The conclusion made when statistical evidence suggests the null hypothesis is not true.

Statistical Models

Mathematical representations of observed data used to understand relationships between variables.