Analysis of Variance (ANOVA) Lecture Notes

These flashcards cover essential vocabulary and concepts related to the Analysis of Variance (ANOVA) as discussed in the lecture notes, aiming to help students review key terms and their definitions for examination preparation.

Analysis of Variance (ANOVA)

A statistical method used to compare the means of three or more groups.

One-Way ANOVA

A type of ANOVA that analyzes the impact of a single independent variable on a dependent variable.

F-Test

A statistical test used to compare variances between groups in ANOVA.

Independent Variable

The variable that is manipulated or categorized in an experiment.

Dependent Variable

The variable that is measured or impacted in an experiment.

Null Hypothesis (H0)

A hypothesis that assumes no significant difference or effect exists between groups.

Alternative Hypothesis (H1)

A hypothesis that states there is a significant difference or effect present between groups.

Type I Error

Incorrectly rejecting the null hypothesis when it is true.

F-Statistic

The ratio of the variance between groups to the variance within groups in ANOVA.

F-Critical Value

The value that the F-Statistic must exceed to reject the null hypothesis.

p-value

The probability of obtaining results at least as extreme as the observed results, given that H0 is true.

Variance

A measure of how much values in a data set differ from the mean.

Levene's Test

A statistical test used to assess the equality of variances for a variable calculated for two or more groups.

Group Means

The average values of each group being compared in an ANOVA.

Degrees of Freedom

The number of independent values that can vary in an analysis; calculated as group size minus one.

Sum of Squares (SS)

A measure of the total variability in a data set.

Mean Square (MS)

The average of the sum of squares, calculated by dividing sum of squares by the respective degrees of freedom.

Between-Group Variation

The variation in the means of different groups in an ANOVA.

Within-Group Variation

The variation within each group in an ANOVA.

ANOVA Table

A table that summarizes the results of an ANOVA analysis, displaying sources of variation, sum of squares, degrees of freedom, mean square, and F-statistic.

Random Sampling

Selecting individuals from a population such that each individual has an equal chance of being selected.

Categorical Data

Data that can be divided into specific categories, such as gender or treatment type.

Numeric Data

Data that consists of numbers and can be measured, such as weight or height.

SSGroup

The sum of squares between groups, indicating variation due to the interaction between different groups.

SSWithin

The sum of squares within groups, indicating variability due to differences within each group.

Effect Size

A measure of the strength of a phenomenon, often used to describe the size of the difference between groups.

Post Hoc Tests

Follow-up tests used after ANOVA to determine which specific groups' means are different.

Normal Distribution

A probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence.

Statistical Significance

A determination that the results observed in data are unlikely to have occurred under the null hypothesis.

Multiple Comparisons

Evaluating several groups simultaneously in statistical tests, leading to increased risk of Type I errors.

Sample Size (N)

The total number of observations or data points collected in a study.

Independent Groups

Groups in an experiment where the participants in one group are not related to those in another group.

Dependent Groups

Groups in an experiment where the participants are related or measured at multiple times.

Grand Mean

The overall average of all data points in the study.

Homogeneity of Variance

Assumption that different samples have the same variance.

COVA

An example of a food chain used in ANOVA analysis.

Chick-fil-A

Another food chain example referenced in the context of ANOVA.

Whataburger

The third food chain used in the ANOVA example.

Exam 1

The first examination in the course, referenced in the context of performance analysis.

Repeated Measures ANOVA

A type of ANOVA used when the same subjects are measured multiple times.

Two-Sample t-Test

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

Kenny's Modification

Refers to a specific technique or approach used in statistical analysis.

MSE

Mean Square Error, the average of the squares of the errors used in calculating ANOVA.

Summary Statistic

A single value that is used to represent an entire set of data.

Critical Value

A threshold that determines whether to reject the null hypothesis in hypothesis testing.

Effectiveness Comparison

Examining differences in outcomes, such as programs or treatments, across different groups.

Significance Level

The probability of committing a Type I error, often set at 0.05.

Data Type

The classification of data based on its characteristics, such as qualitative or quantitative.

Statistical Tests

Mathematical procedures used to analyze data and draw conclusions.

Results Interpretation

The process of making sense of data analysis findings and understanding their implications.

Statistical Software

Programs used to perform statistical analysis, including ANOVA, such as SPSS or R.