Analysis of Variance (ANOVA) in Statistics

These flashcards cover key vocabulary and concepts related to Analysis of Variance (ANOVA) in statistics, essential for understanding experimental design and statistical analysis.

Analysis of Variance (ANOVA)

A statistical method used to compare means of three or more groups to determine if at least one mean is different.

Completely Randomized Design

An experimental design where subjects are randomly assigned to different groups.

One-Way ANOVA

A method to evaluate differences among the means of three or more groups based on one independent variable.

Two-Way ANOVA

An extension of ANOVA that examines the effect of two factors on a dependent variable and their interaction.

F-test

A statistical test used to compare two variances by determining if they are significantly different.

Tukey-Kramer Method

A post-hoc test used after ANOVA to find which specific group means are different.

Multiple Comparisons

Statistical methods used to compare multiple groups and assess differences in their means.

Levene Test

A statistical test used to assess the equality of variances across groups.

Homogeneity of Variance

Assumption that different samples have the same variance.

Interaction Effect

Occurs when the effect of one independent variable on a dependent variable depends on the level of another independent variable.

Dependent Variable

The outcome variable that the experimenter measures to determine the effect of different treatments.

Null Hypothesis (H0)

Assumption that there is no effect or difference between groups.

Alternative Hypothesis (H1)

Assumption that there is an effect or difference between groups.

Sum of Squares Total (SST)

The total variation in the data calculated as the sum of squared differences from the mean.

Sum of Squares Among Groups (SSA)

The variation due to differences among group means.

Sum of Squares Within Groups (SSW)

The variation of observations within each group.

Mean Squares Among Groups (MSA)

Calculated by dividing SSA by its associated degrees of freedom.

Mean Squares Within Groups (MSW)

Calculated by dividing SSW by its associated degrees of freedom.

Degrees of Freedom

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

F Statistic

The ratio of the variance among group means to the variance within groups in ANOVA.

P-value

The probability that the observed data would occur if the null hypothesis were true.

Significance Level (α)

A threshold that determines whether to reject the null hypothesis, commonly set at 0.05.

Experimental Design

The plan for assigning experimental units to treatment groups.

Randomization

The process of randomly assigning subjects to different groups to avoid bias.

Normal Distribution

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

Statistically Significant

A term that indicates that a result is unlikely to have occurred under the null hypothesis.

Post-hoc Analysis

Tests conducted after an ANOVA to identify specific differences between group means.

Cell Means Plot

A visual representation used to assess interaction effects in a two-way ANOVA.

Factorial Design

An experimental setup that involves two or more factors whose effects are examined.

Assumptions of ANOVA

Conditions that must be met for ANOVA results to be valid, including independence, normality, and homogeneity of variance.

Kruskal-Wallis Test

A non-parametric test used when ANOVA assumptions are violated, comparing three or more independent groups.

Interaction Plot

A graph showing the effects of two independent variables on a dependent variable, which can indicate interaction.

Tukey's HSD

A specific statistical test used for making pairwise comparisons among group means after ANOVA.

Effect Size

A measure of the strength or magnitude of a relationship among variables.

Sample Size

The number of observations or data points in a sample.

Total Variation

The overall variation in the dataset which can be divided into within-group and among-group variations.

Independent Samples

Samples that are collected in such a way that one sample does not affect the other.

Normal Probability Plot

A graphical technique for assessing if a data set is approximately normally distributed.

Boxplot

A standardized way of displaying the distribution of data based on a five-number summary.

F Distribution

The probability distribution of the ratio of two independent chi-squared variables.

Multicollinearity

A situation in regression analysis where predictor variables are highly correlated.

Main Effects

The direct effects of each independent variable on the dependent variable, independent of interactions.

Linear Model

A model that describes the relationship between a dependent variable and one or more independent variables using a linear equation.

Power of a Test

The probability that the test will correctly reject a false null hypothesis.

Variance Inflation Factor (VIF)

A measure of how much the variance of an estimated regression coefficient increases when your predictors are correlated.

Shift Effect

The difference in outcomes observed due to changes in the independent variable.

ANOVA Table

A structured format that summarizes the results of an ANOVA.

Critical Value

The value that a test statistic must exceed in order to reject the null hypothesis.

Factor A and B

The two independent variables being analyzed in a two-way ANOVA.

Non-parametric Tests

Statistical tests that do not assume a specific distribution for the data.

Cell Count

The number of observations in each cell of a factorial design.

Column Means

The average value of each column in a data set, often used in comparison analysis.

Response Variable

The dependent variable that is measured in an experiment.

Interaction Effect in ANOVA

When the effect of one variable depends on the level of another variable.

Design of Experiments (DOE)

A systematic method used to determine the relationship between factors affecting a process and the output of that process.

Balanced Design

An experimental design where each treatment combination has the same number of observations.