Design of Experiments and Analysis of Variance

A comprehensive set of flashcards that covers key concepts in the design of experiments and analysis of variance based on the lecture notes.

Response Variable

The variable of interest to be measured in an experiment; also known as the dependent variable.

Factors

Variables whose effect on the response is of interest to the experimenter; classified as quantitative or qualitative.

Factor Levels

The values of the factors used in the experiment.

Treatments

The factor-level combinations used in an experiment.

Experimental Unit

The object on which the response and factors are observed or measured.

Designed Experiment

A study in which the analyst controls the specification of treatments and assigns experimental units to each treatment.

Observational Study

A study in which the analyst simply observes the treatments and the response without assigning them.

Completely Randomized Design

An experimental design where experimental units are assigned randomly to treatments.

Analysis of Variance (ANOVA)

A statistical technique used to analyze the data collected from a designed experiment.

Null Hypothesis (H0)

The hypothesis that states there is no significant difference among population means.

Alternative Hypothesis (Ha)

The hypothesis that indicates at least two treatment means differ.

Type I Error

The error of rejecting a true null hypothesis.

Type II Error

The error of failing to reject a false null hypothesis.

F-Test

A test used to compare two or more population means.

Sum of Squares

A measure used in ANOVA to quantify variation within and among groups.

Degrees of Freedom

The number of independent values or quantities that can vary in the analysis.

Critical Value

A threshold value that determines whether to reject the null hypothesis.

Mean Square for Treatment (MST)

The mean square variation due to treatment in ANOVA.

Mean Square for Error (MSE)

The mean square variation due to error in ANOVA.

Balanced Design

A design where sample sizes for each treatment are equal.

Random Assignment

The process of randomly assigning experimental units to treatments to ensure unbiased results.

Normality Assumption

The assumption that the population distributions are approximately normal.

Equal Variances Assumption

The assumption that all population variances are equal.

Factorial Experiment

An experiment where two or more factors are evaluated simultaneously.

Multiple Comparisons

Methods used to compare means from multiple treatment groups.

Tukey Method

A method for pairwise comparison of means in balanced designs.

Bonferroni Method

A method used for pairwise comparisons in either balanced or unbalanced designs.

Scheffé Method

A method used for general contrasts of means in ANOVA.

Experimentwise Error Rate (EER)

The risk of making at least one Type I error when making multiple comparisons.

Kruskal-Wallis H-test

A nonparametric method used when ANOVA assumptions are not satisfied.

ANOVA Summary Table

A table that summarizes the sources of variation, degrees of freedom, sum of squares, mean squares, and F-statistic.

Randomized Block Design

An experimental design that accounts for variations among experimental units by grouping them into blocks.

Factor Levels and Treatments

Factor levels are specific values assigned to factors, while treatments are combinations of these levels used in experiments.

Partitions in Variation

Breaking down total variation into treatment and error components to analyze the differences.

Sampling Variability

Variation that occurs due to sampling; can impact the results of statistical tests.

ANOVA F-Test Hypotheses

H0: µ1 = µ2 = … = µk and Ha: Not All µi Are Equal, indicating treatment effects.

Conditions for Valid F-Test

Conditions include normality of treatment populations and equal variances.

Statistical Software

Tools used to perform statistical calculations and generate ANOVA results.

Substantial Treatment Variation

Indicates that treatment effects are significant and populations means are different.

Random Sampling

The process of selecting a sample from a population where each member has an equal chance of being chosen.