Design of Experiments and Analysis of Variance

A set of vocabulary flashcards derived from lecture notes on the design of experiments and analysis of variance.

Response Variable

The variable of interest to be measured in the experiment, also referred to as the dependent variable.

Factors

Variables whose effect on the response is of interest to the experimenter, can be quantitative or qualitative.

Factor Levels

The values of the factor used in the experiment.

Treatments

The factor-level combinations used in the experiment.

Experimental Unit

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

Designed Experiment

A study where the analyst controls treatments and assigns experimental units to each treatment.

Observational Study

A study where the analyst observes treatments and responses without controlling the assignment.

Completely Randomized Design

Design in which experimental units are randomly assigned to treatments.

ANOVA

A technique called Analysis of Variance used to analyze data collected from a designed experiment.

One-Way ANOVA

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

F-Test

Tests the equality of two or more population means based on sample variances.

Sum of Squares Between

Variation due to differences among treatment means.

Sum of Squares Within

Variation within treatment groups.

Degrees of Freedom

The number of values in a calculation that are free to vary; relevant in ANOVA calculations.

Null Hypothesis (H0)

The hypothesis stating that there is no effect or difference; in ANOVA, it indicates equal population means.

Alternative Hypothesis (Ha)

The hypothesis that there is an effect or difference among groups in an experiment.

Multiple Comparisons

Methods used to compare means across several treatment groups post-ANOVA.

Type I Error

The incorrect rejection of a true null hypothesis, known as a false positive.

Type II Error

Failing to reject a false null hypothesis, also known as a false negative.

Kruskal-Wallis H-test

A nonparametric statistical method used when ANOVA assumptions are not satisfied.

Balanced Design

A design with equal sample sizes for each treatment group.