Statistics for Managers Using Microsoft Excel: Chapter 11 Analysis of Variance

A series of vocabulary flashcards based on Chapter 11: Analysis of Variance from the Statistics for Managers Using Microsoft Excel lecture notes.

Analysis of Variance (ANOVA)

A statistical method used to test differences between two or more group means.

Completely Randomized Design

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

One-Way ANOVA

A statistical test used to determine if there are significant differences between the means of three or more independent groups.

F-test

A statistical test that determines the ratio of variance between groups to the variance within groups.

Tukey-Kramer

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

Levene Test

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

Dependent variable

The outcome variable that is being measured in an experiment.

Independent variable

A variable that is manipulated in an experiment to observe its effect on the dependent variable.

Null hypothesis

A statement that proposes no significant difference exists among specified populations.

Alternative hypothesis

A statement that proposes a significant difference exists among specified populations.

Factorial Design

An experimental design that involves two or more factors.

Interaction effect

When the effect of one independent variable on the dependent variable changes depending on the level of another independent variable.

Multiple comparisons

Post-hoc analyses performed to determine which means differ following ANOVA.

Homogeneity of variance

The assumption that different samples have the same variance.

Random sampling

The selection of samples from a population in such a way that every individual has an equal chance of being selected.

Normal distribution

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

Degrees of freedom

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

Mean square

The average of the squares of the deviations from the mean in a data set.

Sum of squares (SS)

A measure of variation used in statistical modeling.

Total Sum of Squares (SST)

The total variation in the data.

Sum of Squares Among Groups (SSA)

The variation due to differences between group means.

Sum of Squares Within Groups (SSW)

The variation within each group.

F statistic

The ratio of explained variance to unexplained variance in ANOVA.

Significance level

The probability of rejecting the null hypothesis when it is actually true, typically set at 0.05.

Assumptions of ANOVA

Conditions that must be met for the results of ANOVA to be considered valid.

Kruskal-Wallis test

A non-parametric method for testing whether samples originate from the same distribution.

Post-hoc test

Tests conducted after ANOVA to determine which means are different.

Cell means plot

A graphical representation of means for different groups in a factorial design.

Statistically significant

An observed effect or relationship that is unlikely to be due to chance.

Interaction plot

A graphical representation used to visualize the interaction between two factors.

Two-Way ANOVA

An extension of One-Way ANOVA that evaluates the influence of two different categorical independent variables on one dependent variable.

Main effect

The direct effect of an independent variable on the dependent variable.

Replication

Repetition of experiments to verify results.

Independent random samples

Samples selected such that the selection of one does not affect the selection of another.

Experimental design

The plan for a controlled experiment, including how to collect data.

Null hypothesis for One-Way ANOVA

All population means are equal.

Alternate hypothesis for One-Way ANOVA

At least one population mean is different from the others.

Assumption of equal variances

All groups in the ANOVA have the same variance.

Critical range

The range used to determine whether the differences between means are statistically significant.

Confidence interval

A range of values that is likely to contain the population parameter with a specified level of confidence.

Interaction effect significance

Determines if the effect of one factor depends on the level of another factor.

Interaction variation

The variability in the dependent variable that is explained by the interaction between factors in a two-way ANOVA.

Estimation of variance

The process of using data to calculate the variation of a population.

Residuals

The differences between observed values and predicted values from a statistical model.

Type I error

The incorrect rejection of a true null hypothesis.

Type II error

The failure to reject a false null hypothesis.

Tukey's HSD

A test for comparing the means of multiple groups following ANOVA.

Scatter plot

A graph that displays values for typically two variables for a set of data.

Variance

A measure of how far a set of numbers are spread out from their average value.

Normality assumption

The assumption that the data follows a normal distribution when using ANOVA.

Significance test

A statistical test to determine if there is enough evidence to support a specific hypothesis.

Statistical power

The probability of correctly rejecting the null hypothesis when it is false.

Non-parallel line segments

Indicates significant interaction effects in a graphical representation.

Boxplot

A graphical representation of data that shows the distribution, central tendency, and variability.

One-way ANOVA example

Example comparing means of different groups to determine if they are significantly different.

Experimental units

The smallest division of experimental material where the treatment is applied.

F test for interaction effect

Used to determine if the interaction between two factors is statistically significant.

ANOVA output

The results produced from performing an ANOVA analysis, including F values and p-values.

Effect size

A quantitative measure of the magnitude of the experimental effect.

Response variable

The variable that is measured in an experiment and is expected to change as a result of changes in the independent variable.

Influence of factors

The impact that specific factors have on the dependent variable under study.

Cell means

The means calculated for each cell (combination) of factors in a factorial design.

Statistical software

Computer programs used for statistical analysis.

Data transformation

The process of converting data into a different format or structure to meet assumptions.

ANOVA assumptions

Conditions that must be fulfilled in order to perform an ANOVA correctly.