LECTURE 4: ANALYSIS OF VARIANCE

Created by James Tero

is a name for a collection of statistical models and methods that deal with whether or not the variable means differ significantly across observation groups.

Analysis of Variance (ANOVA)

is a statistical method that permits one to make an interpretive statement about overall differences among the means for the groups of observations.

Analysis of Variance (ANOVA)

The ANOVA technique enable us to perform the simultaneous test and as such is considered to be an important __________ in the hands of a researcher.

tool of analysis

ANOVA can be used to test differences among several means for significance without increasing the _________ rate

Type 1 error

This technique is important in the context of all those situations where we want to compare more than two populations.

ANOVA

In _____, such circumstances. we do not want to consider all possible combinations of two populations at a time for that would require a great number of test before we would be able to arrive at a decision

ANOVA

The essence of ANOVA is that the total amount of variation in a set of data is broken down into ______ types

two

The essence of ANOVA is that the total amount of variation in a set of data is broken down into two types, that amount which can be attributed to ______ and that amount which can be attributed to _____

chance, specified causes

The basic principle of ANOVA is to test for differences among the _______ of the populations by examining the amount of ______ within each of these samples, relative to the amount of variation between the samples.

means, variation

In ANOVA, we do an assumption that the ________of data are normally distributed.

experimental errors

In ANOVA, we do an assumption that there are _____ variances between treatments.

equal

In ANOVA, we do an assumption that each _____ is randomly selected and independent.

sample

The purpose of a one-way ANOVA test is to determine the existence of a statistically significant _______ among several group means.

difference

In one-way ANOVA, the test actually uses ______ to help determine if the means are equal or not.

variances

In this analysis, each individual or case must have scores on two variables: a factor and a dependent variable.

one-way ANOVA

In one-way ANOVA, a ____ divides individuals into two or more groups or levels,

factor

In one-way ANOVA, a ____ differentiates individuals on some quantitative dimension.

dependent variables

The One-way: Single Factor from Excel Data Analysis was used to calculate the _____

F-test statistic

If the p-value is lower than the set alpha value, then the mean number is ________ on the other dependent variable of factors

significantly different

tells us that at least one group is different from each other.

one-way ANOVA

Cons of one-way ANOVA

It won’t tell us which groups are different.

There are various methods to conduct the post-hoc test namely:

Bonferroni approach, Least significant difference test, Tukey’s HSD, Dunnett’s C, etc.

If our test returns a significant F-statistic, we may need to run a _______ to tell us exactly which groups have difference means.

post-hoc test

We use t-test: assuming unequal variances if the given data has ____ than 2 of its ratio between largest variance / smallest variance. This means that variaces are not close to each other

more

We use t-test: assuming equal variances if the given data has ____ than 2 of its ratio between largest variance / smallest variance. This means that variances are approximately close or equal to each other (homogeneous)

less