Recent revenue shortfalls in a midwestern state led to a reduction in the state budget for higher education. To offset the reduction, the largest state university proposed a 25% tuition increase. It was determined that such an increase was needed simply to compensate for the lost support from the state. Separate random samples of 50 freshmen, 50 sophomores, 50 juniors, and 50 seniors from the university were asked whether they were strongly opposed to the increase, given that it was the minimum increase necessary to maintain the university's budget at current levels. The results are in the table provided. Why hypotheses would be appropriate for performing a chi-square test?

The null hypothesis is that the distribution of student opinion about the proposed tuition increase is the same for each of the 4 years at the university. The alternative is that the distribution is different for at least 2 of the 4 years.

The null hypothesis is that the closer students get to graduation, the less likely they are to be opposed to tuition increases. The alternative is that how close students are to graduation makes no difference in their opinion.

The null hypothesis is that the mean number of students who are strongly are opposed is the same for each of the 4 years. The alternative is that the mean is different for at least 2 of the 4 years.

The null hypothesis is that year in school and student opinion about the tuition increase in the sample are independent. The alternative is that these variables are dependent.

If the F-ratio is large, what does that suggest?

There’s likely a real difference between groups

There’s little difference between groups

What does the F-ratio represent in ANOVA?

The ratio of between-group variance to within-group variance

The ratio of total variance to sample size

The difference between the highest and lowest means

When can ANOVA give misleading results?

When assumptions like normality or equal variances are violated

Why not just run multiple t-tests instead of ANOVA?

Because running many t-tests increases the chance of Type I error

Because t-tests can’t compare means

Because t-tests require larger samples

Intro to ANOVA

Authored by Maci DeMott

Mathematics

University

CCSS covered

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What kind of variable does the independent variable have to be?

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What kind of variable does the dependent variable have to be?

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How does ANOVA figure out if groups are different?

It checks whether all groups have identical means

It compares variance between and within groups

It runs multiple t-tests

It calculates total variance only

ANOVA stands for

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When do we use ANOVA?

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What are the assumptions for ANOVA?

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What is the formula for the F-statistic?

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Intro to ANOVA

What kind of variable does the independent variable have to be?

What kind of variable does the dependent variable have to be?

How does ANOVA figure out if groups are different?

ANOVA stands for

When do we use ANOVA?

What are the assumptions for ANOVA?

What is the formula for the F-statistic?

If you have less variability within groups, would you have less or more between group variability?

If you have less variability between groups, would have have more or less variability within groups?

What is our 'grouping variable'?

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