Formulae Quizzes (use the learn feature): one, two

*T* test

—*t* Table

—*t* value calculator

—**reporting results of repeated-measures t test example**: Changing the background color from white to red increased the attractiveness rating of the woman in the photograph by an average of M = 3.00 points with SD = 1.50. The treatment effect was statistically significant,

*t*

_{(8)}= 6.00,

*p*< .01,

*r*

^{2}= 0.818.

**ANOVA**

—One-way Formulae

—Critical *F* Calculator

**Correlation**

—Pearson Correlation Computational Formula Worksheet

—Pearson Correlation Definitional Formula Worksheet

—Critical Values for Pearson Correlation

**Chi-square**

—Chi-square Critical Values

**Some basic components of the one-way ANOVA**

Presbycusis is the gradual hearing loss that occurs as a person ages. An estimated one-quarter of Americans between the ages or 65 and 75 and three-quarters of those older than 75 have some degree of hearing loss.

An audiologist is interested in the efficacy of three different types of hearing aids. He gathers three groups of hearing-impaired clients: One group receives analog hearing aids, which convert sound waves into amplified electrical signals; the second group receives digital hearing aids, which use directional microphones to control the flow of sound and convert the sound waves into numerical codes before amplifying them; and the third group receives cochlear implants. The results come in, and a statistician conducts an analysis of variance.

The hypothesis is that at least one of the population means is different from another (in other words, there is an effect of at least one of the treatments).

The hypothesis is that there is no difference between the population means (in other words, there is no treatment effect).

Note: The term “treatment effect” is used even when there is not actually a treatment

The treatments (analog hearing aids, digital hearing aids, and cochlear implants) are .

Which of the following might contribute to within-treatments variance? Check all that apply.

Systematic differences in the efficacy of the different types of hearing aids Systematic differences in the amplitude of voices heard through different types of hearing aids Individual differences in the severity of hearing lossThe

*within-treatments variance*provides a measure of how much difference is reasonable to expect from random and unsystematic factors. In particular, the within-treatments variance measures the naturally occurring differences that exist when there is no treatment effect.

The

*within-treatments variance*provides a measure of how much difference is reasonable to expect from random and unsystematic factors. In particular, the within-treatments variance measures the naturally occurring differences that exist when there is no treatment effect.

The

*within-treatments variance*provides a measure of how much difference is reasonable to expect from random and unsystematic factors. In particular, the within-treatments variance measures the naturally occurring differences that exist when there is no treatment effect.