Presbycusis is the gradual hearing loss that occurs as a person ages. An estimated one-quarter of Americans between the ages of 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. The third group receives cochlear implants. The results come in, and a statistician conducts an analysis of variance. The is that there is no difference between the population means (in other words, there is no treatment effect). The 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). Note: The term “treatment effect” is used even when there is not actually a treatment. The hearing aid type is . The treatments (analog hearing aids, digital hearing aids, and cochlear implants) are . Which of the following might contribute to between-treatments variance? Check all that apply. Systematic differences in the efficacy of the different types of hearing aids Individual differences in a person’s response to hearing aid type Systematic differences in the amplitude of voices heard through different types of hearing aids

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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2. Terms and logic of ANOVA

Presbycusis is the gradual hearing loss that occurs as a person ages. An estimated one-quarter of Americans between the ages of 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. The third group receives cochlear implants. The results come in, and a statistician conducts an analysis of variance.

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

The 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).

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

The hearing aid type is .

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

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

Systematic differences in the efficacy of the different types of hearing aids

Individual differences in a person’s response to hearing aid type

Systematic differences in the amplitude of voices heard through different types of hearing aids

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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