Answered: Twenty-two young asthmatic volunteers…

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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Twenty-two young asthmatic volunteers were studied to assess the short-term effects of sulfur dioxide (SO₂) exposure under various conditions [12]. The baseline data in Table 12.30 were presented regarding bronchial reactivity to SO₂ stratified by lung function (as defined by forced expiratory volume / forced vital capacity [FEV₁/FVC]) at screening.

12.6 Test the hypothesis that there is an overall mean difference in bronchial reactivity among the three lung-function groups.

TABLE 12.30 Relationship of bronchial reactivity
to so, (cm H,O/s) grouped by lung
function at screening among
22 asthmatic volunteers
Lung-function group
Group A
FEV /FVC
Group B
FEV,/FVC
75-84%
Group C
FEV,/FVC
2 85%
S74%
20.8
7.5
9.2
4.1
7.5
2.0
30.0
11.9
2.5
24.7
4.5
6.1
13.8
3.1
7.5
8.0
4.7
28.1
10.3
10.0
5.1
2.2
Source: Based on the American Review of Respiratory Disease, 131(2),
221-225, 1985.

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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