(b) Use Fisher's LSD procedure to test whether there is a significant difference between the means for treatments A and B, treatments A and C, and treatments B and C. Use a = 0.05. A hypothesis test for the population of treatment means can lead to the conclusion that not all the population means are equal, but it does not indicate which population means may differ. Fisher's least significant difference, LSD, procedure can be used to pinpoint where these differences occur. The test statistic will be calculated as the absolute value of the difference between two sample means, ,-,. This test statistic will be compared to the value of LSD, the formula of which given below. The variableta/2 is based on a t distribution with n--k degrees of freedom with a significance level of a, MSE is the mean square error, n, is the number of observations for population i, and n, is the number of observations for population j. LSD = ₁/2 √MSE (2+1) d A significance level of a = 0.05 was specified, so = 0.025 ta/2=0.490233 x This will be the upper tail area of the t distribution with n, - k= 12 degrees of freedom. Use technology to find t/2 rounding the result to three decimal places.
(b) Use Fisher's LSD procedure to test whether there is a significant difference between the means for treatments A and B, treatments A and C, and treatments B and C. Use a = 0.05. A hypothesis test for the population of treatment means can lead to the conclusion that not all the population means are equal, but it does not indicate which population means may differ. Fisher's least significant difference, LSD, procedure can be used to pinpoint where these differences occur. The test statistic will be calculated as the absolute value of the difference between two sample means, ,-,. This test statistic will be compared to the value of LSD, the formula of which given below. The variableta/2 is based on a t distribution with n--k degrees of freedom with a significance level of a, MSE is the mean square error, n, is the number of observations for population i, and n, is the number of observations for population j. LSD = ₁/2 √MSE (2+1) d A significance level of a = 0.05 was specified, so = 0.025 ta/2=0.490233 x This will be the upper tail area of the t distribution with n, - k= 12 degrees of freedom. Use technology to find t/2 rounding the result to three decimal places.
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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Question
![Step 9
(b) Use Fisher's LSD procedure to test whether there is a significant difference between the means for treatments A and B, treatments A and C, and treatments B and C. Use α = 0.05.
A hypothesis test for the population of treatment means can lead to the conclusion that not all the population means are equal, but it does not indicate which population means may differ. Fisher's least significant difference, LSD, procedure can be used to
pinpoint where these differences occur.
The test statistic will be calculated as the absolute value of the difference between two sample means, x₁ - x;. This test statistic will be compared to the value of LSD, the formula of which is given below. The variable t/2 is based on a t distribution with
n, - k degrees of freedom with a significance level of a, MSE is the mean square error, n, is the number of observations for population i, and n, is the number of observations for population j.
/ MSE (171, + 121,)
LSD = ta/2V
A significance level of a = 0.05 was specified, so
ta/2 = 490233
X
= 0.025
. This will be the upper tail area of the t distribution with n - k = 12 degrees of freedom. Use technology to find t/2/ rounding the result to three decimal places.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff7b76bbb-1122-4c75-9c9e-2038b7c47d4e%2F091ec978-c3b5-4f16-8c38-aac3c70bcfc4%2F2bqs7k8_processed.png&w=3840&q=75)
Transcribed Image Text:Step 9
(b) Use Fisher's LSD procedure to test whether there is a significant difference between the means for treatments A and B, treatments A and C, and treatments B and C. Use α = 0.05.
A hypothesis test for the population of treatment means can lead to the conclusion that not all the population means are equal, but it does not indicate which population means may differ. Fisher's least significant difference, LSD, procedure can be used to
pinpoint where these differences occur.
The test statistic will be calculated as the absolute value of the difference between two sample means, x₁ - x;. This test statistic will be compared to the value of LSD, the formula of which is given below. The variable t/2 is based on a t distribution with
n, - k degrees of freedom with a significance level of a, MSE is the mean square error, n, is the number of observations for population i, and n, is the number of observations for population j.
/ MSE (171, + 121,)
LSD = ta/2V
A significance level of a = 0.05 was specified, so
ta/2 = 490233
X
= 0.025
. This will be the upper tail area of the t distribution with n - k = 12 degrees of freedom. Use technology to find t/2/ rounding the result to three decimal places.
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