Refer to Example 8.1. a. For the model yi j=μ++εi j, what are the values of t, n1, n2, and n3 ?

Step 1: Identify the values of u005C( t, n_1, n_2, u005C) and u005C( n_3 u005C) for the model u005C( y_{ij} u003D u005Cmu +

Question

Refer to Example 8.1. a. For the model $y_{i j}=\mu+\tau_i+\varepsilon_{i j}$, what are the values of $t, n_1, n_2$, and $n_3$ ? b. Using the observed data, provide estimates of $\mu, \tau_1, \tau_2, \tau_3$, and $\sigma$ without the constraint $\tau_3=0$. c. Using the observed data, provide estimates of $\mu, \tau_1, \tau_2, \tau_3$, and $\sigma$ with the constraint $\tau_3=0$. d. Compare the differences in the two sets of estimates produced in parts (b) and (c). This illustrates the importance of knowing what constraints are imposed by software programs when estimates are contained in the output of an analysis.

   Refer to Example 8.1.
a. For the model $y_{i j}=\mu+\tau_i+\varepsilon_{i j}$, what are the values of $t, n_1, n_2$, and $n_3$ ?
b. Using the observed data, provide estimates of $\mu, \tau_1, \tau_2, \tau_3$, and $\sigma$ without the constraint $\tau_3=0$.
c. Using the observed data, provide estimates of $\mu, \tau_1, \tau_2, \tau_3$, and $\sigma$ with the constraint $\tau_3=0$.
d. Compare the differences in the two sets of estimates produced in parts (b) and (c). This illustrates the importance of knowing what constraints are imposed by software programs when estimates are contained in the output of an analysis.

An Introduction to Statistical Methods and Data Analysis

R. Lyman Ott,… 7th Edition

Chapter 8, Problem 9

Instant Answer

Step 1

Here, $ t $ represents the number of treatment groups, and $ n_i $ represents the number of observations in each treatment group. Based on the context of Example 8.1, determine the number of treatment groups and the number of observations in each group. Show more…

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Refer to Example 8.1. a. For the model $y_{i j}=\mu+\tau_i+\varepsilon_{i j}$, what are the values of $t, n_1, n_2$, and $n_3$ ? b. Using the observed data, provide estimates of $\mu, \tau_1, \tau_2, \tau_3$, and $\sigma$ without the constraint $\tau_3=0$. c. Using the observed data, provide estimates of $\mu, \tau_1, \tau_2, \tau_3$, and $\sigma$ with the constraint $\tau_3=0$. d. Compare the differences in the two sets of estimates produced in parts (b) and (c). This illustrates the importance of knowing what constraints are imposed by software programs when estimates are contained in the output of an analysis.

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