MATLAB QUESTION Age Group (years) Ages 0–11: 17.2 18.4 17.9 16.6 19.0 18.3 13.6

Question

MATLAB QUESTION

Age Group (years)

Ages 0–11: 17.2 18.4 17.9 16.6 19.0 18.3 13.6 13.5 18.5 19.1 19.1 13.4

Ages 12–24: 14.8 17.6 18.3 17.2 10.0 11.3 10.2 17.0 18.9 19.2

Ages 25–45: 18.4 13.0 14.8 18.4 12.8 17.6 18.8 17.9 18.5 17.5 18.3 15.2 10.8 19.8 17.3 19.2 15.4 13.2

Ages 46+: 15.5 18.2 12.7 15.1 18.2 18.0 14.4 10.2 16.7

Using MATLAB, Use the Tukey-Kramer method to construct confidence intervals for all pair-wise comparison’s of the groups. (Please no R, need matlab.) (please outline your code as well).

Explanation / Answer

Solution ::

Tukey's Method ::
Tukey's method consider the all possible pairwise differences of means at same time.

Tukey method applies parallelly to the set of all the pairwise comparisons {ij}.

Confidence coefficient for the set where all sample sizes are equal is exactly (1). For the unequal sample sizes,confidence coefficient is greater than the (1).

Studentized Range Distribution :

Studentized range q :  
Tukey's method uses studentized range of distribution. Suppose we have the 'r' independent observations y1,…,yr from a normal distribution with the mean & the

variance 2. Let 'w' be the range for the set ,that is the maximum minus the minimum. Suppose that we have estimate s2 of variance 2 which is based on the '' degrees

of freedom & is independent of yi. Studentized range is defined as the
qr,=w/s

Example, let r = 5 & = 10. The 95th percentile is q0.05;5,10 = 4.65 means
P {w/s4.65}=0.95.
That's why if we have the five observations from normal distribution, the probability is 0.95 that their range is not more than the 4.65 times as great as independent

sample standard deviation estimate for which estimator has the 10 degrees of the freedom.

Tukey's Method :
Confidence limits for the Tukey's method :
Tukey confidence limits for all the pairwise comparisons with the confidence coefficient of at least (1) are :

y'iy'j± (1/(2)^1/2)q;
r,Nr^ (2/n)^1/2 where i,j=1,…,r;ij

Set of all the pairwise comparisons :
The set of all the pairwise comparisons consists of
21,31,14,23,24,34.

Syntax for the multi comparision test ::

c = multcompare(stats)
c = multcompare(stats,Name,Value)
[c,m] = multcompare(___)
[c,m,h] = multcompare(___)
[c,m,h,gnames] = multcompare(___)

Explanation :
-> c = multcompare(stats) returns the matrix c of the pairwise comparison results from multiple comparison test using information contained in stats structure.
-> c = multcompare(stats,Name,Value) returns the matrix of the pairwise comparison results, c, using the additional options specified by the one (or) more Name,Value   

pair arguments.
-> [c,m] = multcompare(___) also returns the matrix, m, which contains estimated values of the means for each group and the corresponding standard errors.
-> [c,m,h] = multcompare(___) also returns the handle, h, to comparison the graph.
-> [c,m,h,gnames] = multcompare(___) also returns cell array, gnames, which contains names of the groups.

/// *** Thank You *** ///

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