Why is my mean difference calcuation wrong? % 8.8 Main % Consider table 8.25. As

Question

Why is my mean difference calcuation wrong?

% 8.8 Main

% Consider table 8.25. Assuming 2 scenarios:

% 1) All the data in table comprise 1 set denoted by S_0 and

% 2) the data in each of the 5 pairs of columns represent 5 different sets

% denoted by S_j, j = 1,2,...5

% a) Determine harmonic mean of S_0 and compare to mean and geometric mean.

% Use harmmean

% b) Find mean values and standard dev. of the 6 sets. S_j; j = 0,1,...5

% c) Display vertical box plot of S_j; j = 1,2,...5

% d) Determine confidence limits on the values of S_0 and each S_j using

% 95% confidence. Assume standard dev. unknown but =.

% i) What are the p-values for ech data set?

% ii) Are any mean values statistically different from mean (S_0)?

% iii) Do these conclusions agree with results displayed in (c)?

% -------------------------------------------------------------------------

close all

clear variables

clc

% -------------------------------------------------------------------------

data = [1115, 1310, 1540, 1502, 1258, 1315, 1085, 1567, 1883, 1203, 1270,...

1015, 845, 1674;

1223, 375, 2265, 1910, 1018, 1452, 1890, 1782, 1522, 1792, 1000,...

1820, 1940, 1120;

1055, 1764, 1330, 1608, 1535, 1781, 1750, 798, 1020, 865, 2130,...

1421, 1109, 1481;

1016, 1102, 1605, 706, 2215, 785, 885, 2100, 1594, 2023, 1315,...

1269, 1260, 1888;

910, 1730, 1102, 1578, 758, 1416, 1560, 1501, 1238, 990, 1468,...

1512, 1750, 1642];

S_0 = [data(1,:), data(2,:), data(3,:), data(4,:), data(5,:)];

% Calculate and display a) b) d)

CalculateAndDisplay (data, S_0);

function[] = CalculateAndDisplay (data, S_0)

% calculate and display a)

disp(['Set #0: Geometric mean = ' num2str(geomean(S_0))]);

disp([' Harmonic mean = ' num2str(harmmean(S_0))]);

disp(' ');

% calculate and display b)

xbar = mean(S_0);

Variance = var(S_0);

alpha = (1-.95)/2;

disp(['Set #0: Mean = ', num2str(xbar), ' Std. Dev. = ',...

num2str(sqrt(Variance))]);

LengthS0 = length(S_0);

LengthEachSet = LengthS0/5;

for set = 1:5

Mean = mean(data(set,:));

MeanDifference = mean(data(set,:));

StdDev = std(data(set,:));

disp(['Set #', int2str(set), ': Mean = ', num2str(Mean),...

' Std. Dev. = ', num2str(StdDev)]);

[null(set), prob(set), ci(set,:)] = ttest2(S_0, data(set,:), alpha);

MeanDifference(set) = xbar-Mean;

end

disp(' ');

% calculate and display d)

for set = 1:5

disp(['Set #', num2str(set), ': Lower limit = ', num2str(ci(set,1)),...

' Upper limit = ', num2str(ci(set,2)), ' Mean difference = ',...

num2str(MeanDifference(set)), ' P-value = ', num2str(prob(set))]);

end

end

% plot c)

boxplot_data(data);

% -------------------------------------------------------------------------

% Output

Explanation / Answer

MeanDifference = mean(data(set,:));   

above statement should be removed from for loop because it makes MeanDifference as 1x1 matrix

code should be modified as :-

for set = 1:5
Mean = mean(data(set,:));

StdDev = std(data(set,:));

disp(['Set #', int2str(set), ': Mean = ', num2str(Mean),...

' Std. Dev. = ', num2str(StdDev)]);

[null(set), prob(set), ci(set,:)] = ttest2(S_0, data(set,:), alpha);

MeanDifference(set) = xbar-Mean;
end

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