
%BENKA LAKE GARDEN BAY LAKE BIG LAKE
clear all
close all
  disp('Dorsal Spines')
  set(0, 'DefaultAxesFontSize', 16);
  lw =2.5;  fs = 16;  msize = 10;





stickleback =[...
4.2 4.4 4.9;  ...
4.1 4.6 4.6;  ...
4.2 4.5 4.3;  ...
4.3 4.2 4.9;  ...
4.5 4.4 4.7;  ...
4.4 4.2 4.4;  ...
4.5 4.5 4.5;  ...
4.3 4.7 4.4 ];
lakes = [1 1 1 1 1 1 1 1 ...
2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3];
[p table stats] = anova1(stickleback(:), lakes(:))


% p =    0.0267
% 
% 
% table = 
% 
%     'Source'    'SS'        'df'    'MS'        'F'         'Prob>F'
%     'Groups'    [0.3033]    [ 2]    [0.1517]    [4.3260]    [0.0267]
%     'Error'     [0.7363]    [21]    [0.0351]          []          []
%     'Total'     [1.0396]    [23]          []          []          []
% 
% 
% stats = 
%     gnames: {3x1 cell}
%          n: [8 8 8]
%     source: 'anova1'
%      means: [4.3125 4.4375 4.5875]
%         df: 21
%          s: 0.1872


% (a) Hypothesis $H_0$ stating that the mean lengths of dorsal spines are the same for the three lakes
% is rejected at the level $\alpha = 0.05$ since the $p$-value is 0.0267.
% 
% (b) If the significance level was $\alpha = 0.01$ the hypothesis $H_0$ would not be rejected.




