Peirce's method

Applies Peirce's method for outlier rejection

Description

One of several approaches to outlier rejection, Peirce's method is more general than Chauvenet's method.

As constructed this works on univariate data only.

• MATLAB release: MATLAB 7.6 (R2008a)

[MarC .]

Here is some code that uses the fxn. Copy and paste-able.

% generate random data:

pop_mean = 20;
pop_sd = 2;

% 1) to see how method works on random samples drawn from a normal distribution, use
% this dataset
sample_data1 = pop_mean + pop_sd*randn(1, 25);

% 2) to see how method works on random data that has built-in tendency to
% include outliers, use this method
sample_data2 = pop_mean + pop_sd*randn(1, 20);
% add in 1-4 obs of potentially outlying data
funny_data1 = pop_mean + 2*pop_sd + 3*pop_sd*rand(1, 2 + round(rand(1)));
funny_data2 = pop_mean + 4*pop_sd*randn(1,4);

sample_data2 = [sample_data2 funny_data2];

% 3) Ross example data; contains 2 points which will be rejected by Peirce's
% method

Ross_data = [101.2, 90.0, 99.0, 102.0, 103.0, 100.2, 89.0, 98.1, 101.5, 102.0];
    
% pick which dataset should be used

%mydata = Ross_data;
mydata = sample_data2;

% shuffle data, for the fun of it
mydata = mydata(randperm(length(mydata)));

% apply peirce criterion

[cleaned_data outlier_data] = apply_peirce(mydata);

% prep data for display

% make filter -- to help with display purposes -- (might want to make this
% part of apply_peirce.m)
pass_peirce = zeros(size(mydata));
for j=1:length(cleaned_data)
   pass_peirce = pass_peirce | mydata == cleaned_data(j);
end

obs_index = 1:length(mydata);

% plot data (kept == blue circles) and outliers (red x's)

figure(1);

plot(obs_index, mydata, '.k');
hold on;
plot(obs_index(pass_peirce), mydata(pass_peirce), 'ob', 'MarkerSize', 10);
plot(obs_index(~pass_peirce), mydata(~pass_peirce), 'xr', 'MarkerSize', 15);
hold off;

set(gca, 'XLim', [0 length(mydata)+1]);
set(gca, 'YLim', [min(mydata)-1 max(mydata)+1]);

xlabel('Observation Index');
ylabel('Variable of Interest');

title('Sample Data as Categorized by Peirce Criterion')
legend('datapoint', 'included', 'outlier', 'Location', 'SouthOutside')

[David Reed]

Hi Marc,

Just thought you should know that your code fails to define n_ind if the original data is over 60.

Other than that its a great function.