How to Perform One-Way ANOVA for Hepatocyte Data Across Mice Using MATLAB?
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Hi everyone,
I have an Excel file containing data across three sheets: `CM1`, `CM2`, and `CM3`, representing three different mice from the same experimental group. Each sheet has measurements of hepatocytes taken at 12 different locations (labeled `C1` to `C12`). The data for these locations is spread across rows `A1:A73` in each sheet.
For each of the hepatocyte locations, I want to perform a one-way ANOVA to compare the measurements between the three mice. The variables of interest are listed in columns `B1:AQ1` (e.g., size, circularity, etc.).
What I need:
- A MATLAB code that performs a one-way ANOVA for each variable at each hepatocyte location (`C1` to `C12`).
- The code should compare the data from the same hepatocyte location across the three mice (i.e., compare `C1` from `CM1` with `C1` from `CM2` and `CM3`, and so on).
- Output the results, including which variables show significant differences between the mice (biologically variant) and which remain consistent across all three mice.
I have tried to do this and output something twice but the results I am gettting don't make sense and I am not a long time coder so I would like another opinion.
Thank you in advance!
10 comentarios
Star Strider
el 18 de Oct. de 2024
Editada: Star Strider
el 18 de Oct. de 2024
There are six instances of ‘C1’ through ‘C12’ in each sheet. (All the sheets appear to be the same size and have the same formats.)
How do you want to analyse these data?
The Statistics and Machine Learning Toolbox has several ANOVA functions, as well as the multcompare function. There are several different multcompare functions. I linked to one of them here.
Anyway, importing the data is straightforward —
SN = sheetnames('NEWSHEETUpdate.xlsx');
for k = 1:3
Sheet="CM"+k
MHD{k} = readtable("NEWSHEETUpdate.xlsx", VariableNamingRule="preserve", Sheet="CM"+k); % Mouse Hepatocyte Data For Each Sheet
ArraySize = size(MHD{k})
disp(MHD{k})
end
.
Isabella
el 18 de Oct. de 2024
My pleasure.
It appears tthat you are calculating over the data and the statistics of the data. The statistics appear to include derived data such as skewness and curtosis.
type('onewayanova.m')
type('onewayanova2.m')
I cannot understand what you want to do from reading your code.
It could help if you describe in some detail what you want to do, and what elements of your data you want to analyse.
There are others here who understand these statistical approaches better than I do, and may be able to help you with them.
Also, consider nonparametric tests, since I tend to doubt that any physiological data are normally distributed. (In my experience, they are always lognormally-distributed.)
.
Isabella
el 18 de Oct. de 2024
I admit to being lost.
This is my approach for analysing ‘totalArea’ for ‘C1’ across the three mice using the friedman function —
SN = sheetnames('NEWSHEETUpdate.xlsx');
for k = 1:3
Sheet="CM"+k
MHD{k} = readtable("NEWSHEETUpdate.xlsx", VariableNamingRule="preserve", Sheet="CM"+k); % Mouse Hepatocyte Data For Each Sheet
% ArraySize = size(MHD{k})
% disp(MHD{k})
end
C1mtx = [MHD{1}.totalArea(1:12:end) MHD{2}.totalArea(1:12:end) MHD{3}.totalArea(1:12:end)]
[pC1,ResultC1,SC1] = friedman(C1mtx,1)
figure
boxplot(C1mtx)
xlabel('Mouse #')
ylabel('totalArea')
title('C1 Across Mice')
The ‘totalArea’ value (or other similar variables, those being essentially ‘raw’ data rather than ‘derived’ data such as the mean) would, at least in my view, be most appropriate.
NOTE — Happily, the p value is significant!
.
Isabella
el 18 de Oct. de 2024
Star Strider
el 18 de Oct. de 2024
I would not use derived data (mean, median, variance, standard deviation and the rest). I would instead go with the essentially raw data such as ‘counts’ and ‘area’ since those are the actual data. The mean gives undue weighting to extreme values. The median does not, however neither expresses the data distribution (variance and the others have the same problem as the mean since they use it), and that is what is necessary here. Determining the skewness and kurtosis do not correct for that.
In order to do the sort of analysis I did, you would simply have to loop through all the variables and row names you want to test. That would be relatively easy. See Access Data in Tables for details.
I would first consult a biostatistician to determine that this is the correct approach and the correct procedure before programming it.
I am not posting this as an Answer beecause it isn’t one. An Answer solves the problem. Here I am simply presenting an approach to solving it, with no certainty that it is appropriate. If it turns out to be the solution, I will move it to an Answer so you can Accept it as one.
Isabella
el 18 de Oct. de 2024
Respuesta aceptada
Here it goes —
SN = sheetnames('NEWSHEETUpdate.xlsx');
for k = 1:3
Sheet="CM"+k
MHD{k} = readtable("NEWSHEETUpdate.xlsx", VariableNamingRule="preserve", Sheet="CM"+k); % Mouse Hepatocyte Data For Each Sheet
% ArraySize = size(MHD{k})
% disp(MHD{k})
end
VN = MHD{1}.Properties.VariableNames;
Sel = [2 3 5];
VNSel = VN(Sel)
RN = MHD{1}{:,1};
[RNu,~,uidx] = unique(RN, 'stable');
for k1 = 1:numel(VNSel)
for k2 = 1:12
disp("Variable: "+k1+", Variable name: "+VNSel(k1)+", Row name: "+RNu{k2})
RowIdx = (1:12)+(k2-1);
RowMtx = [MHD{1}{RowIdx,Sel(k1)} MHD{2}{RowIdx,Sel(k1)} MHD{3}{RowIdx,Sel(k1)}];
[p{k1,k2},Result{k1,k2}] = friedman(RowMtx,1);
disp(p{k1})
end
end
return
figure
boxplot(C1mtx)
xlabel('Mouse #')
ylabel('totalArea')
title('C1 Across Mice')
This appears to work, and the results are promising. Expand the number of variables as necessary. To do that, add thier subscripts to this vector:
Sel = [2 3 5];
Bear in mind that statistics is not my area of expertise, so I cannot assure you that this is the correct statistical approach. .
.
32 comentarios
Isabella
el 19 de Oct. de 2024
As always, my pleasure!
You can change my code to use whatever variables you want to analyse —
imshow(imread('IMG_4837.jpeg'))
.
Isabella
el 19 de Oct. de 2024
I had to tweak your code a bit to get it to run, since some lines should have been comments and were not.
I again caution against using derived data such as ‘average’, ‘norm’ or ‘variance’ and such as variables because they are not the actual data.
I would also suggest something similar to:
disp("Variable: "+k1+", Variable name: "+VNSel(k1)+", Row name: "+RNu{k2})
(change it as necessary) that I used, to make the friedman tables easier to interpret, however if you understand the tests you are doing, that is all that is necessary.
Other than these concerns, your results look good.
% % Load the sheet data and variables
% SN = sheetnames('NEWSHEETUpdate.xlsx');
% for k = 1:3
% Sheet = "CM" + k;
% MHD{k} = readtable("NEWSHEETUpdate.xlsx", VariableNamingRule="preserve", Sheet=Sheet); % Mouse Hepatocyte Data For Each Sheet
% end
%
% % Variable and row selection
% VN = MHD{1}.Properties.VariableNames;
% Sel = [4 6 7 8 12 14 15]; % Selected variables by column index
% VNSel = VN(Sel);
% RN = MHD{1}{:, 1};
% [RNu, ~, uidx] = unique(RN, 'stable');
%
% % Initialize matrices to store results
% numVariables = numel(VNSel);
% numLocations = 12;
% p_values = NaN(numVariables, numLocations);
% posthoc_results = cell(numVariables, numLocations);
%
% % Loop through each selected variable and each row (hepatocyte location)
% for k1 = 1:numVariables
% for k2 = 1:numLocations
% % Extract data for the current variable and location across the mice
% RowIdx = (1:12) + (k2 - 1);
% RowMtx = [MHD{1}{RowIdx, Sel(k1)}, MHD{2}{RowIdx, Sel(k1)}, MHD{3}{RowIdx, Sel(k1)}];
%
% % Perform Friedman's test
% [p_values(k1, k2), tbl, stats] = friedman(RowMtx, 1);
%
% % Perform post-hoc analysis if the p-value is significant
% if p_values(k1, k2) < 0.05
% multResults = multcompare(stats, 'CType', 'bonferroni'); % Post-hoc test with Bonferroni correction
% % Store pairwise comparisons results in a cell array
% sigComparisons = multResults(multResults(:,6) < 0.05, [1, 2]);
% posthoc_results{k1, k2} = arrayfun(@(x) sprintf('CM%d vs CM%d', sigComparisons(x, 1), sigComparisons(x, 2)), 1:size(sigComparisons, 1), 'UniformOutput', false);
% else
% posthoc_results{k1, k2} = {'No significant differences'};
% end
% end
% end
%
% % Create a summary table of p-values and post-hoc results
% SummaryTable = table(VNSel', p_values, posthoc_results, 'VariableNames', {'Variable', 'Friedman_pValues', 'PosthocComparisons'});
%
% % Display the summary table
% disp(SummaryTable);
%
% % Create a heatmap of the p-values
% figure;
% h = heatmap(RNu(1:12), VNSel, p_values, 'Colormap', jet, 'ColorLimits', [0 1], 'MissingDataLabel', 'NaN');
% colorbar;
% title('P-value Heatmap for Friedman Test Across Locations');
% xlabel('Hepatocyte Location (C1-C12)');
% ylabel('Variables');
% set(gca, 'FontSize', 12);
%
% % Save the summary table and p-values to an Excel file
% writetable(SummaryTable, 'ANOVA_Posthoc_Results.xlsx', 'Sheet', 'Summary');
% try
% writematrix(p_values, 'ANOVA_Posthoc_Results.xlsx', 'Sheet', 'P-values');
% fprintf('Results saved to ANOVA_Posthoc_Results.xlsx.\n');
% catch saveErr
% fprintf('Error saving p-values to Excel: %s\n', saveErr.message);
% end
% % Load the sheet data and variables
% SN = sheetnames('NEWSHEETUpdate.xlsx');
% for k = 1:3
% Sheet = "CM" + k;
% MHD{k} = readtable("NEWSHEETUpdate.xlsx", VariableNamingRule="preserve", Sheet=Sheet); % Mouse Hepatocyte Data For Each Sheet
% end
%
% % Variable and row selection
% VN = MHD{1}.Properties.VariableNames;
% Sel = [4 6 7 8 12 14 15]; % Selected variables by column index
% VNSel = VN(Sel);
% RN = MHD{1}{:, 1};
% [RNu, ~, uidx] = unique(RN, 'stable');
%
% % Initialize matrices to store results
% numVariables = numel(VNSel);
% numLocations = 12;
% p_values = NaN(numVariables, numLocations);
% posthoc_summary = strings(numVariables, numLocations); % Store summary of pairwise differences
%
% % Loop through each selected variable and each row (hepatocyte location)
% for k1 = 1:numVariables
% for k2 = 1:numLocations
% % Extract data for the current variable and location across the mice
% RowIdx = (1:12) + (k2 - 1);
% RowMtx = [MHD{1}{RowIdx, Sel(k1)}, MHD{2}{RowIdx, Sel(k1)}, MHD{3}{RowIdx, Sel(k1)}];
%
% % Perform Friedman's test
% [p_values(k1, k2), tbl, stats] = friedman(RowMtx, 1);
%
% % Perform post-hoc analysis if the p-value is significant
% if p_values(k1, k2) < 0.05
% multResults = multcompare(stats, 'CType', 'bonferroni'); % Post-hoc test with Bonferroni correction
% % Store significant pairwise comparisons as strings
% sigComparisons = multResults(multResults(:, 6) < 0.05, [1, 2]);
% if ~isempty(sigComparisons)
% pairs = arrayfun(@(x) sprintf('CM%d vs CM%d', sigComparisons(x, 1), sigComparisons(x, 2)), 1:size(sigComparisons, 1), 'UniformOutput', false);
% posthoc_summary(k1, k2) = strjoin(pairs, ', ');
% else
% posthoc_summary(k1, k2) = "No significant differences";
% end
% else
% posthoc_summary(k1, k2) = "No significant differences";
% end
% end
% end
%
% % Create a summary table of p-values and post-hoc results
% SummaryTable = table(VNSel', p_values, posthoc_summary, 'VariableNames', {'Variable', 'Friedman_pValues', 'PosthocComparisons'});
%
% % Display the summary table
% disp(SummaryTable);
%
% % Save the summary table to an Excel file
% writetable(SummaryTable, 'ANOVA_Posthoc_Results.xlsx', 'Sheet', 'Summary');
%
% % Create a heatmap of the p-values for overall significance
% figure;
% h = heatmap(RNu(1:12), VNSel, p_values, 'Colormap', jet, 'ColorLimits', [0 1], 'MissingDataLabel', 'NaN');
% colorbar;
% title('Friedman Test P-value Heatmap');
% xlabel('Hepatocyte Location (C1-C12)');
% ylabel('Variables');
% set(gca, 'FontSize', 12);
%
% % Save the heatmap as an image
% saveas(gcf, 'Friedman_pValue_Heatmap.png');
%
% % Save the p-values to the Excel file as well
% try
% writematrix(p_values, 'ANOVA_Posthoc_Results.xlsx', 'Sheet', 'P-values');
% fprintf('Results saved to ANOVA_Posthoc_Results.xlsx and heatmap image.\n');
% catch saveErr
% fprintf('Error saving p-values to Excel: %s\n', saveErr.message);
% end
close all
clear all
% Load the sheet data and variables
SN = sheetnames('NEWSHEETUpdate.xlsx');
for k = 1:3
Sheet = "CM" + k;
MHD{k} = readtable("NEWSHEETUpdate.xlsx", VariableNamingRule="preserve", Sheet=Sheet); % Mouse Hepatocyte Data For Each Sheet
end
% Variable and row selection
VN = MHD{1}.Properties.VariableNames;
Sel = [4 6 7 8 12 14 15]; % Selected variables by column index
VNSel = VN(Sel);
RN = MHD{1}{:, 1};
[RNu, ~, uidx] = unique(RN, 'stable');
% Initialize matrices to store results
numVariables = numel(VNSel);
numLocations = 12;
p_values = NaN(numVariables, numLocations);
significant_pairs = strings(numVariables, numLocations); % Store significant pairwise differences as strings
pairwise_binary = zeros(numVariables, numLocations, 3); % Binary matrix for heatmap (3 comparisons: CM1 vs CM2, CM1 vs CM3, CM2 vs CM3)
% Loop through each selected variable and each row (hepatocyte location)
for k1 = 1:numVariables
for k2 = 1:numLocations
% Extract data for the current variable and location across the mice
RowIdx = (1:12) + (k2 - 1);
RowMtx = [MHD{1}{RowIdx, Sel(k1)}, MHD{2}{RowIdx, Sel(k1)}, MHD{3}{RowIdx, Sel(k1)}];
% Perform Friedman's test
[p_values(k1, k2), tbl, stats] = friedman(RowMtx, 1);
% Perform post-hoc analysis if the p-value is significant
if p_values(k1, k2) < 0.05
% Perform post-hoc test without displaying the plots
multResults = multcompare(stats, 'CType', 'bonferroni', 'Display', 'off'); % Suppress plotting
% Store significant pairwise comparisons
sigComparisons = multResults(multResults(:, 6) < 0.05, [1, 2]);
% Rest of the code...
% % Perform post-hoc analysis if the p-value is significant
% if p_values(k1, k2) < 0.05
% multResults = multcompare(stats, 'CType', 'bonferroni'); % Post-hoc test with Bonferroni correction
% % Store significant pairwise comparisons
% sigComparisons = multResults(multResults(:, 6) < 0.05, [1, 2]);
if ~isempty(sigComparisons)
% Convert significant pairs to readable form and binary matrix for heatmap
pairs = arrayfun(@(x) sprintf('CM%d vs CM%d', sigComparisons(x, 1), sigComparisons(x, 2)), 1:size(sigComparisons, 1), 'UniformOutput', false);
significant_pairs(k1, k2) = strjoin(pairs, ', ');
% Fill the binary matrix for each pair
pairwise_binary(k1, k2, 1) = any(ismember(sigComparisons, [1 2], 'rows')); % CM1 vs CM2
pairwise_binary(k1, k2, 2) = any(ismember(sigComparisons, [1 3], 'rows')); % CM1 vs CM3
pairwise_binary(k1, k2, 3) = any(ismember(sigComparisons, [2 3], 'rows')); % CM2 vs CM3
else
significant_pairs(k1, k2) = "No significant differences";
end
else
significant_pairs(k1, k2) = "No significant differences";
end
end
end
% Create a summary table of significant pairs
SummaryTable = table(VNSel', significant_pairs, 'VariableNames', {'Variable', 'SignificantPairs'});
% Display the summary table
disp(SummaryTable);
% Save the summary table to an Excel file
writetable(SummaryTable, 'ANOVA_Posthoc_Summary.xlsx', 'Sheet', 'Summary');
% Create heatmaps for each pairwise comparison
pair_labels = {'CM1 vs CM2', 'CM1 vs CM3', 'CM2 vs CM3'};
for pair_idx = 1:3
figure;
h = heatmap(RNu(1:12), VNSel, pairwise_binary(:, :, pair_idx), 'Colormap', [1 1 1; 0 0 1], 'ColorbarVisible', 'off');
title(['Significant Differences: ' pair_labels{pair_idx}]);
xlabel('Hepatocyte Location (C1-C12)');
ylabel('Variables');
set(gca, 'FontSize', 12);
% Save each heatmap as an image
saveas(gcf, ['Significant_Differences_' pair_labels{pair_idx} '.png']);
end
% Save the binary matrix to the Excel file
try
for pair_idx = 1:3
writematrix(pairwise_binary(:, :, pair_idx), 'ANOVA_Posthoc_Summary.xlsx', 'Sheet', pair_labels{pair_idx});
end
fprintf('Results saved to ANOVA_Posthoc_Summary.xlsx and heatmap images.\n');
catch saveErr
fprintf('Error saving pairwise results to Excel: %s\n', saveErr.message);
end
.
Isabella
el 19 de Oct. de 2024
Star Strider
el 19 de Oct. de 2024
As always, my pleasure!
That simply makes it eeasier to keep track of the friedman outputs, so that you can be certain of the assignments of their results.
Isabella
el 19 de Oct. de 2024
I do not understand what of your results seem to be improbable (although I do not understand your experimental design).
Also, I added:
disp("Variable: "+k1+", Variable name: "+VNSel(k1)+", Row name: "+RNu{k2})
to make it easier to understand the Friedman’s ANOVA Table results. This gives each table a context.
Also, you are comparing derived values. The median is likely more representative than the mean, since the mean is strongly influenced by extreme values (are all least-square-derived statistical metrics), while the median is not.
I have problems understanding the ‘consistency’ part of your code, specifically what you are analysing. What makes something ‘consistent’?
This actually appears to be appropriate to me.
What were you expecting and what appears to be improbable?
close all
clear all
% Load the sheet data and variables
SN = sheetnames('NEWSHEETUpdate.xlsx');
for k = 1:3
Sheet = "CM" + k;
MHD{k} = readtable("NEWSHEETUpdate.xlsx", VariableNamingRule="preserve", Sheet=Sheet); % Mouse Hepatocyte Data For Each Sheet
end
% Variable and row selection
VN = MHD{1}.Properties.VariableNames;
Sel = [4 6 7 8 12 14 15 18 20 21 22 26 28 29 32 34 35 36 40 42 43]; % Selected variables by column index
VNSel = VN(Sel);
RN = MHD{1}{:, 1};
[RNu, ~, uidx] = unique(RN, 'stable');
% Initialize matrices to store results
numVariables = numel(VNSel);
numLocations = 12;
p_values = NaN(numVariables, numLocations);
significant_pairs = strings(numVariables, numLocations); % Store significant pairwise differences as strings
pairwise_binary = zeros(numVariables, numLocations, 3); % Binary matrix for heatmap (3 comparisons: CM1 vs CM2, CM1 vs CM3, CM2 vs CM3)
consistency_binary = zeros(numVariables, numLocations); % Binary matrix for consistency (0 = consistent, 1 = inconsistent)
% Loop through each selected variable and each row (hepatocyte location)
for k1 = 1:numVariables
for k2 = 1:numLocations
disp("Variable: "+k1+", Variable name: "+VNSel(k1)+", Row name: "+RNu{k2})
% Extract data for the current variable and location across the mice
RowIdx = (1:12) + (k2 - 1);
RowMtx = [MHD{1}{RowIdx, Sel(k1)}, MHD{2}{RowIdx, Sel(k1)}, MHD{3}{RowIdx, Sel(k1)}];
% Perform Friedman's test
[p_values(k1, k2), tbl, stats] = friedman(RowMtx, 1);
% Perform post-hoc analysis if the p-value is significant
if p_values(k1, k2) < 0.05
% Perform post-hoc test without displaying the plots
multResults = multcompare(stats, 'CType', 'bonferroni', 'Display', 'off'); % Suppress plotting
% Store significant pairwise comparisons
sigComparisons = multResults(multResults(:, 6) < 0.05, [1, 2]);
if ~isempty(sigComparisons)
% Convert significant pairs to readable form and binary matrix for heatmap
pairs = arrayfun(@(x) sprintf('CM%d vs CM%d', sigComparisons(x, 1), sigComparisons(x, 2)), 1:size(sigComparisons, 1), 'UniformOutput', false);
significant_pairs(k1, k2) = strjoin(pairs, ', ');
% Fill the binary matrix for each pair
pairwise_binary(k1, k2, 1) = any(ismember(sigComparisons, [1 2], 'rows')); % CM1 vs CM2
pairwise_binary(k1, k2, 2) = any(ismember(sigComparisons, [1 3], 'rows')); % CM1 vs CM3
pairwise_binary(k1, k2, 3) = any(ismember(sigComparisons, [2 3], 'rows')); % CM2 vs CM3
% Mark as inconsistent since there are significant differences
consistency_binary(k1, k2) = 1;
else
significant_pairs(k1, k2) = "No significant differences";
consistency_binary(k1, k2) = 0; % Mark as consistent
end
else
significant_pairs(k1, k2) = "No significant differences";
consistency_binary(k1, k2) = 0; % Mark as consistent
end
end
end
% Calculate overall consistency for each variable across all locations
overall_consistent = all(consistency_binary == 0, 2);
overall_inconsistent = any(consistency_binary == 1, 2);
% Create a binary table summarizing overall consistency
BinarySummaryTable = table(VNSel', overall_consistent, overall_inconsistent, ...
'VariableNames', {'Variable', 'ConsistentAcrossAllLocations', 'InconsistentAcrossAnyLocation'});
% Display the binary summary table
disp(BinarySummaryTable);
% Save the binary summary table to an Excel file
writetable(BinarySummaryTable, 'ANOVA_Consistency_Summary.xlsx', 'Sheet', 'BinarySummary');
% Create a figure to display the summary in a readable format
figure;
hold on;
title('Consistency Summary Across Mice');
axis off; % Turn off the axis for a clean text display
% Construct the text content for display, listing consistent and inconsistent variables
textContent = "Biologically Consistent Variables:\n\n";
for k1 = 1:numVariables
if overall_consistent(k1)
textContent = textContent + sprintf('Variable: %s\n', VNSel{k1});
end
end
textContent = textContent + "\n\nBiologically Inconsistent Variables:\n\n";
for k1 = 1:numVariables
if overall_inconsistent(k1)
textContent = textContent + sprintf('Variable: %s\n', VNSel{k1});
end
end
% Display the text content in the figure
text(0, 0.5, textContent, 'HorizontalAlignment', 'left', 'VerticalAlignment', 'middle', 'FontSize', 10);
hold off;
% Save the list as a text file for reference
fid = fopen('Biologically_Consistency_Summary_List.txt', 'wt');
fprintf(fid, textContent);
fclose(fid);
% Save result
disp('Results saved to ANOVA_Consistency_Summary.xlsx and Biologically_Consistency_Summary_List.txt');
.
Isabella
el 22 de Oct. de 2024
Star Strider
el 23 de Oct. de 2024
I don’t know what ‘W1’ is. I can’t find a reference to it in any of the sheets, or a specific variablee by that name in your posted code, although it would appear to be the sheet. That aiside, whatever is, it must have the same characteristics as the ‘Cell’ because no statistical test permits comparing two different types of data, and have the result make sense.
It appears that:
data = [MHD{1}{RowIdx, Sel(k1)}, MHD{2}{RowIdx, Sel(k1)}, MHD{3}{RowIdx, Sel(k1)}];
is doing the same as:
RowMtx = [MHD{1}{RowIdx,Sel(k1)} MHD{2}{RowIdx,Sel(k1)} MHD{3}{RowIdx,Sel(k1)}];
in my code, so anova1 is appraently getting the same data as friedman did in my code.
So I’m not certain why you’re getting anomalous results with anova1 when friedman produced reasonable results, other than that your data may not be normally distributed, or exhibit some other violation of what anova1 wants (and assumes). The Friedman test makes no such assumptions, other than that the data have the same distribution (whatever it may be).
I’m not certain what the problem may be, other than that anova1 may not be appropriate for your data. That’s the reason I opted for friedman, from what I know about physiological variables.
% Load the sheet data and variables
SN = sheetnames('NEWSHEETUpdate.xlsx');
for k = 1:3
Sheet = "CM" + k;
MHD{k} = readtable("NEWSHEETUpdate.xlsx", VariableNamingRule="preserve", Sheet=Sheet); % Mouse Hepatocyte Data For Each Sheet
end
% Variable and row selection
VN = MHD{1}.Properties.VariableNames;
% Sel = [4 6 7 8 12 14 15 18 20 21 22 26 28 29 32 34 35 36 40 42 43]; % Selected variables by column index
% VNSel = VN(Sel);
% RN = MHD{1}{:, 1};
% [RNu, ~, uidx] = unique(RN, 'stable');
% disp(MHD{1})
% disp(MHD{2})
% disp(MHD{3})
.
Isabella
el 23 de Oct. de 2024
It’s difficult for me to follow what you’re doing. When I run my original code with the new file, everything still looks good. This first does the friedman calculations and display, and I added a separate second loop for the anova1 calculations and display. The computation is relatively fast, however it takes a while to render all of this, so I deleted the full results here.
The full analysis is in the commented-out section, so un-comment that to run it.
The second two loops are much shorter, and since it takes a while to run the full version, am using the shorter one here. Use the first two loops in your analysis and delete the second two loops.
The boxplot results are instructive. If the data are normally distributed, the nonparametric and parametric results should be close to identical. That they are not here leads me to believe that the data violate some of the assumptons of the anova1 test. I defer to you to sort that.
% Load the sheet data and variables
filename = "NEWSHEETUpdate-2.xlsx";
SN = sheetnames(filename)
Sheets = {'Sheet9', 'Sheet2', 'Sheet3'};
for k = 1:numel(Sheets)
% Sheet = "CM" + k;
MHD{k} = readtable(filename, VariableNamingRule="preserve", Sheet=Sheets{k}); % Mouse Hepatocyte Data For Each Sheet
end
% Variable and row selection
VN = MHD{1}.Properties.VariableNames;
Sel = [2 3 4 5 6 7 8]; % Selected variables by column index
VNSel = VN(Sel);
numVariables = numel(VNSel);
numLocations = 12;
% Sel = [4 6 7 8 12 14 15 18 20 21 22 26 28 29 32 34 35 36 40 42 43]; % Selected variables by column index
% VNSel = VN(Sel);
% RN = MHD{1}{:, 1};
% [RNu, ~, uidx] = unique(RN, 'stable');
disp(MHD{1})
disp(MHD{2})
disp(MHD{3})
% fprintf([repmat('=',1,70) '\n\n\nFRIEDMAN —\n\n'])
%
% for k1 = 1:numel(VNSel)
% for k2 = 1:12
% disp("Variable: "+k1+", Variable name: "+VNSel(k1)+", Row #: "+k2)
% RowIdx = (1:12)+(k2-1);
% RowMtx = [MHD{1}{RowIdx,Sel(k1)} MHD{2}{RowIdx,Sel(k1)} MHD{3}{RowIdx,Sel(k1)}];
% [p{k1,k2},Result{k1,k2}] = friedman(RowMtx,1);
% disp(p{k1,k2})
% end
% end
%
% fprintf([repmat('=',1,50) '\n\n\nANOVA1 —\n\n'])
%
% for k1 = 1:numel(VNSel)
% for k2 = 1:12
% disp("Variable: "+k1+", Variable name: "+VNSel(k1)+", Row #: "+k2)
% RowIdx = (1:12)+(k2-1);
% RowMtx = [MHD{1}{RowIdx,Sel(k1)} MHD{2}{RowIdx,Sel(k1)} MHD{3}{RowIdx,Sel(k1)}];
% [p{k1,k2},Result{k1,k2}] = anova1(RowMtx);
% disp(p{k1,k2})
% end
% end
%
% fprintf(['\n\n' repmat('=',1,70) '\n\n'])
fprintf([repmat('=',1,120) '\n\n\nFRIEDMAN —\n\n'])
for k1 = 1:numel(VNSel)
for k2 = 1:2
disp("Variable: "+k1+", Variable name: "+VNSel(k1)+", Row #: "+k2)
RowIdx = (1:12)+(k2-1);
RowMtx = [MHD{1}{RowIdx,Sel(k1)} MHD{2}{RowIdx,Sel(k1)} MHD{3}{RowIdx,Sel(k1)}];
[p{k1,k2},Result{k1,k2}] = friedman(RowMtx,1);
disp(p{k1,k2})
end
end
fprintf([repmat('=',1,120) '\n\n\nANOVA1 —\n\n'])
for k1 = 1:numel(VNSel)
for k2 = 1:2
disp("Variable: "+k1+", Variable name: "+VNSel(k1)+", Row #: "+k2)
RowIdx = (1:12)+(k2-1);
RowMtx = [MHD{1}{RowIdx,Sel(k1)} MHD{2}{RowIdx,Sel(k1)} MHD{3}{RowIdx,Sel(k1)}];
[p{k1,k2},Result{k1,k2}] = anova1(RowMtx);
disp(p{k1,k2})
end
end
fprintf(['\n\n' repmat('=',1,120) '\n\n'])
.
Isabella
el 23 de Oct. de 2024
Star Strider
el 23 de Oct. de 2024
I used the line in your code to define ‘Sheets’ as:
Sheets = {'Sheet9', 'Sheet2', 'Sheet3'};
for k = 1:numel(Sheets)
% Sheet = "CM" + k;
MHD{k} = readtable(filename, VariableNamingRule="preserve", Sheet=Sheets{k}); % Mouse Hepatocyte Data For Each Sheet
end
The rest of my code then useed the ‘MHD’ cell arrays as:
for k1 = 1:numel(VNSel)
for k2 = 1:2
disp("Variable: "+k1+", Variable name: "+VNSel(k1)+", Row #: "+k2)
RowIdx = (1:12)+(k2-1);
RowMtx = [MHD{1}{RowIdx,Sel(k1)} MHD{2}{RowIdx,Sel(k1)} MHD{3}{RowIdx,Sel(k1)}];
[p{k1,k2},Result{k1,k2}] = friedman(RowMtx,1);
disp(p{k1,k2})
end
end
and:
for k1 = 1:numel(VNSel)
for k2 = 1:2
disp("Variable: "+k1+", Variable name: "+VNSel(k1)+", Row #: "+k2)
RowIdx = (1:12)+(k2-1);
RowMtx = [MHD{1}{RowIdx,Sel(k1)} MHD{2}{RowIdx,Sel(k1)} MHD{3}{RowIdx,Sel(k1)}];
[p{k1,k2},Result{k1,k2}] = anova1(RowMtx);
disp(p{k1,k2})
end
end
So it’s essentially the same code for both.
The way I read the documenetation for both functions, that should be correct.
I will change my code if this approach is not correct for one or both functions. I will need a documentation citation as well in that instance, since I will want to understand any errors in my documentation interpretation, assumptions or code.
As it stands, this appears to me to be correct.
.
Isabella
el 23 de Oct. de 2024
I cannot determine if it is correct because I do not understand what you are doing. I also do not understand what ‘C’, ‘S’ and ‘W’ are, although so long as they are the same sorts of data although under differeent conditions, that isn’t important. (I continue to have problems with your using derived data rather than the original data. The skewness and kurtosis of normally-distributed data should both be close to zero, and according to your determiinations of them, they are definitely not. It would likely be best to do the friedman test on the original data, or a representative random sample of it.)
I added a stem3 plot of the p-values for my interest. The two analyses do not agree on many of them.
% Load the sheet data and variables
filename = "NEWSHEETUpdate.xlsx";
SN = sheetnames(filename);
Sheets = {'Sheet9', 'Sheet2', 'Sheet3'}; % S, W, and C cell types
for k = 1:numel(Sheets)
MHD{k} = readtable(filename, VariableNamingRule="preserve", Sheet=Sheets{k}); % Data for each sheet
end
% Variable and row selection
VN = MHD{1}.Properties.VariableNames;
Sel = [2 3 4 5 6 7 8]; % Selected variables by column index
VNSel = VN(Sel);
numVariables = numel(VNSel);
locations = 5:9; % Analyze locations 5 to 9
numLocations = numel(locations);
% Initialize matrices to store results
p_values_friedman = NaN(numVariables, numLocations);
p_values_anova = NaN(numVariables, numLocations);
binary_matrix = zeros(numVariables, numLocations, 3); % Store significant differences for each comparison (S vs W, S vs C, W vs C)
% Loop through each selected variable and each location (cell type)
for k1 = 1:numVariables
for k2 = 1:numLocations
disp("Variable: "+VNSel{k1}+", Location #: "+locations(k2))
% Adjust RowIdx to extract data corresponding to locations 5-9
RowIdx = (1:12) + (locations(k2) - 1);
RowMtx = [MHD{1}{RowIdx, Sel(k1)} MHD{2}{RowIdx, Sel(k1)} MHD{3}{RowIdx, Sel(k1)}];
% Perform Friedman's test
[p_friedman, ~, stats] = friedman(RowMtx, 1, 'off');
p_values_friedman(k1, k2) = p_friedman;
% Perform ANOVA1 test
[p_anova, ~, stats_anova] = anova1(RowMtx, [], 'off');
p_values_anova(k1, k2) = p_anova;
% Perform post-hoc pairwise comparisons if significant
if p_friedman < 0.05 || p_anova < 0.05
% Post-hoc test to determine which pairs differ using 'multcompare'
multResults = multcompare(stats, 'CType', 'bonferroni', 'Display', 'off');
% Analyze pairwise comparisons (1: S vs W, 2: S vs C, 3: W vs C)
binary_matrix(k1, k2, 1) = any(multResults(:, 1) == 1 & multResults(:, 2) == 2 & multResults(:, 6) < 0.05); % S vs W
binary_matrix(k1, k2, 2) = any(multResults(:, 1) == 1 & multResults(:, 2) == 3 & multResults(:, 6) < 0.05); % S vs C
binary_matrix(k1, k2, 3) = any(multResults(:, 1) == 2 & multResults(:, 2) == 3 & multResults(:, 6) < 0.05); % W vs C
end
end
end
% Create heatmaps for each pairwise comparison
pair_labels = {'S vs W', 'S vs C', 'W vs C'};
for pair_idx = 1:3
figure;
h = heatmap(locations, VNSel, binary_matrix(:, :, pair_idx), 'Colormap', [1 1 1; 0 0 1], 'ColorbarVisible', 'off');
title(['Significant Changes: ' pair_labels{pair_idx}]);
xlabel('Location (5-9)');
ylabel('Variables');
set(gca, 'FontSize', 12);
% Save each heatmap as an image
saveas(gcf, ['Significant_Changes_' pair_labels{pair_idx} '_Locations_5_9.png']);
end
p_values_friedman
p_values_anova
[X,Y] = ndgrid(1:7, 1:5);
figure
stem3(X, Y, p_values_friedman, '.', 'DisplayName','friedman')
hold on
stem3(X, Y, p_values_anova, '.', 'DisplayName','anova1')
hold off
grid on
xlabel('Rows')
ylabel('Columns')
zlabel('\itp\rm-values')
legend('Location','best')
% Save the detailed binary matrix and p-values to an Excel file
T = array2table(binary_matrix(:, :, 1), 'VariableNames', strcat('Loc', string(locations)), 'RowNames', VNSel);
writetable(T, 'Binary_Matrix_Significant_Changes_S_vs_W_Locations_5_9.xlsx', 'WriteRowNames', true);
T2 = array2table(binary_matrix(:, :, 2), 'VariableNames', strcat('Loc', string(locations)), 'RowNames', VNSel);
writetable(T2, 'Binary_Matrix_Significant_Changes_S_vs_C_Locations_5_9.xlsx', 'WriteRowNames', true);
T3 = array2table(binary_matrix(:, :, 3), 'VariableNames', strcat('Loc', string(locations)), 'RowNames', VNSel);
writetable(T3, 'Binary_Matrix_Significant_Changes_W_vs_C_Locations_5_9.xlsx', 'WriteRowNames', true);
% Display a message to confirm the save
disp('Detailed binary matrices and results saved to Excel files.');
.
Isabella
el 23 de Oct. de 2024
Star Strider
el 23 de Oct. de 2024
I don’t beleive you incorporated them. My problem is that you’re analysing derivative data, such as the mean and norm rather than the data themselves. Using derivatives of the data removes too much informaiton, and that could possibly lead to an erroneous interpretation of the results of your experiment. The median might be more informative, since it’s not affected by extreme values, as is the mean, however it’s still not the same as analysing the data themselves.
The stem3 plot graphically compares the p-values of the friedman and anova1 analyses for the same variables. I generally get more qualitative information from plots than from text. It’s not necessaary for the analysis, so you can delete it.
Isabella
el 23 de Oct. de 2024
Star Strider
el 24 de Oct. de 2024
I understand that. My problem is that the mean reduces the entire vector, with all its inherent complexity, to a single value that may not capture any of that complexity. That’s the problem I have with your analysis.
If the data are normally distributed, the anova1 and friedman results should be similar if not exactly the same, at least as I understand parametric and nonparametric statistical tests. The stem3 plot allows me to understand that anova1 may not be appropriate because the data violate its assumptions about them. The friedman test ‘cares’ only that the data have identical distribtuons, not what the distributions are. The anova1 test, and all parametric tests, ‘cares’ very much about how they are distributed.
Isabella
el 24 de Oct. de 2024
Star Strider
el 24 de Oct. de 2024
Some of your data are labelled exactly that. For example, ‘normTotalArea’, ‘AvgSize’ and others. I’m not certain how best to describe scattered data (although one example might be to use median instead), however that might be worth exploring.
I suggest that you consult with your biostatistician about this. There may be a way to consider the original data in a way that would make your results meaningful. The differences between the parametric and nonparametric results concern me.
Isabella
el 24 de Oct. de 2024
Star Strider
el 24 de Oct. de 2024
The diffeerennce means thtat there’s a problem with thee data somewhere. If they’re normally distributed, the p-values should be close to equal. That they aren’t impliees that the assumptions of one of them (most likely anova1 since nonnparametric tests aren’t distribution-sensitive) aren’t being met. And that’s my concern.
Isabella
el 24 de Oct. de 2024
Star Strider
el 24 de Oct. de 2024
I am not sufficiently familiar with your study to determiine that. It might be be better to use the median value for all derived values and be consistent with it, however there may be ways to make your analyses robust that I have not thought of. If you must use derived values, I would use the same derived value (median would be my preference) for all of them.
Unless I am absolutely certain that the variables I am working with are normally distributed (those usually involve differences, since differences can have posittive, negative or zero values, while any variables that cannot have negative or zero values are generally lognormally distributed), I generally prefer nonparametric to parametric tests. Physiological variables are almost always lognormally distributed (I have actually never discovered any that were not, however there may be exceptions), so nonparametric tests are usually preferable in these instances.
Isabella
el 24 de Oct. de 2024
Star Strider
el 24 de Oct. de 2024
You need to consult with your biostatisticians on that.
My point is that if the data are not normally distributed — and are not of the same metric — a parametric approach may not produce the correct analysis.
Isabella
el 24 de Oct. de 2024
Star Strider
el 24 de Oct. de 2024
A ‘metric’ is simply a way of measuring something. (It’s a relatively common mathematical term.) In general, it is defined specifically (such as a distance from a reference), however it can be anything that produces a single value representation of a group of numbers.
Your metrics are not all the same, at least as I understand them. The norm is the square root of the sum of the squares of the vector (with the default options), and the mean (or average) is the sum of the data divided by the number of them in the vector. The median is the value at which half the data are greater and half lesser (the 50th percentile value). Of these, only the median is not affected by extreme values, the reason I prefer it.
I am just going on the names you gave your data, assuming that the names are accurate descriptions of the proccesses you used to create them. Some use the term ‘average’ and some ‘norm’.
Star Strider
el 24 de Oct. de 2024
I don’t understand what you’re doing in any detail, and I’ve never worked extensively with histology or histopathology. I still prefer median to mean, for the reason I stated earlier.
‘... perhaps it’s reasonable not to expect a normal distribution pattern in this analysis.’
That’s essentially true for every physiological or biomedical measurement, at least in my experience. If you check the original data with the histfit function, you can see that the logmormal distribution is more appropriate than the normal distribution. You can also check the distributions of the data with the kruskalwallis test to see if they share the same distribution.
As always, my pleasure!
.
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