What you have is a 2 x 4 within-subjects design. The independent variables are "Method" (2 levels) and "Case" (4 levels). You didn't provide a name for the dependent variable. Let's call it "Measurement".
To simplify the analysis, I reorganized your data (see attached), positioning the measurements for each participant on the same row.
The script below performs the anova usning MATLAB's ranova function and produces a conventional ANOVA table using a custom function, given at the end.
Results: There is a significant effect of Method on Measurement (F(1,7) = 33.58, p = .0007). There is also a significant effect of Case on Measurement (F(3,21) = 39.44, p < .0001). However, the Method x Case interaction effect on Measurement is not significant (F(3,21) = 1.54, p = .233).
For the other parts to your question, visit the examples provided in the documention for MATLAB's boxplot, boxchart, mauchly (for a spericity test), and histogram functions.
T = readtable('data2.xlsx', 'range', 'B3');
T.Properties.VariableNames = {'v1', 'v2', 'v3', 'v4', 'v5', 'v6', 'v7', 'v8'};
withinDesign = table([1 1 1 1 2 2 2 2]',[1 2 3 4 1 2 3 4]','VariableNames',{'Method','Case'});
withinDesign.Method = categorical(withinDesign.Method);
withinDesign.Case = categorical(withinDesign.Case);
rm = fitrm(T, 'v1-v8 ~ 1', 'WithinDesign', withinDesign);
%mauchly(rm)
AT = ranova(rm, 'WithinModel', 'Method*Case');
disp(anovaTable(AT, 'Measurement'));
% -------------------------------------------------------------------------
% Function to create a conventional ANOVA table from the overly-complicated
% and confusing ANOVA table created by the ranova function.
function [s] = anovaTable(AT, dvName)
c = table2cell(AT);
% remove erroneous entries in F and p columns
for i=1:size(c,1)
if c{i,4} == 1
c(i,4) = {''};
end
if c{i,5} == .5
c(i,5) = {''};
end
end
% use conventional labels in Effect column
effect = AT.Properties.RowNames;
for i=1:length(effect)
tmp = effect{i};
tmp = erase(tmp, '(Intercept):');
tmp = strrep(tmp, 'Error', 'Participant');
effect(i) = {tmp};
end
% determine the required width of the table
fieldWidth1 = max(cellfun('length', effect)); % width of Effect column
fieldWidth2 = 57; % width for df, SS, MS, F, and p columns
barDouble = repmat('=', 1, fieldWidth1 + fieldWidth2);
barSingle = repmat('-', 1, fieldWidth1 + fieldWidth2);
% re-organize the data
c = c(2:end,[2 1 3 4 5]);
c = [num2cell(repmat(fieldWidth1, size(c,1), 1)), effect(2:end), c]';
% create the ANOVA table
s = sprintf('ANOVA table for %s\n', dvName);
s = [s sprintf('%s\n', barDouble)];
s = [s sprintf('%-*s %4s %11s %14s %9s %9s\n', fieldWidth1, 'Effect', 'df', 'SS', 'MS', 'F', 'p')];
s = [s sprintf('%s\n', barSingle)];
s = [s sprintf('%-*s %4d %14.5f %14.5f %10.3f %10.4f\n', c{:})];
s = [s sprintf('%s\n', barDouble)];
end
