ANOVA Comparison of Position Error across Three Robot Control Strategies under Different Payloads

Project info

• Field of studyRobotics and Mechatronics
• LevelUndergraduate thesis (S1)
• Method typeStatistics and Regression
• Estimated build time± 3 working days
• Toolsanova1, multcompare, vartestn (Statistics and Machine Learning Toolbox)
• PriceUS$22 - US$131

Research goal

Model the position error as a function of the control strategy and the payload class using ANOVA and assess the model fit.

Variables

Example result

• 56.578F statistic
• <0.001p-value
• 0.744Eta-squared
• 4.854Mean square error
• 2Significant pairs
• 13.353Grand mean

One-way ANOVA on Position error across 3 groups gives F=56.58 (p=0.000) with eta-squared 0.744; Tukey multiple comparison flags 2 of 3 pairs as significantly different.

Computed from illustrative synthetic data, not from a real study.

About ANOVA and Multiple Comparison

One-way ANOVA (anova1) tests whether the means of several groups differ, and multcompare shows which pairs of groups differ. It is used to compare several treatments or experimental conditions.

Steps

1. 1Arrange the response data and group labels
2. 2Check variance homogeneity with vartestn
3. 3Run anova1 and read the ANOVA table
4. 4If significant, run multcompare (Tukey-Kramer)
5. 5Compute the effect size eta squared
6. 6Plot boxplots and comparison intervals

Assumptions to check

• Residuals are normally distributed
• Group variances are homogeneous
• Observations are independent

Reading and reporting the results

Report F, degrees of freedom, p-value, and eta squared, then the group pairs that differ per multcompare. If assumptions are violated, use kruskalwallis.

Example MATLAB code

A short starting script with this project's variable names. The delivered version is adapted to your data and fully commented.

rng(4);
n = 30;
a = 50 + 6*randn(n, 1);
b = 55 + 6*randn(n, 1);
c = 60 + 6*randn(n, 1);
position_error = [a; b; c];
control_strategy = [repmat({'A'}, n, 1); repmat({'B'}, n, 1); repmat({'C'}, n, 1)];

pLev = vartestn(position_error, control_strategy, 'TestType', 'LeveneAbsolute', 'Display', 'off');
fprintf('Levene p = %.3f\n', pLev);

[p, tbl, stats] = anova1(position_error, control_strategy, 'off');
F = tbl{2, 5};
ssb = tbl{2, 2};  sst = tbl{4, 2};
fprintf('F = %.3f, p = %.5f, eta^2 = %.3f\n', F, p, ssb / sst);

[comp, means] = multcompare(stats, 'Display', 'off');
disp(array2table(comp, 'VariableNames', {'G1', 'G2', 'Lower', 'Diff', 'Upper', 'p'}));

figure;
subplot(1,2,1); boxplot(position_error, control_strategy); ylabel('Response');
subplot(1,2,2); errorbar(1:3, means(:,1), means(:,2), 'o'); xlim([0.5 3.5]);
set(gca, 'XTick', 1:3, 'XTickLabel', {'A', 'B', 'C'}); ylabel('Mean +/- SE');

Packages and prices

Choose how much help you need. Each higher package includes everything in the lower ones. Prices exclude 11% VAT.

• Payment: 50% down payment before work starts, balance after the deliverables are handed over
• Tax: Prices exclude 11% VAT
• Data and academic integrity: Results are computed from your own research data; you write and stand behind your manuscript, we help with the analysis and your understanding of it
• Revisions: Up to 2 revisions are included in the price (Package 3: 3 rounds)

Frequently asked questions