MDS (Multi-Dimensional Scaling)
MDS (Multi-Dimensional Scaling) is one of the statistical analyses applied automatically in MerQur. This page illustrates — on a Sport Sciences sample dataset — how the analysis is run, what the MerQur output looks like, and how the result is reported in APA 7 format.
🎯 What is it for?
MDS (Multi-Dimensional Scaling) automatically applies in the background all the assumption checks required for the relevant data type (normality, homogeneity of variance, etc.) and presents the results with a clear table + chart. Automatic interpretation to the APA 7 standard, effect sizes such as Cohen’s d/η²/R², and 95% confidence intervals are reported.
📌 When is it used?
- Statistical analysis of measurements in the Sport Sciences domain
- To produce APA 7-compatible result tables for academic publications
- Hypothesis testing and decision-making processes
- Undergraduate / master’s / PhD theses after the appropriate method has been selected
📐 Assumptions
- Appropriate scale — Variables must be at the measurement level required by the analysis (nominal/ordinal/interval/ratio)
- Independent observations — Observations must come from individuals independent of one another
- Sufficient sample size — The minimum n requirement for the analysis must be met
- Outlier check — Outliers must be detected and evaluated
If assumptions are violated, MerQur automatically suggests a non-parametric or robust alternative.
🛠 How to do it in MerQur
Load the data. Select the sample file from File → Open. MerQur auto-detects column types.
Select the analysis. From the left side select MDS (Multi-Dimensional Scaling).
Panel assignments (form fields in the program):
- feature_cols:
['sporcu_id', 'VO2', 'esneklik', 'sprint', 'denge'] - n_dimensions:
2 - metric:
False - distance:
euclidean
Optional settings. Effect size ✓ · 95% confidence interval ✓ · Assumption checks (automatic).
▶ Run — click the button. Results are produced automatically as a table + chart.
📄 Export to Word. APA 7-formatted report with italic statistical symbols.
📊 Sample Dataset — Sport Sciences
ℹ Note: The scenario, MerQur output and interpretation below were produced by actually running the real example dataset in MerQur. Numeric results on your own data will differ; the goal is to show how the analysis is set up and interpreted end-to-end.
🎬 Example File
This analysis is demonstrated on the following example dataset for Sport Sciences:
Spor_Bilimleri/71_mds_3grup.xlsx
🎬 Scenario
We place the inter-athlete similarity structure onto a 2D map. For similarity maps, MDS is appropriate.
⚙️ Variable Selection
- Variables: VO2
- Variables: flexibility
- Variables: sprint
- Variables: balance
Data Preview (First 5 Rows)
| athlete_id | VO2 | flexibility | sprint | balance |
|---|---|---|---|---|
| 1.0 | 59.3 | 14.8 | 11.45 | 74.4 |
| 2.0 | 41.9 | 18.0 | 11.27 | 74.0 |
| 3.0 | 47.1 | 15.3 | 11.66 | 64.2 |
| 4.0 | 54.0 | 14.4 | 11.5 | 69.3 |
| 5.0 | 50.5 | 14.9 | 11.48 | 70.0 |
n = 51 · Columns: athlete_id, VO2, flexibility, sprint, balance
📈 MerQur Output
💬 Interpretation
We placed the distance/similarity structure among athletes onto a 2-dimensional map with low stress (0.08): low stress means the map represents the true distances well. MDS positions observations in an interpretable space by preserving inter-observation distances; its difference from t-SNE is the aim of preserving global distance structure. In sports science it is used to draw athlete/group similarity maps and for positioning between groups.
⚠ Common Mistakes
- Misidentifying the data type (e.g., loading a categorical variable as numeric)
- Skipping assumption checks and going straight to the p-value
- Failing to report effect size — APA 7 requires both p and effect size
- Failing to apply a Type I error correction (Bonferroni/Tukey) in multiple comparisons
- Not switching to a non-parametric alternative when n is insufficient
📹 Video Walkthrough
Watch the video below for an end-to-end walkthrough of this analysis on a Sport Sciences file.
▶ MDS (Multi-Dimensional Scaling) — video walkthrough
This section is part of the Kümeleme ve Boyut İndirgeme video (6 analyses in one video). The link below jumps straight to 6:03, where this analysis begins. Narration is in Turkish.
🎓 Education Sciences · 🧪 Natural Sciences & Mathematics · 🏛 Architecture, Planning & Design · ⚙ Engineering · 🏥 Health Sciences · 📊 Social, Humanities & Admin Sciences · 🌾 Agriculture, Forestry & Aquatic
📚 If You Used This Analysis, Cite MerQur
If you performed this analysis using MerQur in a scientific study, please use the citation below as part of your academic citation obligations (APA 7):
Örücü, Ö. K. (2026). MerQur: Integrated Academic Data Analysis & Reporting Platform [Computer software] (Version 1.0.0). https://doi.org/10.53463/merqur.2026001
For BibTeX, RIS, EndNote and the English citation form: all citation formats →
- American Psychological Association. (2020). Publication manual of the American Psychological Association (7th ed.).
- Field, A. (2018). Discovering statistics using IBM SPSS Statistics (5th ed.). Sage.
- Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Lawrence Erlbaum.