MDS (Multi-Dimensional Scaling)
MDS (Multi-Dimensional Scaling) is one of the statistical analyses applied automatically in MerQur. This page illustrates — on a Education 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 Education 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:
[ogrenci_id, GPA, calisma, +3 daha] - 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 — Education 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 Education Sciences:
Egitim_Bilimleri/71_mds_student_distance.xlsx
🎬 Scenario
Suppose we have 51 students described by their academic profile – GPA, weekly study time, and their math, science, and language scores. We want to map how similar or different students are to one another, so that students with comparable profiles sit close together on a two-dimensional plot. Multidimensional Scaling is the right tool here because it takes the pairwise distances between students across all five academic features and reconstructs a low-dimensional spatial map that preserves those distances as faithfully as possible, letting us visually spot clusters of academically similar learners.
⚙️ Variable Selection
- Coordinates / Variables: GPA
- Coordinates / Variables: study
- Coordinates / Variables: math
- Coordinates / Variables: science
- Coordinates / Variables: language
Data Preview (First 5 Rows)
| student_id | GPA | study | math | science | language |
|---|---|---|---|---|---|
| 1.0 | 1.83 | 1.0 | 54.3 | 40.3 | 55.6 |
| 2.0 | 2.08 | 6.3 | 54.6 | 47.9 | 51.3 |
| 3.0 | 1.91 | 4.9 | 51.6 | 43.1 | 57.7 |
| 4.0 | 2.06 | 8.6 | 60.8 | 60.4 | 57.9 |
| 5.0 | 1.53 | 6.6 | 56.4 | 47.2 | 46.5 |
n = 51 · Columns: student_id, GPA, study, math, science, language
📈 MerQur Output
💬 Interpretation
MDS maps the similarity among students into two dimensions — students with similar profiles placed near, dissimilar ones far. Stress = 0.054 is a “good” fit; this means the student-similarity structure fits two dimensions successfully (low stress = reliable map). Students close on the map have similar academic profiles. MDS is the classic way to visualise multivariate similarity/distance data; the stress value honestly tells how much we can trust the map. It is used to see student grouping and profile similarity.
⚠ 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 Education Sciences file.
▶ MDS (Multi-Dimensional Scaling) — video walkthrough
This section is part of the Kümeleme ve Boyut İndirgeme video (4 analyses in one video). The link below jumps straight to 3:31, where this analysis begins. Narration is in Turkish.
🧪 Natural Sciences & Mathematics · 🏛 Architecture, Planning & Design · ⚙ Engineering · 🏥 Health Sciences · 📊 Social, Humanities & Admin Sciences · 🏃 Sport 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.