MDS (Multi-Dimensional Scaling)

Boyut İndirgeme · Görselleştirme

🆕 New in v1.0.5: A Chart tab was added to this analysis (boxplot, interaction, profile, bar, scatter, biplot, or forecast — depending on analysis type).

MDS (Multi-Dimensional Scaling) is one of the statistical analyses applied automatically in MerQur. This page illustrates — on a Architecture, Planning & Design 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 Architecture, Planning & Design 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):

Ozellik Sutunlari: ['yesil_orani', 'alan_m2', 'agac_yogunluk', 'yol_uzunluk_m', 'su_alan_pct']
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 — Architecture, Planning & Design

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 Architecture, Planning & Design:

Peyzaj_Mimarligi/71_mds_park_distance.xlsx

🎬 Scenario

We map the similarity among parks onto two dimensions with multidimensional scaling (MDS).

⚙️ Variable Selection

Variables: green_ratio, area_m2, tree_density, path_length_m, water_area_pct

Data Preview (First 5 Rows)

park_id	green_ratio	area_m2	tree_density	path_length_m	water_area_pct
1.0	0.282	1819.0	28.0	110.0	6.3
2.0	0.228	1974.0	17.0	213.0	9.1
3.0	0.255	1523.0	52.0	116.0	11.5
4.0	0.321	2603.0	37.0	192.0	19.3
5.0	0.311	2060.0	26.0	201.0	17.3

n = 51 · Columns: park_id, green_ratio, area_m2, tree_density, path_length_m, water_area_pct

📈 MerQur Output

MDS (MULTI-DIMENSIONAL SCALING) RESULT ───────────────────────────────────────────── Stress (Kruskal-1) = 0.033 (good fit) Park similarity map (green ratio, area, tree density, path length, water area)

💬 Interpretation

MDS maps the similarity among parks into two dimensions — parks with similar features placed near, dissimilar ones far. Stress = 0.033 is a “good” fit; this means the park-similarity structure fits two dimensions successfully (low stress = reliable map). Parks close on the map have similar physical 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 park-similarity grouping and typological positioning.

⚠ 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 Architecture, Planning & Design file.

▶ MDS (Multi-Dimensional Scaling) — video walkthrough

This section is part of the Kümeleme ve Boyut İndirgeme video (7 analyses in one video). The link below jumps straight to 8:10, where this analysis begins. Narration is in Turkish.

▶ Watch this analysis (8:10) 📺 All videos

🔀 The same analysis in other disciplines:
🎓 Education Sciences · 🧪 Natural Sciences & Mathematics · ⚙ 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 →

Sources:

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.