One-Sample t-Test
One-Sample t-Test 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?
The One-Sample t-Test automatically performs all required assumption checks (normality, homogeneity of variance, etc.) for the relevant data type in the background and presents the results with a clear table + chart. Automatic interpretation in 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 One-Sample t-Test.
Panel assignments (form fields in the program):
- Value Column:
GPA - Tested μ:
2.9
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/03_one_sample_t_GPA.xlsx
🎬 Scenario
Our district sets a benchmark GPA of 2.50 that public school students are expected to reach on average. We collected GPA data from 100 students in a public school and want to know whether their mean GPA differs significantly from that benchmark value. A one-sample t-test is the correct tool because we are comparing the mean of a single continuous variable against a known reference value, with no second group involved.
⚙️ Variable Selection
- Test variable: GPA
- Test (reference) value: 2.50
- >> ADVANCED PARAMETERS (optional in the form — what they do):
- Hypothesis direction (two-sided / right / left): one-sided is more powerful when the direction is known beforehand.
- Hedges g: small-sample bias-corrected Cohen’s d.
- Effect-size CI: confidence interval around d.
- Shapiro-Wilk / K-S: normality assumption checks.
- Descriptives: mean/SD/SE/median/min/max/skewness/kurtosis.
- Bootstrap CI: distribution-free CI for the mean by resampling.
Data Preview (First 5 Rows)
| student_id | school_type | GPA | age |
|---|---|---|---|
| 1 | public | 3.01 | 16 |
| 2 | public | 2.06 | 15 |
| 3 | public | 2.91 | 15 |
| 4 | public | 3.65 | 18 |
| 5 | public | 2.51 | 17 |
n = 100 · Columns: student_id, school_type, GPA, age
📈 MerQur Output
💬 Interpretation
We compared a school’s mean GPA against the 2.5 passing/reference threshold. The result: mean 2.90, significantly above the threshold — t(99) = 8.05, p < .001, large effect size d = 0.81. So student achievement exceeds the reference threshold by more than chance can explain. The one-sample t-test is the right way to compare a group mean against a known standard (passing grade, national average, target value) — a very common question in educational evaluation. The effect size shows the difference is not just significant but practically important too. >> ADVANCED PARAMETERS (optional in the form — what they do): – Hypothesis direction (two-sided / right / left): one-sided is more powerful when the direction is known beforehand. – Hedges g: small-sample bias-corrected Cohen’s d. – Effect-size CI: confidence interval around d. – Shapiro-Wilk / K-S: normality assumption checks. – Descriptives: mean/SD/SE/median/min/max/skewness/kurtosis. – Bootstrap CI: distribution-free CI for the mean by resampling.
⚠ 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.
▶ One-Sample t-Test — video walkthrough
This section is part of the Veriye İlk Bakış ve Parametrik Testler video (14 analyses in one video). The link below jumps straight to 5:12, where this analysis begins. Narration is in Turkish.
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📚 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.