Quantitative Data Analysis and Interpretation Examples for Your Thesis

Running the statistics is only half of quantitative data analysis. Markers award most of the credit for how clearly you report and interpret the results: whether the numbers are complete and correctly formatted, and whether you explain what they actually mean for your research questions. This guide gives worked quantitative data analysis and interpretation examples you can model in your own thesis or dissertation results chapter.

If you need a refresher on choosing and running the tests themselves, start with our step-by-step guide to quantitative data analysis from descriptive statistics to t-tests, ANOVA and regression.

All figures below are illustrative examples based on a fictional survey of 120 students, so you can see the format. Always report your own data.

How to structure your quantitative results chapter

1. Introduction: one short paragraph reminding the reader of your research questions or hypotheses.
2. Data screening: missing data, outliers and assumption checks such as normality and homogeneity of variance.
3. Descriptive statistics: sample characteristics and the means and standard deviations of your key variables.
4. Inferential results: one subsection per hypothesis, with the test, the result and a one-line interpretation.
5. Summary: a short table or paragraph showing which hypotheses were supported.

Keep the results chapter factual. Comparisons with previous studies, explanations and implications belong in the discussion. For typical chapter lengths, see our guide to dissertation structure and word count.

Quantitative data analysis and interpretation examples

Example 1: Descriptive statistics

How to write it: Participants (N = 120; 68 female, 52 male) were aged 19 to 46 (M = 24.6, SD = 5.3). On average, participants reported moderate academic stress (M = 3.42, SD = 0.71) on a five-point scale.

What it means: The mean tells the reader the typical score and the standard deviation shows how spread out the scores are. Always describe your sample before any inferential test, and say what the scale range is so a mean of 3.42 is meaningful.

Example 2: Independent samples t-test

How to write it: An independent samples t-test showed that online students (M = 4.05, SD = 0.62) reported significantly higher course satisfaction than campus students (M = 3.78, SD = 0.58), t(118) = 2.45, p = .016, d = 0.45.

What it means: The difference is statistically significant (p is below .05), and Cohen’s d of 0.45 is a small-to-medium effect. In plain terms, online students were somewhat more satisfied, but the two groups overlapped considerably. Hypothesis 1 was supported.

Example 3: One-way ANOVA

How to write it: A one-way ANOVA found a significant effect of teaching method on exam scores, F(2, 87) = 5.12, p = .008, η² = .11. Tukey post hoc tests showed that students taught with Method C (M = 68.4) scored higher than those taught with Method A (M = 59.7, p = .006); no other differences were significant.

What it means: An eta squared of .11 means teaching method explained about 11% of the variation in exam scores, a medium effect. The post hoc test tells you exactly which groups differ, which the overall F test cannot.

Example 4: Chi-square test of independence

How to write it: A chi-square test of independence showed a significant association between year of study and use of university support services, χ²(1, N = 200) = 6.84, p = .009, φ = .18.

What it means: The two variables are related, but phi of .18 indicates a small association. Report the percentages in each group (for example, 41% of final-year students used support services compared with 24% of first-years) so the reader can see the direction of the relationship.

Example 5: Pearson correlation

How to write it: There was a moderate positive correlation between weekly study hours and academic self-efficacy, r(118) = .38, p < .001.

What it means: Students who studied more tended to feel more confident academically. Squaring r gives r² = .14, so the two variables share about 14% of their variance. A correlation does not show that one causes the other, so avoid causal wording.

Example 6: Multiple regression

How to write it: A multiple regression showed that social support, workload and sleep together explained 27% of the variance in academic stress, R² = .27, F(3, 116) = 14.30, p < .001. Social support (β = −.34, p < .001) and workload (β = .29, p = .001) were significant predictors, but sleep was not (β = −.12, p = .14).

What it means: The model as a whole is significant and explains just over a quarter of the variation in stress. The standardised betas show that higher social support predicts lower stress and higher workload predicts higher stress, with social support the stronger predictor. Sleep did not add significant explanatory power once the other variables were included.

Common mistakes when interpreting quantitative results

• Reporting p values without effect sizes. A significant result can still be trivially small.
• Writing “p = .000”. SPSS rounds; report it as p < .001.
• Treating non-significant results as proof of no effect. Say the result was not statistically significant, not that there is no difference.
• Using causal language for correlations, such as “study hours increase confidence”.
• Pasting raw SPSS output. Build clean APA-style tables with only the values the reader needs.
• Interpreting in the results chapter. Keep links to the literature for the discussion.

Many of these problems start at the design stage. If you are collecting survey data, our guide to survey design and questionnaire development explains how to build valid, reliable measures, and our guide to choosing a research methodology covers sampling and design. Psychology students can also see how results are reported in our psychology dissertation guide.

Need help analysing or interpreting your data?

If you have collected your data but are unsure which tests to run or how to explain the output, our dissertation data analysis specialists can run the analysis in SPSS, R, Stata or Excel and help you write up a clear results chapter. Our SPSS data analysis service includes annotated output and APA-formatted tables, and our research methodology help can review your design before you collect data. Use any support as guidance for your own writing and check your university’s academic integrity policy.

Frequently asked questions

How do you interpret quantitative data in a thesis?

Report the descriptive statistics first, then each inferential test in the order of your research questions or hypotheses. For every test, give the test statistic, degrees of freedom, exact p value and an effect size, then state in plain words what the result means for your hypothesis. Save wider interpretation and links to the literature for the discussion chapter.

What should a quantitative results chapter include?

A short introduction, data screening (missing data and assumption checks), descriptive statistics, the inferential tests for each hypothesis with tables or figures, and a brief summary. It should present findings objectively without discussing their implications.

What is the difference between statistical significance and effect size?

The p value tells you how likely a result at least this large is if there were no real effect. The effect size, such as Cohen’s d, eta squared or r, tells you how big the difference or relationship is. Large samples can make tiny effects significant, so always report both.