Statistical analysis in a master’s thesis translates research questions into calculations that describe the data collected, compare groups or assess relationships between variables. It does not start with choosing software or searching for a ‘significant result’. First establish what you want to examine, how it was measured and what conclusions the study design permits.
This guide takes you from an analysis plan to reporting results. It covers common types of tests, the difference between a p-value and effect size, and an example of a complete report comparing two groups. The methodological guidance draws on Polish scientific publications found through Google Scholar and Polish documentation of statistical methods. The bibliography is at the end.
The route from question to conclusion: research aim → variables and measurement → data checks → descriptive statistics → appropriate analysis → effect size and uncertainty → interpretation within the study’s limits.
Not every thesis needs hypothesis testing. If the aim is to describe the group studied, a properly conducted descriptive analysis may suffice.
From research question to analysis plan
Before running calculations, make a short note for each question: which variables you are analysing, how they are recorded, whom the comparison covers and what result you need. Establish whether the measurements concern different people or the same participants measured repeatedly. This distinction affects the choice of test.
Describing the group studied
Question: ‘How often do students make use of consultations?’ You need response counts and percentages. State whether percentages are based on all participants or only those who answered the particular question.
Comparing scores
Question: ‘Do stress levels differ between students who work and those who do not?’ You need stress scores and group membership information, followed by an estimate of the difference.
Relationships between variables
Question: ‘Are hours worked associated with stress scores?’ You need two measurements for each person. Analysing an association does not automatically establish cause and effect.
If your aim, research question and hypothesis do not yet fit together, start with the guide Research methodology in a thesis. Do not tailor the hypothesis afterwards to whichever test produced the smallest p-value.
Prepare the analysis plan before collecting data. Define the main comparisons, instrument scoring, missing-data handling and significance level. Exploratory research can search for new associations, but clearly distinguish these from previously planned analyses in your text.
Data preparation and descriptive statistics
A convenient basic dataset has one participant per row and one variable per column. Prepare a variable dictionary recording names, code meanings, units and permitted values. A column containing 1, 2 and 3 does not itself tell you whether these are categories, ordered responses or an actual measurement.
- Check completeness. A missing response is not automatically zero. Record how many observations each analysis uses and why any data were omitted.
- Check consistency. Remove only confirmed duplicates or erroneous entries, following an explicit rule. Do not remove an unusual value merely because it changes the conclusion.
- Score the instrument according to its instructions. Account for reverse-scored items, summation rules and missing responses. A single response on an ordinal scale does not automatically become a quantitative measurement.
- Examine the distribution. Check plots, spread, skewness and outliers. Do not base your choice of test solely on a single normality test result.
For categorical variables, report counts and percentages. For quantitative measurements, choose measures of location and spread: the mean with standard deviation or the median with quartiles, depending on the distribution and purpose. The mean shows the average score, while the standard deviation describes variation between observations. Do not replace it with the standard error without explanation: the latter describes uncertainty in the estimated mean.
We cover the technical aspects of preparing a spreadsheet, calculating percentages and making charts separately in the guide How to analyse questionnaire results for a thesis: Excel and examples. If you are still developing the instrument, also see how to design a questionnaire for your thesis.
How do you choose a statistical test for a master’s thesis?
The examples below are a starting point for your decision, not an automatic selection guide. Consider the measurement scale, independence of observations, group sizes, distribution, variances and the parameter you want to compare. Justify the method in relation to your own study.
Two independent groups
An independent-samples t-test may be considered when comparing means of quantitative scores. The pooled-variance version assumes equal population variances. Unequal variances require a method that accounts for them, rather than ignoring the problem.
The Mann-Whitney U test analyses the ordering of scores. It is not a universal test of mean differences; interpreting it as a median difference requires additional conditions concerning the shapes of the distributions.
Two measurements of the same people
In a before-and-after design, you analyse pairs, not two independent groups. A paired-samples t-test concerns the mean of the differences and assumptions about those differences. For suitable data, the Wilcoxon signed-rank test may be considered.
Three or more groups
Comparing means may require analysis of variance, while rank analysis may call for an appropriate non-parametric method such as Kruskal-Wallis. A significant overall result does not yet identify which groups differ. Further comparisons need justification and control for multiple testing.
Two quantitative or ordinal variables
Pearson’s correlation describes a linear relationship. Spearman’s rank correlation may be considered for suitable ordinal measurements or a monotonic relationship. Start with a scatterplot: individual observations can strongly affect the coefficient.
Two categorical variables
A chi-squared test of independence may be considered for a cross-tabulation of categories. Assess expected counts; sparse categories may require an exact method, such as Fisher’s exact test in a suitable arrangement. Percentages cannot replace the counts needed for calculations.
A more complex design
Repeated measurements, participants clustered in classes or multiple predictors require you to account for the data structure. A simple two-group test may not suit such a design. Do not add regression merely to make the analysis look more advanced.
Zbigniew Śleszyński (2020) discusses the basics of linear correlation. Pearson’s coefficient ranges from -1 to 1: its sign indicates the direction, and its absolute value the strength of the linear relationship. A value close to zero does not rule out a non-linear relationship. The coefficient alone does not prove causation.
P-values, effect sizes and confidence intervals
A sound analysis report combines the test result with an estimate of the size of the phenomenon and its uncertainty. These address different questions and do not replace one another.
The p-value: a result under the null hypothesis
The p-value is the probability of obtaining a result at least as extreme as the observed one if the null hypothesis and the model assumptions hold. It is not the probability that the null hypothesis is true. Nor is it the probability that the result ‘happened by chance’.
With a pre-specified significance level of 0.05, p < 0.05 permits rejection of the null hypothesis. A result of p ≥ 0.05 means there are insufficient grounds to reject it in this analysis, not proof of no effect. Łukasz Budzicz (2017) highlights the importance of context and the limits of interpretation.
Effect size: how large is the difference or association?
Report the difference in the original units and, where justified, a standardised measure too. For a comparison of two means, this may be Cohen’s d; for a correlation, the coefficient r itself. The measure must suit the analysis.
Arkadiusz Prajzner (2022) discusses effect-size measures. A small p-value alone does not establish the strength of a phenomenon. Do not apply conventional ‘small’, ‘medium’ and ‘large’ thresholds without considering the measurement, field and practical meaning of the result.
Confidence intervals: precision of estimation
State the confidence level, bounds and unit, for example a 95% confidence interval for the mean difference from 1.33 to 6.67 points. Its width indicates uncertainty in the estimate.
In a frequentist interpretation, 95% describes a property of the procedure repeated across many studies meeting the assumptions. It does not mean that 95% of participants score within the interval, or that the parameter is randomly drawn within those bounds after the interval has been calculated.
Statistical significance is not the same as practical importance. In a large sample, even a small difference can be significant. In a small sample, non-significance can accompany imprecise estimation. Read the p-value, effect size and confidence interval together.
An example of statistical analysis in a master’s thesis
Illustrative data. All figures below are fictional and demonstrate how to report results. They are neither client results nor a study published in the sources cited.
We compare an illustrative quantitative stress score for students who work and those who do not. For demonstration purposes, we assume independent observations, appropriate measurement, distributional conditions and equal variances as required for a pooled-variance t-test. Means and standard deviations alone are insufficient to check these assumptions.
Students who work
- Sample size: n = 40.
- Mean: M = 28 points.
- Standard deviation: SD = 6 points.
Students who do not work
- Sample size: n = 40.
- Mean: M = 24 points.
- Standard deviation: SD = 6 points.
The mean difference is 28 - 24 = 4 points. The standard error of this difference is √(6²/40 + 6²/40), approximately 1.34 points. The t statistic is 4/1.34 ≈ 2.98 with 78 degrees of freedom. A two-sided test gives p ≈ 0.004.
- 95% confidence interval for the difference: from 1.33 to 6.67 points.
- Cohen’s d: 4/6 ≈ 0.67, with a pooled standard deviation of 6.
- Direction of the difference: a higher mean among students who work.
How should you report this result in a thesis?
In the illustrative data, students who worked had a higher mean stress score (n = 40; M = 28.00; SD = 6.00) than those who did not (n = 40; M = 24.00; SD = 6.00). A two-sided independent-samples t-test with pooled variance showed a difference: t(78) = 2.98; p = 0.004. The mean difference was 4.00 points, 95% CI [1.33; 6.67], with Cohen’s d = 0.67.
This reports the comparison, sample sizes, group descriptions, test result, and the size and uncertainty of the difference. Do not end the interpretation with ‘hypothesis confirmed’, however. Explain what four points mean on the scale used and how the finding relates to the research question.
What does this result not prove?
If people were not randomly allocated to groups, the comparison alone cannot establish that paid work caused stress. The groups may also differ in age, financial circumstances or study workload. If participants were selected for convenience, for example from one accessible group, be cautious about generalising to all students. A significant p-value does not fix sampling limitations.
How do you describe analysis methods in the methodology chapter?
Readers should understand how the data were prepared and why you used those calculations. Describe the methods according to the analysis actually conducted. Do not paste in a catalogue of tests you did not use.
- Dataset preparation: coding, instrument scoring, missing data and criteria for including observations.
- Descriptive analysis: measures used for each variable type.
- Main analyses: tests linked to questions or hypotheses, the independence or dependence of measurements, and assessment of assumptions.
- Inference rules: significance level, one-sided or two-sided testing, and how multiple comparisons were handled.
- Reporting: selected effect-size measures and confidence intervals, plus the software name and actual version used.
A template to complete with your own information
“The dataset was prepared according to [coding and missing-data rules]. Variables of type [type] were described using [measures]. To answer question [number and wording] we used [method and rationale]. Assumptions were assessed through [procedures actually carried out]. We adopted [significance level and type of testing]. We reported [effect-size measures and confidence level]. Calculations were performed in [software, version].”
There is no single required number of respondents for every analysis. Sample planning depends on factors including the type of analysis, expected effect, target power or required precision, division into groups and recruitment method. ‘100 questionnaires’ alone does not establish that a study is sound.
How do you present results and avoid overinterpretation?
Organise the chapter around research questions rather than the order of software windows. For each finding, identify the comparison, report the actual n, describe the data and give the relevant analysis parameters. Report exact p-values with a sensible number of digits; for very small values, write p < 0.001 rather than p = 0.000.
Non-significant findings also need to be reported. Do not replace them with ‘there is no relationship at all’ if the confidence interval still allows practically important effects. When conducting many tests, consider the risk of chance findings and justify how you control it. Selecting only convenient results distorts the picture of the study.
- Do not confuse an effect with a cause. Correlation and observational group differences do not replace a design that permits causal inference.
- Do not mix results with discussion. First show what you found, then relate it to the literature and limitations.
- Do not interpret output without variable names. Every number must refer to a specific question and measurement.
- Do not treat the software as a justification. The fact that software can run a test does not mean the test suits the design.
After preparing the results chapter, turn to the guide The discussion in a bachelor’s or master’s thesis. It will help you distinguish reporting calculations from discussing their meaning, comparing them with publications and considering limitations.
Checklist before submitting the analysis
- Every analysis answers a specific question or hypothesis.
- The measurement type and dependence between observations suit the selected method.
- Missing data and exclusions are described; sample sizes match the calculations.
- Descriptive measures show both the location and variation of scores.
- Test results include the appropriate parameters, p-values and suitable measures of effect and uncertainty.
- Multiple comparisons are justified, and exploratory analyses are labelled.
- Interpretation accounts for sampling and measurement limitations.
- The text agrees with the dataset, charts and software output.
Frequently asked questions about statistical analysis
Does every survey or thesis require statistical tests?
No. The scope of the analysis depends on the aim of the work and the research questions. Sometimes counts, percentages, and descriptive statistics are enough. If the study concerns differences or relationships, I check which methods are appropriate for the data and whether the conditions for their application are met.
A thesis based on interpreting regulations, a literature review, qualitative analysis of interviews, or an individual case study may not require testing statistical hypotheses. In qualitative research, the analysis may focus on the meaning of the statements. In that case, the appropriate support may be methodology, material analysis, or text editing. I do not add calculations just to make the thesis look more scientific or advanced.
How many people are needed for statistical analysis in a master's thesis?
There is no single number suitable for every thesis. The planned test, the number and size of groups, the expected effect size, and the required power and precision of the analysis are important. A small sample limits inference. It is best to discuss the sample size before starting data collection.
Are charts from Google Forms sufficient for statistical tests?
Usually, a database of individual responses is required, for example an export to XLSX or CSV. Aggregate charts alone often do not allow reconstructing relationships between answers or calculating correlations. Please also send the questionnaire and the scoring key for scales, if used.
Is a p-value < 0.05 sufficient to confirm a hypothesis?
No. With a pre-set significance level of 0.05, a p-value < 0.05 allows rejecting the null hypothesis within the adopted model and its assumptions. It does not mean that the research hypothesis is true with 95% probability.
Describe the direction and size of the effect, the confidence interval, the sample size, and the limitations of measurement and participant selection. Also consider multiple testing. A significant result alone does not prove causality or the practical importance of the difference.
How should I describe a confidence interval in a master's thesis?
State the confidence level, the estimated parameter, and the interval limits, for example: the mean difference was 4 points, and its 95% confidence interval ranged from 1.33 to 6.67 points. Maintain the unit of measurement and specify for which comparison the interval was calculated.
In a frequentist interpretation, the 95% level refers to the procedure: in repeatedly conducted studies meeting the assumptions, approximately 95% of such intervals would contain the true parameter. It does not mean that 95% of participants obtained a result between the given limits. A wide interval indicates lower precision of the estimate.
Bibliography and methodological basis
Polish scientific publications found through Google Scholar and checked in full text:
- Budzicz, Ł. (2017). Interpretacja statystyk w artykułach naukowych - wskazówki dla praktyków. Psychologiczne Zeszyty Naukowe, 1, 143-157.
- Prajzner, A. (2022). Wybrane wskaźniki wielkości efektu w badaniach psychologicznych. Annales Universitatis Mariae Curie-Skłodowska. Sectio J, Paedagogia-Psychologia, 35(4), 139-157. DOI: 10.17951/j.2022.35.4.139-157.
- Śleszyński, Z. (2020). Wyznaczanie współczynników korelacji liniowej - podstawy. Wiadomości Statystyczne. The Polish Statistician, 65(6), 69-87. DOI: 10.5604/01.3001.0014.2347.
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