Statistics
Common Statistical Analysis Methods in Academic Research
A practical map of the tests and models researchers use most often, what each one assumes, and the questions it can and cannot answer.
Statistical choice follows from three things: the type of research question, the measurement level of your variables, and whether the data meet the assumptions of the test. The overview below groups the most common methods by the question they answer.
Start with three questions
- What is your research question asking you to do: describe, compare, relate or predict?
- What is the measurement level of each variable: nominal, ordinal, interval or ratio?
- Are your observations independent, or are the same people measured more than once?
Describing data
Means, medians, standard deviations, frequencies and cross-tabulations. Always report these first; they give readers the context for everything that follows. For skewed data, report the median and interquartile range rather than the mean and standard deviation.
Comparing groups
| Situation | Usual test | Alternative when assumptions fail |
|---|---|---|
| Two independent groups, continuous outcome | Independent-samples t-test | Mann–Whitney U test |
| The same participants measured twice | Paired-samples t-test | Wilcoxon signed-rank test |
| Three or more independent groups | One-way ANOVA | Kruskal–Wallis test |
| The same participants measured three or more times | Repeated-measures ANOVA | Friedman test |
| Two categorical variables | Chi-square test of independence | Fisher’s exact test for small expected counts |
After a significant ANOVA, use post-hoc tests such as Tukey’s HSD to find which groups differ, and report an effect size such as eta-squared alongside the p-value.
Examining relationships
- Pearson and Spearman correlation for the strength of association.
- Multiple linear regression for predicting a continuous outcome.
- Logistic regression for binary outcomes.
- Moderation and mediation analysis for conditional and indirect effects.
Correlation shows association, not causation. Regression lets you control for other variables, but causal claims still depend on your research design.
Modelling constructs
Exploratory and confirmatory factor analysis establish whether survey items measure the intended constructs. Structural equation modelling then tests relationships among those constructs while accounting for measurement error.
- Check reliability with Cronbach’s alpha or composite reliability.
- Check convergent validity with the average variance extracted, and discriminant validity with the Fornell–Larcker criterion or HTMT.
- Report model fit, for example CFI, TLI, RMSEA and SRMR, against accepted thresholds.
Before you run anything
- Check normality, linearity, homoscedasticity and multicollinearity where relevant.
- Handle missing data deliberately and document the approach.
- Decide the significance level and effect-size measures in advance.
- Report confidence intervals, not only p-values.
A worked example
Suppose you surveyed 300 employees and want to know whether engagement differs between three departments, and whether supervisor support predicts engagement. The first question compares three independent groups on a continuous outcome, so a one-way ANOVA fits, or the Kruskal–Wallis test if the scores are badly skewed. The second question relates two continuous variables while other factors, such as tenure, may matter, so multiple regression with tenure as a control fits.
Before either analysis, you would check the reliability of the engagement and support scales, look at the distributions, and decide how to handle incomplete responses. Each research question gets its own test, chosen before you look at the results.
Reporting results
For each analysis, report the test used, the test statistic, degrees of freedom, p-value, effect size and confidence interval, then say in plain words what the result means for your research question. Follow the reporting style your discipline expects, such as APA.
A result is only as useful as its interpretation. Every number needs a sentence that says what it means.
Common mistakes
- Running many tests without adjusting for multiple comparisons.
- Treating a non-significant result as proof that there is no effect.
- Reporting p-values without effect sizes or confidence intervals.
- Removing outliers without a rule decided in advance and reported.
- Choosing the test after seeing which one gives a significant result.
Choosing software
SPSS and jamovi are approachable for standard tests. R and Python offer the widest range of methods and make analyses reproducible through scripts. AMOS, lavaan in R and SmartPLS are common for structural equation modelling. Choose the tool your field uses and your supervisor can review.