How to Report Quantitative Data Analysis and Statistical Analysis?

What Should the Statistical Analysis Section Show?

• Software and version
• Data screening procedures
• Missing-data handling
• Outlier assessment
• Distribution and assumption checks
• Tests mapped to research questions
• Significance level
• Effect sizes and confidence intervals

Data Screening

Before inferential analysis, review entry errors, missingness, outliers, coding, reverse-scored items, computed scores, and distributional features.

Missing Data and Outliers

Missing-data methods may include complete-case analysis, appropriate variable-level approaches, imputation, multiple imputation, or likelihood-based methods depending on the design and missingness pattern.

Outliers should be investigated rather than removed automatically. Standardised scores, boxplots, Mahalanobis distance, Cook's distance, leverage, and residuals may be useful depending on the analysis.

Normality and Test Assumptions

Normality should not be judged from a single significance test. Histograms, Q-Q plots, skewness, kurtosis, and tests such as Shapiro-Wilk may be considered together. Test choice should also reflect independence, variance structure, scale of measurement, and other assumptions.

Descriptive Statistics

Use mean and standard deviation, median and interquartile range, range, and n (%) as appropriate to the data structure.

Group Comparisons

Two independent groups: independent-samples t test or an appropriate non-parametric alternative.

Paired measurements: paired t test or Wilcoxon signed-rank test.

Three or more groups: ANOVA or Kruskal-Wallis, with suitable post hoc comparisons where needed.

Categorical Data

Chi-square tests may be used for associations between categorical variables. Fisher's exact test or another method may be needed when expected cell counts are small.

Correlation

Pearson: for linear associations between continuous variables under suitable conditions.

Spearman: for ordinal data or monotonic relationships where Pearson assumptions are not appropriate.

Correlation describes association, not causation.

Regression

Report coefficients, standard errors, confidence intervals, R²/adjusted R², model tests, and standardised coefficients where useful.

Assess linearity, residual behaviour, homoscedasticity, independence, multicollinearity, and influential observations as appropriate.

Logistic Regression

For binary outcomes, report the coefficient, standard error, odds ratio, confidence interval, and p value where appropriate.

Mediation and Moderation

Mediation: report relevant paths, direct and indirect effects, and bootstrap confidence intervals.

Moderation: report main effects, interaction coefficient, confidence interval, p value, and simple slopes or conditional effects where useful.

Structural Equation Modelling

Describe the estimator, fit indices, standardised paths, standard errors, p values, confidence intervals, explained variance, and direct/indirect effects. Measurement and structural models should be clearly distinguished.

Effect Sizes and Confidence Intervals

Statistical significance does not by itself indicate scientific importance. Depending on the analysis, report measures such as Cohen's d, Hedges' g, eta squared, partial eta squared, r, R², odds ratios, or risk ratios together with confidence intervals where appropriate.

Reporting p Values

Report exact values where practical, e.g. p = .032.

For very small values use p < .001, not p = .000.

Non-Significant Findings

Results with p > .05 may still be scientifically informative. Interpret them with effect size, confidence interval, sample size, measurement precision, and theory.

Multiple Testing

Bonferroni, Holm, false-discovery-rate procedures, or other corrections may be appropriate depending on the multiplicity structure. Automatic correction is not necessary in every study.

Bootstrap

Bootstrap methods can be useful for indirect effects, confidence intervals, and settings where some distributional assumptions are weak. Report resample counts and interval methods when relevant.

Planned vs Exploratory Analyses

Distinguish analyses specified before examining the data from exploratory analyses conducted afterwards. This improves transparency.

Suggested Methods Flow

Software → Data screening → Descriptive statistics → Assumptions → Tests by research question → Effect sizes / confidence intervals → Significance level

Example Analysis Paragraph

Example: Data were analysed using IBM SPSS Statistics 29. Continuous variables were summarised using means and standard deviations or medians and interquartile ranges where appropriate; categorical variables were summarised as counts and percentages. Distributional characteristics were assessed using graphical methods and skewness/kurtosis values. Independent-samples t tests were used when assumptions were met, chi-square tests for categorical variables, and Pearson or Spearman correlations as appropriate. Multivariable associations were assessed using regression models and estimates were reported with 95% confidence intervals. Statistical significance was evaluated using two-sided p < .05.

Common Mistakes

• Selecting tests without reference to the research question
• Using a single normality test as the sole decision rule
• Deleting outliers without justification
• Failing to describe missing-data handling
• Running unnecessary numbers of tests
• Reporting p = .000
• Reporting only p values
• Ignoring effect sizes
• Suppressing non-significant findings
• Inferring causality from correlation
• Ignoring model assumptions or multicollinearity
• Assessing mediation only from individual path p values
• Evaluating SEM from one fit index
• Changing hypotheses after analysis

Before Submission, Check

• Do analyses match the research questions and hypotheses?
• Are data screening and missing-data procedures described?
• Are outlier procedures reported?
• Were relevant assumptions assessed?
• Are descriptive statistics appropriate to the data?
• Are test names and software reported correctly?
• Are p values formatted correctly?
• Are effect sizes reported where appropriate?
• Are confidence intervals provided where useful?
• Were multiplicity issues considered?
• Are non-significant findings reported?
• Are causal claims consistent with the design?