Writing a statistical analysis means clearly describing what tests you used, why you chose them, and what the numbers actually show. Whether you’re drafting the methods section of a research paper or reporting results, the goal is the same: give readers enough detail to understand your approach and evaluate your conclusions. Here’s how to do that, section by section.
Start With Your Methods Section
The methods section is where you lay out your analytical plan before presenting any results. Think of it as a recipe: someone reading it should be able to replicate your analysis from scratch. There are four core elements every statistical methods section needs.
Name each test and explain why you used it. Match each variable type to the appropriate test. For example, you might use a chi-square test or Fisher exact test for categorical variables (like yes/no outcomes) and a t-test or its nonparametric equivalent for continuous variables (like blood pressure or test scores). If your data weren’t normally distributed, say so, and explain that you used a nonparametric alternative. Citing a reference that supports your choice of test strengthens this justification, especially for less common methods.
State your significance threshold. The most common convention is p < .05, meaning you’d accept a less than 5% probability that your results occurred by chance. Write it plainly: “P < .05 was considered statistically significant.” Some fields or study designs call for a stricter threshold (like .01) or a more flexible one (like .10 for exploratory analyses with small samples). If you deviated from .05, briefly explain your reasoning.
Describe your sample size calculation. Readers need to know you enrolled enough participants to detect a meaningful difference. This means reporting your power analysis: what effect size you expected, what power level you targeted (typically 80% or 90%), and how those inputs determined your sample size.
Specify your software. Name the program and its version number. For example: “Statistical analyses were carried out using R 4.1.0.” If you relied on specific packages or libraries within that software, name those too, along with their version numbers. In R, you can pull the correct citation format by running citation("packagename") in the console.
Reporting Descriptive Statistics
Before getting into comparisons or models, you’ll summarize your data. This typically means reporting averages and some measure of spread for continuous variables, and counts or percentages for categorical ones. The choice between standard deviation (SD) and standard error of the mean (SEM) matters more than many writers realize.
Standard deviation describes how spread out your individual data points are. Standard error describes how precisely you’ve estimated the average. Most of the time, your reader wants to know the variability in your sample, which means SD is the right choice. Some researchers default to SEM because it produces a smaller number, making data look tidier, but this is misleading. SEM shrinks automatically as your sample size grows, regardless of how variable the data actually are. Several journal editors now explicitly require SD over SEM for descriptive summaries.
Use SEM only when your specific goal is to communicate the precision of your estimate of the population mean, such as when constructing confidence intervals. In graphs and figures, SD is generally preferred.
For normally distributed data, report the mean ± SD. For skewed data, report the median along with the interquartile range (the 25th to 75th percentile values). State which format you used and why: “Continuous variables are presented as mean ± SD for normally distributed data, or median (interquartile range) for skewed distributions.”
Checking and Reporting Assumptions
Most statistical tests assume certain things about your data. Common assumptions include that your data follow a bell-shaped distribution (normality) and that the variability is roughly equal across groups (homoscedasticity, often called “equal variances”). Skipping these checks, or failing to mention them, is one of the most frequent weaknesses in statistical write-ups.
You don’t need to go into heavy mathematical detail. A sentence or two is usually enough: “Normality was assessed using the Shapiro-Wilk test. Levene’s test was used to evaluate equality of variances across groups.” Then state the outcome. If assumptions were met, proceed with your planned test. If they weren’t, explain what you did instead, such as switching to a nonparametric test or applying a data transformation.
This transparency lets readers trust your results. It also protects you during peer review, where unstated assumptions are easy targets for criticism.
Presenting Your Results
When you move from methods to results, shift from describing your plan to reporting what happened. Here are the formatting conventions that make statistical results clear and credible.
P-Values
Report exact p-values to two or three decimal places. Write p = .03 or p = .006, not just “p < .05.” The one exception: when p is extremely small, report it as p < .001 rather than writing out a long string of zeros. In tables and figures, follow the same rule. Use italics for statistical symbols like p, t, F, and R² when your formatting allows it.
Effect Sizes
A p-value tells you whether a difference is likely real. An effect size tells you whether it’s meaningful. These are different questions, and a thorough analysis reports both.
Three families of effect sizes cover most situations. For comparing group averages, use a standardized mean difference (often called Cohen’s d), which expresses the gap between two groups in standard deviation units. For relationships between variables, report a correlation coefficient. For outcomes that are binary (like disease versus no disease), use an odds ratio, risk ratio, or risk difference. Each of these tells the reader something a p-value alone cannot: how large the effect actually is.
Resist the urge to label every effect as “small,” “medium,” or “large” based on rigid cutoffs. Cohen’s original benchmarks (0.2, 0.5, 0.8 for d) were meant as rough guides, not universal standards. What counts as a meaningful effect depends entirely on your field and context. A “small” effect size in a public health intervention affecting millions of people can be enormously important.
Confidence Intervals
Confidence intervals give readers a range of plausible values for your estimate, which is often more informative than a single point estimate plus a p-value. A 95% confidence interval for a mean difference, for instance, tells the reader: “We’re reasonably confident the true difference falls somewhere in this range.” Report them in brackets after the estimate, like: mean difference = 4.2 points, 95% CI [1.8, 6.6].
Handling Multiple Comparisons
Every time you run a statistical test, there’s a small chance of a false positive. Run 20 tests at the .05 level, and on average one will come back “significant” purely by chance. This is the multiple comparisons problem, and how you handle it needs to be explicit in your write-up.
The most common correction is the Bonferroni method, which divides your significance threshold by the number of tests you’re running. It’s straightforward but conservative, meaning it can make you miss real effects. False discovery rate (FDR) methods offer a less strict alternative that controls the expected proportion of false positives among your significant results rather than guarding against any single false positive.
The key point for your write-up: state whether you corrected for multiple comparisons, name the method, and explain why it was appropriate. Corrections are most clearly justified when you’re testing a single overarching hypothesis through multiple individual tests. If your comparisons address genuinely separate questions, a correction may not be warranted, but you should still acknowledge the issue and explain your reasoning.
Using Tables and Figures
Tables work best for exact values, especially when you’re reporting results across multiple variables or groups. A well-structured table might show each variable in its own row, with columns for group means (± SD), test statistics, and p-values. Give every table a clear, descriptive title that tells the reader what they’re looking at without needing to read the surrounding text.
Figures work best for showing patterns, distributions, and comparisons visually. Bar charts, box plots, and forest plots each serve different purposes. When marking statistically significant differences on a figure, use a consistent notation system (like asterisks) and define it in the figure legend. One asterisk for p < .05, two for p < .01, and three for p < .001 is a common convention.
Don’t duplicate the same data in both a table and a figure. Choose whichever format communicates the finding more effectively, and reference it in your text without simply repeating every number the reader can already see.
Putting It All Together
A complete statistical analysis write-up follows a logical sequence: describe your analytical plan and software in the methods, summarize your data with appropriate descriptive statistics, report each test’s results with exact p-values and effect sizes, and present the information visually where it helps. Throughout, the principle is transparency. Every decision you made, from choosing a test to adjusting for multiple comparisons, should be visible to the reader. The goal isn’t to impress with complexity. It’s to make your analysis reproducible and your conclusions trustworthy.