How to Analyse Quantitative Data

Quantitative analysis goes wrong long before the first test is run. Most errors come from skipping the unglamorous steps between data collection and statistics.

Students often treat analysis as the moment they open a statistics package and click through menus. In practice, the tests are the smallest part of the job. The work that decides whether your findings stand up is the cleaning, the checking and the decisions you make about what each variable actually measures. This guide walks through the sequence in the order it should happen, so that by the time you report a p-value you can defend every step that produced it.

Start from the research question, not the data

Before touching the dataset, write your research question and any hypotheses at the top of a working document. Each analysis you run should map to one of them. Without that anchor, it is easy to run dozens of tests, notice the ones that came out significant and build a story around them after the fact. Examiners call this fishing, and it undermines otherwise careful work.

For each question, note the outcome variable, the predictor or grouping variable, and the comparison you expect to make. That short list becomes your analysis plan, and it will save hours later.

Clean the dataset before anything else

Raw data is almost never ready for analysis. Survey exports contain test responses, duplicate submissions and participants who clicked the same answer for every item. Spreadsheets contain typing errors, inconsistent codes and values that are physically impossible, such as an age of 245.

• Remove or flag duplicates and test entries, and record how many.
• Check every variable’s range for impossible or implausible values.
• Make coding consistent — “F”, “female” and “2” cannot all mean the same thing.
• Reverse-score negatively worded items before building any scale totals.

Keep the original file untouched and do all cleaning in a copy, ideally with a log or script that records each change. If an examiner asks why your sample is 184 rather than the 212 who responded, you should be able to answer precisely.

Decide how to handle missing data

Missing values are normal, but how you deal with them changes your results. Deleting every case with any missing value is the default in many packages and can quietly shrink your sample by a third. Before choosing an approach, look at how much is missing and whether it follows a pattern — if one group skipped a question far more than another, the gap itself is a finding.

For small amounts of randomly scattered missingness, analysing the available cases is usually defensible. For more, consider whether multiple imputation is appropriate and whether your supervisor expects it. Whatever you choose, report it.

Describe before you test

Descriptive statistics are not a formality to get through before the real analysis. They tell you what your sample looks like, whether your variables behave as expected and whether the tests you planned are even appropriate. Report counts and percentages for categorical variables, and means with standard deviations — or medians with interquartile ranges for skewed data — for continuous ones.

Plot everything. A histogram reveals skew, outliers and floor effects that a mean conceals. A scatterplot shows whether a relationship is linear before you fit a straight line to it.

Check the assumptions of your planned tests

Every parametric test makes assumptions: approximately normal residuals, similar variances across groups, independent observations and, for regression, a linear relationship. Check them rather than asserting them. Visual checks such as Q-Q plots and residual plots are often more informative than formal tests, which become oversensitive in large samples.

Run the analysis that answers the question

With a clean dataset and checked assumptions, run the tests in your plan. Resist the urge to add more because the first results were disappointing. Null findings are findings, and a well-powered study that finds no difference has told you something useful. If you do run additional exploratory analyses, label them clearly as exploratory so readers weigh them accordingly.

Where you run many comparisons, consider whether a correction for multiple testing is needed. Ten independent tests at the 0.05 level give roughly a forty per cent chance of at least one false positive.

Report effect sizes, not just significance

A p-value tells you whether an effect is unlikely to be zero; it says nothing about whether it matters. With a large enough sample, trivial differences become statistically significant. Report an effect size — Cohen’s d, a correlation coefficient, an odds ratio or a difference in means — with a confidence interval, and interpret it in the context of your field.

Present results in tables and figures that stand alone

Each table or figure should be readable without the surrounding text: a clear title, labelled axes, units, sample sizes and a note explaining abbreviations. Do not repeat every number in both a table and the prose. Use the text to direct the reader to what matters, and let the table carry the detail.

Follow the formatting conventions of your referencing style for statistics — APA, for instance, specifies italicised test symbols and the number of decimal places.

Separate results from interpretation

The results chapter states what you found; the discussion explains what it means. Mixing the two makes it hard for readers to see where evidence ends and argument begins. In results, report the analysis plainly. Save causal language, comparisons with the literature and speculation about mechanisms for the discussion, where they can be properly qualified.

Keep a record you could hand to someone else

The final test of a quantitative analysis is whether another person could repeat it from your notes and get the same numbers. Keep the cleaned dataset, a codebook describing every variable, and the syntax or script used for each analysis. Many supervisors now ask for these as appendices, and even where they do not, having them makes corrections after feedback quick rather than painful.