Explaining Numbers Without Overstating Your Findings

Numbers can make an academic argument precise, but only if readers know what was counted and how the value was produced. A percentage without a denominator, a change without a baseline, or an average without variation can invite the wrong conclusion. You do not need advanced mathematics to improve numerical reporting. Start by defining the measure, checking the calculation and matching your words to what the data actually show.

State the base and unit

“Forty per cent improved” raises immediate questions: forty per cent of whom, improved by what measure and compared with when? Report the count and denominator when useful, especially for small samples. Use consistent units across comparisons. If the analysis excluded missing responses, say how many remained. A change from two to four cases is a 100% increase but also only two additional cases; both pieces of information can matter.

Distinguish average from spread

An average can hide wide differences. Report a range or suitable measure of variation when it affects interpretation and the assignment permits it. Check whether an extreme value is an error, a real observation or a reason to present a different summary. Do not switch from mean to median simply because one produces a more favourable story. Explain the measure you chose and why it fits the data.

Separate association from causation

If two variables move together, ask whether the design establishes which came first and whether other factors could explain the pattern. A study without a suitable comparison cannot support a confident effect claim merely because its chart rises. Use phrases such as “was associated with” where appropriate. If you report an intervention, examine how groups were formed and whether outcomes were measured comparably.

Handle uncertainty honestly

A point estimate is not the whole result when sampling or measurement is uncertain. If your course expects confidence intervals or other uncertainty measures, report them correctly and explain their role. Avoid presenting a small difference as decisive based on decimal places alone. For qualitative counts, clarify that a count of coded comments is not automatically a count of participants or a population estimate.

Check every value against its source

Recompute important percentages from the underlying counts and confirm that text, table and figure agree. If you cite an external statistic, read the original definition and time period. Do not combine figures from different datasets as if they used the same measurement. A brief note on data limitations can prevent an otherwise strong report from making a claim the evidence cannot bear.

Worked example

If 12 of 20 respondents report a preference, write “12 of 20 respondents (60%) in this sample” rather than “60% of students prefer this”. The first sentence identifies the sample and result; the second projects it to an undefined population. If the recruitment was voluntary, mention that limit when interpreting the pattern. The arithmetic can be correct while the claim remains too broad.

An arithmetic and wording audit

Select one percentage in your draft and write the calculation in full: numerator divided by denominator, multiplied by 100, with the period and population named. Repeat for any reported percentage change, because “increased by five percentage points” and “increased by five per cent” mean different things. Check whether the spreadsheet excluded missing values and whether that exclusion is described. Then read the surrounding sentence as though you did not know the study. Would you assume the number describes all students, only respondents, or only a subgroup? Make the base explicit. Finally, compare the prose with the table and chart generated from the same data. This small audit catches both arithmetic errors and truthful numbers wrapped in misleading language.

Checklist before you submit

Report count, denominator and unit.
Choose a summary that reflects variation.
Use causal language only when the design supports it.
Reconcile numbers across prose, tables and figures.

Questions students ask

Are more decimal places more accurate?

No. Use precision that reflects the measurement and the conventions of your field.

Can a percentage from a small sample be useful?

Yes, with counts and context. Avoid treating it as a precise estimate for a much wider population.