DATIMORE · SYNTHETIC DEMONSTRATION · WEB-061

Trace a survey comparison from answers to percentages

All 55 records are invented. This is a calculation example, not a real survey, client result or estimate about a population. The example does not test a group difference or estimate how much a result could vary in a real survey.

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1. Know what the records mean

An invented programme collects voluntary feedback after morning, evening and weekend sessions in one reporting period. Each record stands for one person returning one survey, including those who skipped this question. People belong to one session group only. All receive the same question: “Was it easy to find the session information?” The choices are Yes and No.

Download the bilingual example pack (ZIP). It includes both language pages, 55 synthetic response records and the calculated cross-tab in CSV files. The files use the codes below. Open them in a spreadsheet to count each group's answers. These files do not say how many people were invited, so we cannot work out what share returned the survey.

• synthetic_id: a unique invented record identifier.
• session_group: morning, evening or weekend.
• answer: yes, no or skipped. Skipped means no answer was recorded; it is not No.
• weight: 1 for every record. All answers count equally; there is no adjustment to represent a wider population.

2. Check that the counts add up

Each group's total returns must equal Yes + No + skipped. The denominator, meaning the number we divide by, is Yes + No for that group's Yes percentage. It excludes skipped answers. Keep the skipped count alongside the result.

3. Read the output and the exception

• Morning: 18 ÷ 30 × 100 = 60% Yes among those who answered.
• Evening: 8 ÷ 10 × 100 = 80% Yes among those who answered.
• Weekend: zero answered. Division by zero is undefined. The CSV leaves yes_percent empty and marks percent_status as undefined_no_answers; it does not report 0%.

Wrong label, different result: 18 ÷ 40 × 100 = 45% is the share of all morning returns containing Yes. It is not the share of those who answered the question. This is why every percentage needs a visible denominator.

Small-group check: if one evening answer changes from Yes to No, the denominator stays 10 and 7 ÷ 10 × 100 = 70%. That is ten percentage points below 80%. This only shows what changing one answer does to the percentage. It does not estimate how much a real survey result might vary.

4. Keep the interpretation within the evidence

The table describes only these invented answers. It does not show that session timing caused a better experience or that the evening result would hold for all participants. In a real voluntary survey, people who do not take part and people who skip the question can affect the result. A larger count alone would not remove those concerns.

Before using this approach on real data, agree the groups, valid answers, denominator and missing-answer treatment with a method reviewer. They should check how people were chosen, whether some answers count more than others, and how many people are in each group. Ask them which further calculations, if any, the study supports. There is no universal minimum group size established by this example. Record who checks the interpretation and who owns the follow-up.