The target population for Natsal is the British general population but it’s not feasible to interview the millions of adults living in Britain. Instead, Natsal just looks at a sample of the British general population.

For Natsal-3, the size of this sample was 15,162 people aged 16 to 74 years. This sample size was worked out using a statistical formula so that enough people would be included to give sufficient ‘statistical power’ to confidently detect ‘statistically significant’ differences between key groups – like gender or age-groups for the main behaviours and attitudes of interest. However, there may not be sufficient numbers of people from minority groups in the overall sample to be able to detect differences as statistically significant for these smaller groups or ‘sub-populations’ as well as outcomes that are less common.

It is important to therefore recognise that a difference in percentages between groups may not correspond to a true or genuine difference in the population. For example, if 45% of women who identify as heterosexual report something but only 25% of women who identify as bisexual or lesbian do, then while this may seem like a true difference it might not be because of the relatively small number of lesbian and bisexual participants in the overall sample.

We analyse data from a sample of the overall ‘target population’ as it’s not feasible (or necessary) to collect data from everyone in Britain. This means that we are using what Natsal participants tell us so that we can estimate what’s going on in the population as a whole.

For example, from the Natsal-3 sample we can estimate the proportion of the population that has had sex for the first time at a young age. This is possible because the larger the sample then the more confident we can be about the precision of the estimate we generate from our sample and what this means for the population as a whole.

Statisticians use formulae to work out how large is large enough to get estimates for the population that are sufficiently precise for those who need to use the estimates, like policymakers. This means that we don’t waste resources collecting data from a sample that is unnecessarily large.

You may have heard the expression “lies, damn lies, and statistics” which originates from data and statistics being misused and/or used to intentionally mislead.

It is really important therefore to be as transparent as possible about the data and statistics underlying any analyses. This includes stating the data source (e.g. Natsal-3), who the statistics are based upon (e.g. everyone regardless of their sexual experience or just those reporting that they had had sex during a particular timeframe), any exclusions (e.g. people who refused to answer the corresponding question – especially if this is a considerable number), and the statistical techniques used (e.g. rather than just saying ‘average’ state the type of average – mean or median).

As a result, tables and charts often end up having lots of footnotes, but this is good practice. Because all those details help to maximise transparency and enhance the reader’s trust in the reported findings.

Differences can be statistically significant even if they’re small in absolute terms. This reflects the size of the sample upon which the statistics are based and therefore the amount of ‘statistical power’ available to detect a difference as ‘statistically significant’.

These elements – ‘statistical power’ and ‘statistical significance’ – are taken into consideration when a study like Natsal is planned and decisions are made regarding how many people to include in the study’s sample. For example, where an outcome is relatively rare in the target population, such as the proportion of the general population that is HIV positive, then a larger sample will be needed to detect statistically significant differences between groups, than an outcome that is relatively common.

It is worth remembering that a difference maybe statistically significant but it may not necessarily be of clinical or public health significance where other criteria may need to be taken into consideration. It is therefore really important to look at the percentages and the corresponding numbers in the groups being compared.

Numbers generated from a survey like Natsal can be incredibly useful for understanding what is going on in the population, but they can’t tell us everything. It is important to recognise this limitation and consider how quantitative data (that is, data derived from numbers) can complement - and be complemented by - qualitative data (that is, data which are not derived from numbers and include spoken words).

Typically, we can think about quantitative data helping us to understand the ‘what, when, where’ questions, while qualitative data can provide insights into the ‘why’ and ‘how’ questions.

For this reason, sometimes quantitative research can be useful to provide pointers as to the questions qualitative research needs to ‘unpack’, while other times, qualitative research is first needed to help identify the questions and response options that a survey should ask. Indeed, research often benefits from both quantitative and qualitative methods being used iteratively.

If you would like to learn more about statistics, then there are a number of free courses available to you. For instance, OpenLearn’s course called “Prices, location and spread” covers the mean and median (and compares these) in the section on “Measuring location”. The free course “Mathematics for science and technology” provides even more information, with the sections on “Statistics and repeated measurements” and “Statistics and sampling” being particularly relevant.