# Precision in sampling

If you interviewed every single client – the whole client population – your dataset would be completely precise. If you calculated the percentage of clients that are in the bottom two wealth quintiles, the result would be the ‘true’ percentage of the client population in the bottom two quintiles. This is usually impossible, so you interview a sample of clients. The only downside of this is that a sample is different to the client population, so the results from the sample will be a little different to the ‘true’ percentages.

You can think of the ‘true’ client population percentage as being within a range around the sample percentage. If your sample is 100 respondents, the range will be around +/- 10%. For example, if 55% of your sample is in the bottom two national quintiles and your sample is 100 respondents, then the ‘true ’ figure will probably be between 45% and 55%. If the sample is 1000 respondents, the range will be around +/- 5%. If your sample has 1000 respondents and 55% of the sample was in the bottom two quintiles, you could be confident that true percentage would be between 40% and 50%. The bigger your sample, the more precise it is, the smaller the range.

The most critical factor in determining the sample size is how large a range you are willing to accept. The minimum sample sizes given in this toolkit will give you a range of about +/- 10% is quite a big range. If you would like a smaller range, so you can be more confident in your results, you’ll have to increase the sample size.

The ‘range’ is often referred to as the ‘95% confidence interval’, because you can be 95% sure that the true percentage is within that range.

Summary

• WE KNOW: Percentage from the sample
• WE WANT: Percentage from the population
• A sample gives you a range within which the population percentage probably is (the range is called a 95% confidence interval)