## Required limits of accuracy

It also makes sense at an intuitive level to accept that the larger the size of the sample the more accurate the results are likely to be as a predictor of population values. Once again, the statistical formula of sampling theory makes it possible to quantify this relationship. The relationship is inverse and square. That piece of statistical jargon simply says that to double the accuracy in the results (i.e. to halve the allowable range in the limits of accuracy) it would be necessary to multiply the size of the sample by 4. In the example above, if the sample of 400 respondents indicated that at the 95% level of confidence 28% of all households had a separate freezer within limits of accuracy of 10%, this would indicate between 25.2 and 30.8% of all homes have separate freezers. For greater precision the limits of accuracy must be reduced. To halve this to +5 or - 5% (i.e. between 26.6 and 29.4%) a sample size of 1600 would be required.

To summarize, then, sampling theory indicates that in random samples three factors should be taken into account in deciding the size of the sample: variability in the population, the level of confidence wanted in the results, and the limits of accuracy acceptable to the decision maker. All of these can be decided before the survey takes place, and the sample size calculated to meet the requirements for confidence and accuracy in the results.

However, three further factors need to be considered before the size of sample can be determined, as follows.

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