## Required level of confidence

In discussing the virtues of random sampling earlier in this chapter, it was pointed out that one of these lies in being able to calculate the level of confidence one can have that the results achieved by the sample are likely to give a true indication of results in the underlying population. Common sense, and the statistical formula, indicate that the higher the level of confidence required in the results then the larger the size of sample necessary. What common sense does not make clear but the formula does, is that to increase the level of confidence from the 68% level (i.e. a 1 in 3 risk of the sample not being a good one) to the 95% level more commonly used (i.e. only a 1 in 20 risk that the sample is not a good one) it is necessary to multiply the sample size by a factor of 4. If a survey of 100 respondents indicated that 28% of all households had a separate freezer at the 68% level of confidence, to increase the level of confidence in the results to the 95% level, a survey of 400 respondents would be required.

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