# Sample Size Calculator

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The sample size calculator is a free resource from ibp Strategy and Research which takes the pain out of calculating confidence intervals and sample sizes for quantitative research projects.

To use the tools, simply scroll down to the bottom of the page. However, it may be worthwhile to go over some of the definitions which are used commonly.

Remember, we are always happy to provide advice on a no obligation basis, just call Eddy Graham on 01698 846825 or e-mail e.graham@ibp.eu.com.

## Confidence Interval

The confidence interval is the figure you usually see in opinion polls which would be expressed as something like +3%. For a random sample and a given confidence level (see below) it tells you that, if the sample answered in a given way, then if you had asked everyone in the survey population, the answer would fall within the parameters set by the confidence interval (e.g. for a confidence interval of 3, results would be +3%).

## Confidence Level

The confidence level, on the other hand, tells you how "sure" you can be. A 95% confidence level is usually quoted which would mean that you would be 95% certain that results for the whole population would lie within the confidence interval given by the sample.

What determines Confidence Levels?

Three main factors need to be taken into account:

Sample size: The larger the sample size then the smaller your confidence interval. However, this is not a linear relationship; doubling the sample size does not halve the confidence interval.

Percentage response: The confidence interval also depends on the percentage of your sample that choose a given answer. If 90% of people respond in a given way, then the chances of an error are much lower than, if say, 50% of people respond that way. The rule of thumb is to calculate the confidence interval on the worst case percentage (50%) and also to use this percentage to determine a general confidence interval for a given sample size.

Population size: Population size only really matters when the sample is more than a few percent of the total population. For a population of, say 100,000 in a Council area the difference in confidence interval between sample sizes of 500 and 1,000 would be quite small. If, however, the "population" is 2,000 Housing Association tenants, then this change in sample size does make more of a difference.

Technically, all of this only holds true if you have a genuinely random sample. This does not mean that you can just pick anyone to interview. On the contrary, a truly random sample requires everyone in the population to have an equal chance of being selected for interview. This means that you have to be very careful to make sure that your sample is not skewed for or against any particular segment of the population. One technique which is often used is quota sampling. This works on the assumption that if a sample has the breakdown characteristics of a random sample (e.g. in relation to age, sex, working status and so on) then it will have the characteristics of a random sample. This is the assumption made in many large-scale surveys and opinion polls.

## A Final Word

Finally, in choosing your sample size or confidence interval, it is important to apply common sense. The purpose of research is to inform decision making and the methodology to be adopted needs to be cost-effective and proportionate in relation to the decision to be made. If you are making low risk, low cost decisions then you may not even need any research; you certainly shouldn't be incurring large costs. If however, you have to make difficult decisions about investment projects, or decisions that could have a big effect on how your organisation is perceived, then robust research, with appropriate sample sizes and well designed data gathering tools, is certainly recommended.

## Sample Size Calculator

(use this if you have a required confidence interval and survey population and need to know how many interviews you need to achieve that confidence interval)

 Confidence Level: 95% 99% Confidence Interval: Population: Sample size needed:

## Confidence Interval Calculator

(use this if you know the sample size and population and want to calculate the confidence interval. Remember, "percentage response" is the proportion of the sample giving a particular response to a question; it is not the proportion of the population who respond to a survey)

 Confidence Level: 95% 99% Sample Size: Population: Percentage Response: Confidence Interval: