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Sample Size Calculator
What does it do?
The sample size calculator on the next page allows you to calculate the required sample size, standard error, RSE, and a confidence interval (95% or 99%) for a proportion estimate, using just one of these criteria as an input. For example, if you know the minimum standard error you require to ensure the precision of your estimate, you can find out the sample size required to achieve that; if you know the likely size of the responding sample you can estimate the standard error of your estimate, and a confidence interval for it.
The Statistical Clearing House recommends that you set the level of precision that will meet needs of the users of your data. The level of precision should be set in conjunction with the users of the data. You should not set the accuracy levels too high, as you will incur higher costs and place additional burden on the community. You should also not set the accuracy levels too low, as your data will not be approriate for your users.
Depending on the intended uses of the information, precision may not be the only concern. Consideration also needs to be be given to cost, turnaround and respondent burden. When deciding whether to increase precision, returns to scale must be considered. A small increase in precision that incurs a large cost may not be justified.
The sample size calculator assumes simple random sampling. The results generated here are intended only as rough guidelines and should only be used as such - they are by no means the definitive "rule" about the size of a sample.
How do I use it?
Simply follow the steps outlined below.
1. Select the confidence level you want to work at.
2. If you are sampling from a finite population (one that isn't very large), enter the size of the population here.
3. If you already roughly know the proportion you're estimating, or want to check the RSE of an existing estimate, fill in the proportion. If left blank it will be assumed to be 0.5.
4. You must fill in one of Confidence Interval Range, Standard Error, Relative Standard Error or Sample Size. Make sure the bullet point corresponding to the one you wish to specify is selected.
5. Press Calculate to perform the calculation, or Clear to start again.
What do the categories mean?
Confidence Level
This is the chance that the true value will be inside the confidence interval calculated. You can select 95% or 99%.
Population Size
This option allows you to specify the size of the population of interest. This option can be left blank, in which case it will be assumed to be very large (typically, populations of size more than 100,000 are considered very large).
Proportion
This option allows you to specify the estimated proportion, if it is approximately known. This assists in calculating the estimate standard errors which are appropriate for your situation. The proportion may be sourced from previous cycles of the survey or by a educated guess.
Confidence Interval +/-
The Sample Size Calculator allows you to express the precision in terms of "some value plus or minus an amount". For example, if you want your result to be accurate to within 5% (ie. plus or minus 5%) then you should specify 0.05 here. Note that the value must be entered as a proportion, not as a percentage.
Upper and Lower
These are the upper and lower bounds of the confidence interval. You cannot enter them, but they will be displayed once the calculation is made.
Standard Error
This is the standard error of the estimate. Standard error is a measure of the variation of any estimate that is produced by sampling a given population. This gives us an idea of the likelihood that the estimate is near the true value. The standard error is expressed in the same units as the estimate (in the case of any calculations done with this calculator, it is a proportion). A higher standard error means the estimate is more variable.
Relative Standard Error (RSE)
This is the Standard Error expressed as a percentage of the estimate itself. For example if the estimate is 0.5 and the standard error is 0.05, then the RSE will be 10%. RSE is often used in preference to standard error when comparing the variability of samples of different magnitudes. The RSE places the Standard Error in the context of the estimate. For example, for an estimate of 0.01, a standard error of 0.1 would be of much greater issue than for an estimate of 0.5. In the first case, the RSE is 1000%, while in the second case it is much smaller (20%).
Sample Size
This is the sample size required for the standard error or confidence intervals displayed. You can also specify the sample size to have standard error and the confidence interval calculated for you.
What do the results mean?
The Confidence Level, Population Size, and Proportion were all entered as inputs to the calculation.
The Confidence Interval p+/- field shows the precision of the estimate in terms of the plus or minus value. In this case, 0.1 was entered (since the bullet point next to this field is selected), because we wanted to know what sample size was needed to be 95% sure that the proportion within 0.1 of 0.3 (ie. 0.3 +/- 0.1).
The Upper and Lower fields show the upper and lower bounds of the confidence interval. In this case, we know with 95% certainty that the proportion lies between 0.2 and 0.4.
The Standard Error is a measure of the variability of the estimate of 0.3 that would be formed from a sample size of 75.
The Relative Standard Error, in this case 17.01%, is the standard error expressed as a percentage of the estimate of p. In this case it is given by:
This can be used to directly compare the precision of different estimates (including both estimates of different values of p, and ones with different sample size).
The Sample Size is the minimum number of respondents required to achieve the precision specified (in this case, to be 95% sure that the value of p is between 0.2 and 0.4 we would need to have at least 75 respondents). This does not take into account any kind of non-sampling error, and assumes that the respondents are randomly sampled from a population (that is, every unit in the population has an equal chance of responding).
Click here to begin using the Sample Size Calculator...
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