 # Survey Probability Calculator

This calculator requires the use of Javascript enabled and capable browsers. This calculator is designed to give a reasonable set of results concerning survey sampling numbers. In order to get accurate information in the field, we have surveyed survey organizations. The information presented here and the method of projecting the sample information is a compilation of those interviews and public domain information on the subject.

There are actually two calculators; one for establishing the size requirements of a sample group, based on information you provide, and the other to establish the confidence value factor required in the sample size calculator, assuming that you don't already know it. With these tools, you can determine how many people to interview to get a desired plus or minus base figure for your survey's answers reflective of the target overall group as precisely as needed. You can also ascertain the approximate level of precision you have in an existing sample. Before using the sample size calculator, there are definitions that you need to understand in concept. They are confidence value and confidence level. The confidence value is the plus or minus figure usually reported in media opinion poll results; it is often termed incorrectly as accuracy ratio. For example, if you use a confidence value of 8, and 40% percent of voters select one candidate, the poll is valid in that if all voters were questioned about candidate choice, between 32% (40-8) and 48% (40+8) would have picked that candidate. The confidence level tells you how sure you can be. It is expressed as a percentage and represents how often the true percentage of the overall group who would pick, in the case of our voters, a particular candidate, lies within the confidence value. The 95% confidence level means you can be 95% certain; the 99% confidence level means you can be 99% certain. Most researchers use the 95% confidence level. When you put the confidence level and the confidence value together, you can say that you are 95% sure that the true percentage of the overall group is between 32% and 48%. The wider the confidence value you are willing to accept, the more certain you can be that the whole overall group answers would be within that range. As an example, if you asked a sample of 1000 voters in a city which candidate they preferred, and 70% selected candidate one, you can be very certain that between 50 and 90% of all the voters in the city actually would select that candidate, but the call is uncertain that between 69 and 71% of the voters would choose that candidate.

There are three factors that determine the size of the confidence value for a given confidence level. These are sample size, percentage and overall group size. The larger your sample, the more sure you can be that their answers truly reflect the overall group. This indicates that for a given confidence level, the larger your sample size, the smaller your confidence value; the smaller the confidence value, the more accurate your survey. This relationship, unfortunately, is not linear in that doubling the sample size does not reduce the confidence value by 50%. The accuracy also depends on the percentage of the sample that picks a particular candidate. If 99% of your sample selected candidate one and 1% selected candidate two, the possibility of error is very low, no matter what the sample size. However, if the percentages are 55% and 45% respectively, the possibility of error is much higher. It is easier to establish validity of extreme answers than very close ones. When determining the sample size needed for a given level of accuracy you must use the worst case laws of probability percentage, which is fifty percent (50%). You should also use this percentage if you want to determine a general level of accuracy for a sample you already have.

To determine the confidence value for a specific selection your sample has given, you can use the percentage picking that selection and get a smaller value. How many people are there in the overall group your sample represents? This may be the number of people in a city you are studying, the number of people who own computers, the number of people who surf the Internet or anything similar. Often you may not know the exact group size. This does not present an insurmountable problem; in fact it is not really a problem at all. The mathematical laws of probability provide proof the size of the overall group is not entirely relevant, unless the size of the sample exceeds a few percent of the total overall group being evaluated. This means that a sample of 500 people is equally useful in examining the opinions of a state of 15,000,000 as it would a city of 100,000. For that reason, this calculator and most survey organizations ignore the overall group size when it is very large (in comparison to the sample) or if it is unknown. Overall group size is only a possible factor when you work with a relatively small and known group of people that are likely to have similar views or ideas. In that situation, you are likely to know the size of the overall group anyway. The confidence value calculations assume you have a genuine random sample of the relevant overall group. If your sample is not truly random, you cannot rely on the values. Non-random samples usually result from a poorly conceived sampling procedure, thus generating flawed data. An example of such a flaw is to only call people during the day, and miss almost everyone who works. Such a procedure is obviously flawed and for most purposes (in this example), the non-working overall group cannot be assumed to accurately represent the entire (working and non-working) overall group.

Enter the value for confidence level by selecting either 95% (default) or 99%, and the confidence value with a numeric value; the default is 6. The lower the confidence value, the larger your sample size will be. (If you don't know the confidence value, use the lower calculator to establish it.) If the overall group is very large or unknown, leave the population field empty, the default condition. Click on Calculate for the returned sample size requirement.

To establish the confidence value, enter the value for confidence level by selecting either 95% (default) or 99%. Also enter the sample size number and the overall group number, if you have it. The default for the sample size is 1000 and the overall group is blank. The laws of probability percentage default is the worst case scenario, 50%. You may alter that to a lower or higher value if your sample group AND overall group is controlled to some degree. Either way will lower the confidence value since 50% is already the worst case scenario. Then, click on Calculate to determine a confidence value.

 Designation Number Determine Sample Size Required Data Entry Confidence Level 95% 99% Confidence Value Overall Group Calculated Results Sample Size Required
 Designation Number Find Confidence Value Required Data Entry Confidence Level 95% 99% Sample Size Overall Group Percentage Calculated Results Confidence Value
Updated 8.15.11

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