How To Calculate Sampling Error in 6 Steps

 How To Calculate Sampling Error in 6 Steps

Statistical error is a type of sampling error wherein the random fluctuation or deviation from true result occurs. In most cases, the sample size is small and therefore a large margin of error exists.

The most common method for calculating sampling error in market research is known as "margin of error". It is defined as half the level of confidence interval with absolute value given that value as a decimal. For example, if you would like to have your results to be 95% accurate, then the margin of error will need to be 0.05 multiplied by itself which equals 0.1025 (this translates into 10.25%).

When it comes to rounding off numbers, always round down unless otherwise specified (i.e., if it's 11.49%, round it down to 11%).

Margin of error is also often referred to as "confidence interval." They are the same thing. Confidence level simply means the probability your research results are true for the entire population of interest, while margin of error is the maximum amount by which you expect your statistics could be off before they would no longer be accurate.

The formula for calculating margin of error in 6 steps:

1. Determine your confidence level (CL) and sample size (n).

2. Multiply CL with n.

3. Divide result from step 2 by 6.94 or 1/√(6*n) . For more accurate calculations, use 6.94.

4. Take the square root of this result and round it off to 2 decimals or 1 significant digit, respectively.

5. Multiply your answer from step 3 by 100.

6. Add your answer from step 5 to itself to get the final value for margin of error (ME).

The formula in words: The margin of error equals one-half the level of confidence interval with absolute value given that value as a decimal times itself plus one hundred percent minus the product's square root divided by six point nine four or one over the square root of 6*n or 1/√(6*n) multiplied by 100%. Most calculators will do these calculations for you - input confidence level and sample size and hit the button.

Confidence Level (CL)

Sample Size (n)

Margin of Error (ME)

95%

500

0.1025

99%

100

0.0049

90%

1000

0.2254

The margin of error is a statistic expressing the amount of random sampling error in a survey's results. For example, if you ask a sample of 1,000 people their opinion on something, the margin of error tells you that your results are not going to be accurate to within 3 percentage points 95% of the time. It's also important to understand that one should never report a margin of error without also saying what the level of confidence is for that number. A 95% level of confidence means that, if this survey were to be repeated using exactly the same questions and the same methodology (with an infinite number of samples), it would produce the true percentage in the long run 95% of the time.

The margin of error can either be positive or negative depending on whether you're dealing with a Republican or Democrat pollster. If your candidate takes 48 percent in a national poll and has a 3-point lead, he's doing pretty well – but maybe not as well as other polls suggest. Why? Probably because it's only a random sample and there could be fluctuations from random sampling error that cause results to vary from the actual election results. The margin of error is a way to quantify those random fluctuations and calculate how accurate we think our survey sample is, based on how many people we actually sampled.

Now that's something you can expect for sure! If I had to guess what percentage of Americans vote Republican, I would say it's around 55%. But if the national total was 51% last time (Romney) or 47% (McCain), then my guess was off by several points – maybe even enough that I'd be wrong in saying that most Americans are Republicans.

The margin of error reflects what statisticians call sampling variation; since the findings from different samples might differ slightly, the size of those differences may be described quantitatively as the margin of error. The margin of error can be defined in several different ways, but in general it represents the level of inaccuracy that exists with a sampling method because only a sample – and not everyone – was questioned. While this may seem confusing, the calculation of the margin of error merely provides an estimate for how much larger or smaller a specific percentage is from one research study to another – for instance, if 20 out of 30 people sampled were Republican supporters, the 60% support level could actually range between 56-64%.

There are many factors that influence the size of the margin of error which depend on both the size and nature of the statistical difference being measured as well as on who's being surveyed. In addition to issues such as question wording and the order in which questions are asked, the margin of error is also affected by population size. The margin of error shrinks as the sample size grows, so it's especially important to have a large sample size when measuring small percentages.

There are two ways to calculate the margin of error: the standard error and the confidence interval. The standard error is the more common calculation and it's simply the standard deviation divided by the square root of the number of samples. The confidence interval takes into account both the standard error and the level of confidence, which is why it's usually reported instead of the margin of error. The confidence interval is calculated by multiplying the standard error by 1.96 (1/sqrt(2)) and then adding or subtracting that number to the sample estimate.

In conclusion, the margin of error is a statistic used in survey sampling which measures how much a result might vary from one similar study to another. The margin of error can either be positive or negative depending on whether you're dealing with a Republican or Democrat pollster and is usually reported along with the level of confidence that applies to it (95%, for example).

The calculation of the margin of error is affected by many factors including population size, question wording and order, and who was surveyed – but this figure is useful because it tells us how accurate we think our results are based on random variation. It's important to note that everyone interviewed was not actually sampled so there could be more or less Republican supporters than the poll reflects. Read about Sample Management Software.

Thanks for reading!