What the Margin of Error Tells You About a Statistical Sample
How to Create a Confidence Interval for the Difference of Two Means with Unknown Standard Deviations and/or Small Sample Sizes
How to Find the Cutoff Point for Rejecting a Null Hypothesis

Why Margin of Error and Confidence Intervals Matter in Statistics

Statistical results should always include a margin of error and confidence intervals. This information is important because you often see statistics that try to estimate numbers pertaining to an entire population based on a survey of only a part of the population; in fact, you see these statistics almost every day in the form of survey results. For example, the media tells you what the average gas price is in the U.S., how Americans feel about the job the president is doing, or how many hours people spend on the Internet each week.

But no one can give you a single-number result and claim it’s an accurate estimate of the entire population unless he collected data on every single member of the population. For example, you may hear that 60 percent of the American people support the president’s approach to healthcare, but you know they didn’t ask you, so how could they have asked everybody? And since they didn’t ask everybody, you know that a one-number answer isn’t going to cut it.

What’s really happening is that data is collected on a sample from the population (for example, the Gallup Organization calls 2,500 people at random), the results from that sample are analyzed, and conclusions are made regarding the entire population (for example, all Americans) based on those sample results.

The bottom line is, sample results vary from sample to sample, and this amount of variability needs to be reported (but it often isn’t). The statistic used to measure and report the level of precision in a study’s sample results is called the margin of error. In this context, the word error doesn’t mean a mistake was made; it just means that because you didn’t sample the entire population, a potential gap will exist between your results and the actual value you are trying to estimate for the population.

For example, someone finds that 60% of the 1,200 people surveyed support the president’s approach to healthcare and reports the results with a margin of error of plus or minus 2%. Then the final result would be reported that the support for the president’s approach to healthcare is likely between 58% and 62%. This range is called a confidence interval.

Everyone is exposed to results including a margin of error and confidence intervals, and with today’s data explosion, many people are also using them in the workplace. Be sure you know what factors affect margin of error (like sample size and level of confidence) and what the makings of a good confidence interval are and how to spot them. You should also be able to find your own confidence intervals when you need to.

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Creating a Confidence Interval for the Difference of Two Means with Known Standard Deviations
How to Calculate the Margin of Error for a Sample Mean
How to Determine the Confidence Interval for a Population Proportion
How to Calculate the Margin of Error for a Sample Proportion
How to Calculate a Confidence Interval for a Population Mean When You Know Its Standard Deviation
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