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include the margin of error. The general formula for the margin of error for a sample proportion (if certain conditions are met) is where is the sample proportion, n is the sample size, and z* is the appropriate z*-value for your desired level of confidence (from the following table). z*-Values for Selected (Percentage) Confidence Levels Percentage Confidence z*-Value 80 1.28 90 1.645 95 1.96 98 2.33 99 2.58 Note that these values are how to calculate margin of error in statistics taken from the standard normal (Z-) distribution. The area between each z* value and the negative of that z* value is the confidence percentage (approximately). For example, the area between z*=1.28 and z=-1.28 is approximately 0.80. Hence this chart can be expanded to other confidence percentages as well. The chart shows only the confidence percentages most commonly used. Here are the steps for calculating the margin of error for a sample proportion: Find the sample size, n, and the sample proportion. The sample proportion is the number in the sample with the characteristic of interest, divided by n. Multiply the sample proportion by Divide the result by n. Take the square root of the calculated value. You now have the standard error, Multiply the result by the appropriate z*-value for the confidence level desired. Refer to the above table for the appropriate z*-value. If the confidence level is 95%, the z*-value is 1.96. Here's an example: Suppose that the Gallup Organization's latest poll sampled 1,000 people from the United States, and the results show that 520 people (52%) think the president is doing a good job, compared to 48% who don't think so. First, assume you want a 95% level of confidence, so z* = 1.96. The number of Americans in the sample who said they ap

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test AP formulas FAQ AP study guides AP calculators Binomial Chi-square f Dist Hypergeometric Multinomial Negative binomial Normal Poisson t Dist Random numbers Probability Bayes rule Combinations/permutations Factorial Event counter Wizard Graphing Scientific Financial Calculator books AP calculator review Statistics AP study guides http://stattrek.com/estimation/margin-of-error.aspx Probability Survey sampling Excel Graphing calculators Book reviews Glossary AP practice exam Problems and solutions Formulas Notation Share with Friends Margin of Error In a confidence interval, the range of values above and below the sample statistic http://www.genroe.com/blog/how-to-calculate-margin-of-error-and-other-stats-for-nps is called the margin of error. For example, suppose we wanted to know the percentage of adults that exercise daily. We could devise a sample design to ensure that our sample estimate will not differ from the margin of true population value by more than, say, 5 percent (the margin of error) 90 percent of the time (the confidence level). How to Compute the Margin of Error The margin of error can be defined by either of the following equations. Margin of error = Critical value x Standard deviation of the statistic Margin of error = Critical value x Standard error of the statistic If you know the standard deviation of the statistic, use the margin of error first equation to compute the margin of error. Otherwise, use the second equation. Previously, we described how to compute the standard deviation and standard error. How to Find the Critical Value The critical value is a factor used to compute the margin of error. This section describes how to find the critical value, when the sampling distribution of the statistic is normal or nearly normal. The central limit theorem states that the sampling distribution of a statistic will be nearly normal, if the sample size is large enough. As a rough guide, many statisticians say that a sample size of 30 is large enough when the population distribution is bell-shaped. But if the original population is badly skewed, has multiple peaks, and/or has outliers, researchers like the sample size to be even larger. When the sampling distribution is nearly normal, the critical value can be expressed as a t score or as a z score. When the sample size is smaller, the critical value should only be expressed as a t statistic. To find the critical value, follow these steps. Compute alpha (α): α = 1 - (confidence level / 100) Find the critical probability (p*): p* = 1 - α/2 To express the critical value as a z score, find the z score having a cumulative probability equal to the critical probability (p*). To expre

Score® Net Promoter Software Overview Features Reports Survey Audits CX Implementation Implementation Overview Customer Journey Mapping Achieving Customer Focus Root Cause Analysis and Action Net Promoter® Net Promoter Score® Best Practice Implementation B2B Services CustomerGauge Software Net Promoter Benchmarking Blog How to calculate Margin of Error and other stats for NPS® By Adam Ramshaw 31 Comments Your boss walks in with a chart of the last 12 months of transactional Net Promoter® survey results and he’s not happy! The score went down last month and he want's to know why. Looks like you’ll have to hunt around to find a reason for the change; or will you? Just because your survey score has gone down, or up, doesn’t mean that there has actually been a change in the overall business NPS. It might just be a fluke of the sample you have collected. The change might be within the Margin of Error. What is Margin of Error? When you run a survey, say NPS, you are trying to determine the NPS of all your customers. The problem is that you are never able to collect a response from every single customer. In reality you make do with a sample; maybe 10% of your customers respond. So, rather than calculating the NPS of all your customers you are only estimating it based on the customers who responded. Now, by random chance in this survey you might get responses from a set of very happy or very unhappy customers. This results in the actual score being lower or higher than you the score for the sample you have collected. The problem is: how do you know how close your estimate is to the actual NPS? You can discover this by calculating a Margin of Error. This will tell you that you can be, say, 95% certain that the NPS for all your customers is between your sample score plus the Margin of Error and the sample score minus the Margin of Error. So before you break out the hard hats and wait for the blame game to start you need to determine if a real change has occurred. The problem with Net Promoter is that the statistics that you normally use for survey scores don’t work so well for NPS. However, there is an approach that you can use to determine if the change is s

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