Big Margin Error
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accurate, assuming you counted the votes correctly. (By the way, there's a whole other topic in math that describes the errors people can make when they try to measure things like that. But, for now, let's assume you how is margin of error calculated in polls can count with 100% accuracy.) Here's the problem: Running elections costs a lot of money. It's high margin of error definition simply not practical to conduct a public election every time you want to test a new product or ad campaign. So companies, campaigns and how to find margin of error news organizations ask a randomly selected small number of people instead. The idea is that you're surveying a sample of people who will accurately represent the beliefs or opinions of the entire population. But how many people do you need margin of error sample size to ask to get a representative sample? The best way to figure this one is to think about it backwards. Let's say you picked a specific number of people in the United States at random. What then is the chance that the people you picked do not accurately represent the U.S. population as a whole? For example, what is the chance that the percentage of those people you picked who said their favorite color was blue does not match the percentage
Margin Of Error Vs Standard Error
of people in the entire U.S. who like blue best? Of course, our little mental exercise here assumes you didn't do anything sneaky like phrase your question in a way to make people more or less likely to pick blue as their favorite color. Like, say, telling people "You know, the color blue has been linked to cancer. Now that I've told you that, what is your favorite color?" That's called a leading question, and it's a big no-no in surveying. Common sense will tell you (if you listen...) that the chance that your sample is off the mark will decrease as you add more people to your sample. In other words, the more people you ask, the more likely you are to get a representative sample. This is easy so far, right? Okay, enough with the common sense. It's time for some math. (insert smirk here) The formula that describes the relationship I just mentioned is basically this: The margin of error in a sample = 1 divided by the square root of the number of people in the sample How did someone come up with that formula, you ask? Like most formulas in statistics, this one can trace its roots back to pathetic gamblers who were so desperate to hit the jackpot that they'd even stoop to mathematics for an "edge." If you really want to know the gory details, the formula is derived from the standard d
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Margin Of Error Ti 84
email Submit RELATED ARTICLES How Sample Size Affects the Margin of Error Statistics margin of error ap gov Essentials For Dummies Statistics For Dummies, 2nd Edition SPSS Statistics for Dummies, 3rd Edition Statistics II for Dummies Load more margin of error excel EducationMathStatisticsHow Sample Size Affects the Margin of Error How Sample Size Affects the Margin of Error Related Book Statistics For Dummies, 2nd Edition By Deborah J. Rumsey In statistics, the two most important http://www.robertniles.com/stats/margin.shtml ideas regarding sample size and margin of error are, first, sample size and margin of error have an inverse relationship; and second, after a point, increasing the sample size beyond what you already have gives you a diminished return because the increased accuracy will be negligible. The relationship between margin of error and sample size is simple: As the sample size increases, the margin of http://www.dummies.com/education/math/statistics/how-sample-size-affects-the-margin-of-error/ error decreases. This relationship is called an inverse because the two move in opposite directions. If you think about it, it makes sense that the more information you have, the more accurate your results are going to be (in other words, the smaller your margin of error will get). (That assumes, of course, that the data were collected and handled properly.) 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 you find z* using 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 From the table, you find that z* = 1.96. The number of Americans in the sample who said they approve of the president was found to be 520. This means that the sample proportion, is 520 / 1,000 = 0.52. (The sample size, n, was 1,000.) The margin of error for this polling question is calculated in the following way: Accord
discussed in the previous section, the margin of error for sample estimates will shrink with the square root of the sample size. For example, a typical margin of error for sample percents for different sample sizes is given in Table https://onlinecourses.science.psu.edu/stat100/node/17 3.1 and plotted in Figure 3.2.Table 3.1. Calculated Margins of Error for Selected Sample Sizes Sample Size (n) Margin of Error (M.E.) 200 7.1% 400 5.0% 700 3.8% 1000 3.2% 1200 2.9% 1500 2.6% 2000 2.2% 3000 1.8% 4000 1.6% 5000 1.4% Let's look at the implications of this square root relationship. To cut the margin of error in half, like from 3.2% down to 1.6%, you need four times as big of a margin of sample, like going from 1000 to 4000 respondants. To cut the margin of error by a factor of five, you need 25 times as big of a sample, like having the margin of error go from 7.1% down to 1.4% when the sample size moves from n = 200 up to n = 5000.Figure 3.2 Relationship Between Sample Size and Margin of Error In Figure 3.2, you again find that as the sample size increases, margin of error the margin of error decreases. However, you should also notice that there is a diminishing return from taking larger and larger samples. in the table and graph, the amount by which the margin of error decreases is most substantial between samples sizes of 200 and 1500. This implies that the reliability of the estimate is more strongly affected by the size of the sample in that range. In contrast, the margin of error does not substantially decrease at sample sizes above 1500 (since it is already below 3%). It is rarely worth it for pollsters to spend additional time and money to bring the margin of error down below 3% or so. After that point, it is probably better to spend additional resources on reducing sources of bias that might be on the same order as the margin of error. An obvious exception would be in a government survey, like the one used to estimate the unemployment rate, where even tenths of a percent matter. ‹ 3.3 The Beauty of Sampling up 3.5 Simple Random Sampling and Other Sampling Methods › Printer-friendly version Navigation Start Here! Welcome to STAT 100! Faculty login (PSU Access Account) Lessons Lesson 2: Statistics: Benefits, Risks, and Measurements Lesson 3: Characteristics of Good Sample Surveys and Comparative Studies3.1 Overview 3.2 Defining a Common Language for Sampl