Margin Of Error Derivation
Contents |
of Error for Small Populations” teaser: “A comment on why does a pollster reported a narrow margin of error despite the small sample.” date: 2015-10-13 09:00:00 categories: - R tags: - R - Survey - Margin of error comments: true show_meta: false — I receive an margin of error calculator email asking for a possibly wrong doing with the margin of error calculated by the
Margin Of Error Excel
Datafolha’s newest poll. This polling firm often survey the population with a regular sample (1000/2400), usually calculating a margin of error of +/-3% to
Margin Of Error Confidence Interval Calculator
+/-2%. However, this time, the pollster sampled 340 congressmen out of 594 (513 deputies + 81 senators), reporting a margin of error of 3%. This puzzled the attentive reader who knows the margin of error is an inverse square root
Margin Of Error Definition
function of the sample size, so she asked: “Is the margin of error reported here is correct? Shouldn’t it be something around 5.4% given the reduced sample size? First of, I found the poll very interesting. Datafolha should conduct polls like that more often. So, we can get to know about the average position of our representatives. My answer to the inquiry was “sort of”. Firstly, given the fact the population of congressmen is a finite population, we must apply margin of error in polls a corrector factor for finite populations (FPC), which will reduce the standard error of the mean. This corrects for the fact that although the sample is small, it comes from a small population too. Below, I go through the calculation steps, which will show that by omitting decimal digits, the pollster arbitrarily narrowed the confidence interval (2 * the margin of error) in about 1%. It’s not that usual to round margins of error when reporting them, as a decimal digit may imply in huge differences in the sample size as illustrated in the graph from Marcelino and Angel’s paper. For pedagogical reasons, I won’t go through the simplified formula. So, let do it step-by-step. The derivation of the maximum margin of error formula is given by: MOE = (1.96)sqrt[p(1-p)/n] = (1.96)sqrt[(0.5)(0.5)/n] = (1.96)sqrt[(0.25)/n] = (1.96)(0.5)sqrt[1/n] = (0.98)sqrt(1/n) If we sample a n = 340, we get MOE = (0.98)sqrt(0.05423) = 0.05315, or 5.315%. Finite Population Margin of Error The two formulas above are accurate if the random samples are drawn from extremely large populations. However, when the total population for a survey is much smaller, or the sample size is more than 5% of the total population, we should multiply the margin of error by the Finite Population Correction Factor (FPCF). The forumula is FPCF = sqrt[(N-n)/(N-1)] If we multiply the resulting MOE above by the FPCF, we get: MOE with FPCF = sqrt[(594-340)/(594-1)](0.05315) = sqrt[
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 margin of error sample size books AP calculator review Statistics AP study guides Probability Survey sampling Excel Graphing calculators margin of error vs standard error Book reviews Glossary AP practice exam Problems and solutions Formulas Notation Share with Friends Margin of Error In a confidence level confidence interval, the range of values above and below the sample statistic is called the margin of error. For example, suppose we wanted to know the percentage of adults that exercise daily. We could http://www.statsblogs.com/2015/10/13/understanding-margins-of-error/ devise a sample design to ensure that our sample estimate will not differ from the 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 http://stattrek.com/estimation/margin-of-error.aspx Margin of error = Critical value x Standard error of the statistic If you know the standard deviation of the statistic, use the 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 s
we need In the polls, sometimes the margin of error is simply taken as , why? Answer: margin of error Exercise: (i) show this, (ii) under what circumstance the two are equal? Using gives a conservative formula because the true error is actually likely to be smaller. Here are pdf files for the 4 documents he used: Document 1 Document 2 Document 3 Document 4 Susan Holmes 2000-11-28