Introduction to Sampling Distributions. Introduction to Sampling Distributions Prerequisites Distributions, Inferential Statistics Learning Objectives Define inferential statistics Graph a probability distribution for the mean of a discrete variable Describe a sampling distribution in terms of "all possible outcomes. " Describe a sampling distribution in terms of repeated sampling Describe the role of sampling distributions in inferential statistics Define the standard error of the mean Suppose you randomly sampled 10 people from the population of women in Houston Texas between the ages of 21 and 35 years and computed the mean height of your sample. You would not expect your sample mean to be equal to the mean of all women in Houston.
Discrete Distributions We will illustrate the concept of sampling distributions with a simple example. All possible outcomes are shown below in Table 1. Notice that all the means are either 1.0, 1.5, 2.0, 2.5, or 3.0. The distribution shown in Figure 2 is called the sampling distribution of the mean. Standard Error. Standard error of the mean. When you take a sample of observations from a population, the mean of the sample is an estimate of the parametric mean, or mean of all of the observations in the population.
If your sample size is small, your estimate of the mean won't be as good as an estimate based on a larger sample size. Here are 10 random samples from a simulated data set with a true (parametric) mean of 5. The X's represent the individual observations, the red circles are the sample means, and the blue line is the parametric mean. As you can see, with a sample size of only 3, some of the sample means aren't very close to the parametric mean. The first sample happened to be three observations that were all greater than 5, so the sample mean is too high. The second sample has three observations that were less than 5, so the sample mean is too low. With 20 observations per sample, the sample means are generally closer to the parametric mean.
Here's a figure illustrating this. Similar statistics Example Spreadsheet. Audit Sampling Requires Auditor Judgment. December 1994 The goal of an agency audit is to insure compliance with the client's work standards, evaluate performance and maximize profits. Obviously, no matter how competent the auditor or how sophisticated the collection software, reviewing each account is a physical impossibility. Even if 100 percent of the information could be tested, the cost of testing would likely exceed the expected benefits (the assurance that accompanies examining 100 percent of the total) to be derived.
What is required is a sampling of the accounts. To accomplish this, the auditor needs to examine a representative sample or cross-section of the various type of accounts (e.g., legal, good telephone, skip, payment arrangements, settled, closed) as well a review of the remittance history. How the sample should be selected and how large the sample should be are critical issues for researchers as well as auditors. According to researchers M. Simple Random Sampling Systematic (Interval) Sampling Haphazard Selection. Glossary. You can use the "find" (find in frame, find in page) feature of your browser to search the glossary. 0-1 box A box of numbered tickets, in which each ticket is numbered either 0 or 1.
See box model. Affine transformation. See transformation. Affirming the antecedent. A valid logical argument that concludes from the premise A → B and the premise A that therefore, B is true. Affirming the consequent. A logical fallacy that argues from the premise A → B and the premise B that therefore, A is true. Alternative Hypothesis. In hypothesis testing, a null hypothesis (typically that there is no effect) is compared with an alternative hypothesis (typically that there is an effect, or that there is an effect of a particular sign). And, &, conjunction, logical conjunction, ∧. An operation on two logical propositions. Ante. The up-front cost of a bet: the money you must pay to play the game. Antecedent. In a conditional p → q, the antecedent is p. Appeal to Ignorance. Applet. Association. Average. Bayes' Rule. Bin. Statistics Tutorial: Stratified Random Sampling.