Sampling Gone Well Lesson 2 Unit 3 - Sampling Methods

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1 Sampling Gone Well Lesson 2 Unit 3 - Sampling Methods

2 Population vs. Sample We draw samples from a population because we are interested in inferring something about the population based on the sample. We sample when a census is impractical (ex: too big of a size). In order to draw a sample, we identify the population of interest and then choose a sample that is representative (hopefully) of the population of interest.

3 POPULATION = the group we WANT information about SAMPLE = the group we GET information about

4 Sample Surveys A sample survey is a study that uses an organized plan to choose a sample that represents some specific population. 1. Define a population we want to describe. 2. Say exactly what we want to measure (i.e. the variable(s) ). 3. Decide how to choose a sample from the population.

5 Why do we sample? sample Statistics corresponding parameters of interest

6 A political scientist wants to know how college students feel about the Social Security system. She obtains a list of the 3,456 undergraduates at her college and mails a questionnaire to 250 students selected at random. Only 104 questionnaires are returned. (a) What is a possible population in this study? Be careful: what group does she want information about? (b) What is the sample? Be careful: from what group does she actually obtain information?

7 An archaeological dig turns up large numbers of pottery shards, broken stone implements, and other artifacts. Students working on the project classify each artifact and assign it a number. The counts in different categories are important for understanding the site, so the project director chooses 2% of the artifacts at random and checks the students' work. What are the population and sample here?

8 Class averages: Front side of Federalist Papers activity

9 Table of Random Digits The table contains a long string of digits 0, 1, 2, 3, 4, 5, 6, 7, 8, & 9 Each entry in the table is equally likely to be any of the 10 digits 0 to 9 The entries are independent of each other. That is, knowledge of one part of the table gives no information about any other part Read successive groups of digits that are the same length as you used for the labels from the table of random digits to find the sample of individuals whose labels are found in the table

10 How to use the Table of Random Digits: 1. LABEL - Give each member of the population a numerical label of the same length. 2. TABLE - read successive groups of digits that are the same length as you used for the labels from the table of random digits to find the sample of individuals whose labels are found in the table 3. Deal with the issue of numbers outside of your population when using a table and the issue of repeated values for both methods - too big? repeats?

11 Let's choose a random sample of five students from our class...

12 class averages: Federalist Papers activity - back page

13 Class dotplots: "random" selection average word length random selection average word length truly random selection average word length

14 There are several ways to select a sample. The sampling design or sampling method describes exactly how to choose the sample

15 When sampling goes well... The statistician s remedy is to allow impersonal chance to choose the sample. A sample chosen by chance rules out both favoritism by the sampler and self-selection by respondents. Random sampling, the use of chance to select a sample, is the central principle of statistical sampling.

16 Simple Random Samples A simple random sample (SRS) of size n consists of n individuals from the population chosen in such a way that every set of n individuals has an equal chance to be the sample actually selected. Methods that use SRS: 1. Table of Random Digits (Refer back to the Federalist Paper Activity) - we'll focus on this method more. 2. Choosing samples from a hat (Like in Hunger Games)

17 A firm wants to understand the attitudes of its minority managers toward its system for assessing management performance. Below is a list of all the firm's managers who are members of minority groups. Using the table of random digits select a simple random sample of size 6 to be interviewed in detail about the performance appraisal system.

18 To gather data on a 1200-acre pine forest in Louisiana, the U.S. Forest Service laid a grid of 1410 equally spaced circular plots over a map of the forest. A ground survey visited a sample of 10% of these plots. (a) How would you label the plots? (b) What is the total sample size for this study? (c) Choose the first 10 plots.

19 Stratified Random Sample 1. Divide the population (or sampling frame) into strata which are homogenous groups of individuals that are similar in some way that is important to the response 2. Choose an SRS from each strata

20 In a class of 100 students, 85 are female and only 15 are male. Suppose I am taking an SRS of 20 students in order to conduct an experiment. The responses are suspected to differ significantly between females and males so we want to gather a stratified random sample. How many females should be in our SRS? Choose a stratified random sample.

21 A club has 30 students: Abel Fisher Huber Miranda Reinmann Carson Ghosh Jimenez Moskowitz Santos Chen Griswold Jones Neyman Shaw David Hein Kim O'Brien Thompson Deming Hernandez Klotz Pearl Utts Elashoff Holland Liu Potter Varga and 10 faculty members: Andrew Fernandez Kim Moore West Besicovitch Gupta Lightman Vicario Yang The club can send 4 students and 2 faculty members to a convention. It decides to choose those who will go by random selection. Use the table of random digits, starting at line 130, to choose a stratified random sample of 4 students and 2 faculty members.