DATA COLLECTION METHODS SAMPLING 1

Class Objective After this class, you will be able to - Use Simple Random Sampling (SRS) to collect data 2

Copyright ©2011 Brooks/Cole, Cengage Learning 3 Types of Statistics Descriptive Statistics: using numerical and graphical summaries to characterize a population. Inferential Statistics: using sample information to make conclusions about a broader range of individuals than just those observed.

Copyright ©2011 Brooks/Cole, Cengage Learning 4 Populations and Samples Population: the entire group of units about which inferences are to be made. Sample: the smaller group of units actually measured or surveyed. Census: every unit in the population is measured or surveyed.

Copyright ©2011 Brooks/Cole, Cengage Learning 5 Survey – collect data One type of observational study (VS experiment) The population/sample is questioned on a set of topics No manipulation of respondents’ behavior Sample Survey: a subgroup of a large population questioned on set of topics

Class Task Answer the questions in the Classwork worksheet on your own You have 5 minutes 6

Class Task Discuss with a partner You have 10 minutes Explain why and present your answers to the class. 7

Class Task Why do we do sampling? 8

Copyright ©2011 Brooks/Cole, Cengage Learning 9 Advantages of a Sample Survey over a Census Sometimes a Census Isn’t Possible when measurements destroy units Speed especially if population is large Accuracy devote resources to getting accurate sample results Cost less costly

Copyright ©2011 Brooks/Cole, Cengage Learning 10 The Fundamental Rule for Using Data for Inference Available data can be used to make inferences about a much larger group if the data can be considered to be representative with regard to the question(s) of interest.

Class Task What is the opposite term for “representative” in statistics? 11

Class Task What does of a biased sample mean? 12

Biased Samples A sample is biased if it systematically favors certain outcomes Results based on a survey are biased if method used to obtain those results would consistently produce values that are either too high or too low. Example Voluntary response sample

Copyright ©2011 Brooks/Cole, Cengage Learning 14 Bias: How Surveys Can Go Wrong Selection bias occurs if method for selecting participants produces sample that does not represent the population of interest. Nonparticipation bias (nonresponse bias) occurs when a representative sample is chosen but a subset cannot be contacted or doesn’t respond. Biased response or response bias occurs when participants respond differently from how they truly feel.

Copyright ©2011 Brooks/Cole, Cengage Learning 15 Example Do First Ladies Represent Other Women? Past First Ladies are not likely to be representative of other American women, nor even future First Ladies, on the question of age at death, since medical, social, and political conditions keep changing in ways that may affect their health.

Copyright ©2011 Brooks/Cole, Cengage Learning 16 Example Do Cornell Students Represent Other College Students? If question of interest = average SAT Scores of Cornell students? => No If question of interest = how fast ever driven a car? => No, since Cornell is in rural area with open spaces, county roads, little traffic.

Class Task Come up with your own biased sample 17

Copyright ©2011 Brooks/Cole, Cengage Learning 18 Populations, Samples, and Simple Random Samples Simple Random Sample: every conceivable group of units of the required size from the population has the same chance to be the selected sample. Helps ensure sample data will be representative of population, but can be difficult to obtain.

How do we do random sampling? Create a Random Number Table 1. Let’s cut 10 small piece of paper of equal size 2. Put the paper into a bag, mix them and draw 1 out 3. Write the number on the board 4. Repeat step 2 and 3 5. Arrange the number in groups of 5 and 4 groups in a row ( It could be groups of any number and in rows of any number – The groups and rows have no meaning) 19

Based on the Random Number Table, select a random sample Situation: Mike’s small accounting firm serves 30 business clients. Mike wants to interview a sample of 5 clients to find ways to improve client satisfaction. Goal: To select the sample without bias Class Activity: How do you do it? 20

Based on the Random Number Table, select a random sample Situation: Mike’s small accounting firm serves 30 business clients. Mike wants to interview a sample of 5 clients to find ways to improve client satisfaction. Goal: To select the sample without bias STEP 1: Label – Give each client a numerical label. All labels should have the same number of digits 21

STEP 1 - Label the Companies 01 ABC 02 ADE 03 AFG 04 BXY 05 BXZ 06 BAC 07 CAA 08 CBD 09 HOA 10 HOB JBC 12 JDE 13 JFG 14 KXY 15 KXZ 16 KAC 17 LAA 18 LBD 19 LOA 20 MOB 21 NBC 22 NDE 23 NFG 24 OXY 25 OXZ 26 OAC 27 PAA 28 PBD 29 POA 30 POB

STEP 2 – Use the Table to Select the Random Sample Enter the table anywhere Read two-digit groups (Since we use two digit to label the population) 23

Quick check Use the given Random-Number Table to select a Random Sample Use a random-number table to pick a random sample of 30 cars from a population of 500 Cars Step 1 : Label…. Step 2: Use the Random-Number table…… 24

Copyright ©2011 Brooks/Cole, Cengage Learning 25 Choosing a Simple Random Sample Probability Sampling Plan: everyone in population has specified chance of making it into the sample. Simple Random Sample: every conceivable group of units of the required size has the same chance of being the selected sample.

Copyright ©2011 Brooks/Cole, Cengage Learning 26 Choosing a Simple Random Sample You Need: 1.List of the units in the population. 2.Source of random numbers. Table of Random Digits Random Number Generator Computer Software

Homework Assignment: Chapter 5 Exercise 5.1, 5.3, 5.4, 5.14 and 5.45 Reading: Chapter 5 – p