Elementary Statistics and Inference. Elementary Statistics and Inference. Chapter 19 Sample Surveys. 22S:025 or 7P:025. Lecture 25.

Transcription

1 Elementary Statistics and Inference S:05 or 7P:05 Lecture 5 Elementary Statistics and Inference S:05 or 7P:05 Chapter 9 Chapter 9 Sample Surveys E. Most research is conducted with data from a Sample of observations from a Population. The results of the analyses are used to make an inference regarding the nature of the Population. Population The total number of subjects (observations) in a Universe. Sample A subset of observations from the Population. 3

2 Population Facts Parameters (e.g., mean = µ, std dev = σ). Sample Facts Statistics (e.g., mean =, std dev = S) Investigators estimate population parameters from statistics. 4 B. Bad Estimates Can be Made of Parameters When sampling is not representative of members of the population 936 Literary Digest Poll used telephone directories, and club membership lists to select a sample of.4 million voters did not reflect mood of the country because many were unemployed and had no telephone. 5 C. Dewey vs. Truman 948 Big Sampling Bias quota sampling where interviewer had wide choices in selecting persons to be interviewed not representative of the population. 6

3 D. Using Chance (Probability) in Survey Work Put the name of each survey candidate on a ticket, put the tickets in a box, and randomly select the names of the persons to be surveyed. Each person has the same chance of being selected to answer the survey (Simple Random Sampling). Example: N=000 names on tickets in a box. Randomly select 00 tickets for persons to be surveyed. Everyone has the same chance of being selected for the survey Sampling Without Replacement. 7 More sophisticated methods are now used to select representative samples of the population. Multistage Cluster Sampling 4 geographical regions of USA within each region develop representative population centers within each population center you have wards and within each ward you have precincts

4 The advantage of multistage sampling is that the interviewer has no discretion at all as to whom to interview there is a definite procedure used for selecting the representative sample, and it involves the planned use of chance (probability) in selecting the sample. 0 E. Do Probability Sampling Methods Work? Since 948 the error in estimating the winner in presidential elections has been very small because impartial probability methods have been used to select the sample of likely voters. 4

5 F. A Closer Look At the Gallup Poll In the 984 election, the Gallup Organization tried to screen its survey respondents to include only those who were likely to vote They screened the non voters from the voters, and the undecided. The survey respondent drops his/her preference for the candidate in an enclosed sealed envelope into a box the choice was unknown to the interviewer. 5 5

6 G. Telephone Surveys Cheaper, just as effective since nearly every home has a phone. Sample picked Random area code (e.g., 39) Random exchange within area code (e.g., 430) Bank (e.g., 3) Digits (e.g., 99) Call: H. Chance Errors and Bias Imagine a box with a very large number of tickets with ones and zeros on the tickets. Select a sample of tickets without replacement - percentage of s in sample = percentage of s in the box + chance error. 8 6

7 Questions we will address about chance errors: How big are they likely to be? How do they depend on the size of the sample? the size of the population? How big does the sample have to be to keep the chance errors under control? 9 In complicated samples, the equation has to take bias into account: Estimate = parameter + bias + chance error Exercise Set A (pp ) #,, 3, 4, 5 0 I. Review Exercises (pp ) #, 5, 7, 9, 0 #0. n=00 P( H ) = avg = E(Heads) = n avg = 00 = 50 SD = SE(Heads) n SD = 00 =

8 I would pick because these numbers have the greatest likelihood of representing the number of heads in 00 tosses of the coin 68.7% of the time we would obtain a sum in this range. If you count the end points (73%) #7. p. 35 A coin is tossed 000 times. There are two options: i) To win $.00 if the number of heads is between 490 and 50 ii) To win $.00 if the percentage of heads is between 48% and 5% (480-50) Which option is better? 3 H T 0 avg of the box = SD of the box = E(Heads) = n avg of the box = 000 = 500 SE(Heads) = n SD of the box = 000 = 3.6 =

9 SE= = = = = Heads X Mean Z = SE X Mean Z = SE The chance of number of heads between 480 and 50 is greater than chance of heads between 490 and