Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
"An approximate answer to the right question is worth a good deal more than the exact answer to an approximate question." John Tukey 5.1 DESIGNING SAMPLES (Pages 245-261) OVERVIEW: If one wishes to obtain reliable statistical information from sampling, one must design the sampling process very carefully. Good sampling techniques, which involve the use of chance, can produce meaningful and useful results. Bad sampling techniques often produce worthless data. This section introduces or reinforces many important definitions. Population: is the entire collection of objects you are interested in; statistical measures calculated about a population are called _______________ _________: is a method of data collection in which all of the members of a population are included in the study. Sample: is a subset of the population; statistical measures calculated about a sample are called ______________. The process of drawing conclusions about the nature of the entire population based on the data from the sample is called _____________________. Sample Design: refers to the technique employed to select a subset of participants from the population and gather the data from the population. Voluntary response sample: Consists of people who choose themselves. (As contrasted to being chosen by some designed process.) Two variables are _______________ when their effects on a response variable cannot be distinguished from one another. Example (Pre-test, post-test situation) ...Group asked for opinion (favorable, unfavorable) on political candidate Herkimer. ...Group then reads favorable propaganda about Herkimer for a period of time, and then are once again asked to express an opinion. ...Result: _______________________________________________________________. ...Purpose: ______________________________________________________________. ...But, during the reading period, Herkimer makes headlines by donating a good amount of his personal fortune to a worthwhile charity. -How much did the explanatory variable (reading favorable propaganda) affect the change in attitude? We'll never really know, since some (perhaps most) of the change was undoubtedly due to Herkimer's well-publicized donation to charity. The reading of propaganda and the general knowledge of the charity donation are confounding variables. Convenience sample: Just select individuals easiest to reach. ...Example: Sample is __________ if it systematically favors certain outcomes or excludes individuals with certain traits. Therefore both of the previous methods produce bias because they both contain personal choice. Simple random sample(SRS) of size N: ______________________ - sample chosen in such a way that every set of N individuals has an equal chance of being chance – involves selecting individuals at random from the population without replacement - every member of the population has an equal chance of being included in the sample Careful...the notion of an SRS can be tricky. Here’s an example. A class consists of 4 boys and 4 girls. The teacher wants a sample of two students. She decides to flip a coin. If the coin comes up heads, she will choose two boys by a random process. If tails, she will choose two girls by a random process. Question 1: Does each student have an equal probability of being in the sample? ...Answer: Question 2: Is this an SRS of two students from the class? ...Answer: ..Simplest Example: Choosing a SRS using the Table of Random Digits(table B in back of book) 1. label: 2. table: a. b. c. Probability sample... gives each member of the population a known chance (greater than zero) of being chosen. Stratified random sample... divide population into __________(similar distinct groups), choose an SRS in each group, and combine the SRS's to get a bigger sample (which would not be an SRS). Example: Mr. Surry wants to randomly select twelve students to receive twelve free tickets to a concert. To make sure all classes are represented, he stratifies the population by classes (senior, junior, sophomore, freshman) and then randomly chooses three students from each strata. He then has a randomly chosen sample of twelve Denbigh students who will receive the free tickets. This is not an SRS of twelve Denbigh students, since not all combinations of twelve students can be obtained by this process. Reasons for stratification o o o Multistage sample design...select successively smaller groups within a population by stages. Example ...Population: Residents of California. ...From the collection of counties, randomly pick 20 counties. ...Then, randomly pick 10 cities/towns in each of the selected counties. ...Then, randomly pick 100 individuals from phone listings in each of the selected cities/towns. ...Note: This design does not yield an SRS of California residents.(Why?) Systematic samples… subjects are chosen by using every k th number after the 1st subject is randomly selected from 1 thru k. Example… Sampling Frame: A list of sampling units. (Note: Frame might be different from population. For example, population might be city residents, frame might be telephone book for the city.) Random selections eliminate bias in choosing a sample from the population, however other bias occurs when the population consists of human beings. Types of Bias Undercoverage: Some groups in the population are left out in the process of choosing the sample. Example… Nonresponse: Occurs when individual can't be contacted or refuse to cooperate. Response bias:Refers to a variety of things that can lead to incorrect or false responses. Careful training of the interviewer will limit this bias. Example: Wording of questions... can greatly influence the response. Example (From Statistics: Concepts and Controversies, by David Moore...NY Times/CBS News Poll): -Version 1: Do you think there should be an amendment to the Constitution prohibiting abortions? -Version 2: Do you think there should be an amendment to the Constitution protecting the life of the unborn child? ...Results: Poorly worded questions can confuse those responding to it. Example: Do you think it is wrong when the government doesn’t interfere in potentially dangerous religious matters? YES / NO 1. We want to send 4 students to represent our class to meet on a school improvement team. Explain how you would choose a SRS from lets say 27 students in the class by using line 122 of the random digits table. Line 122 - 13873 81598 95052 90908 73592 75186 87136 95761. 2. A marketing company offers to pay $25 to the first 100 persons who respond to their advertisement and complete a questionnaire regarding displays of their client’s product. This situation is an example of _____________________. 3. A SRS was selected of large urban school districts throughout New England. The selected districts were identified as target districts. Within each district, a SRS of its high schools was chosen and the principals of those high schools were interviewed. Which of the following statements regarding this design is not true? A. This is an example of a multi-stage sample. B. Results from the interviews cannot be used to infer responses of the population of interest. C. The population of interest is the set of all high school principals from large urban school districts in New England. D. Not every subset of principals has the same chance of selection. E. All of the statements are true. 4. A sample at a school of 1,000 students is to be selected using an alphabetical list from the office. A number from 1 to 50 is chosen randomly. The sample consists of the student who is in that position on the list and every tenth student from that position. Give the following requested information: a. Population b. Sampling Method – c. Sampling Valid d. Reason for your answer 5. It is believed that 75% of DHS students do not actually lock their lockers. a. Describe how you would simulate an SRS of 15 students. b. Beginning at line 123 in the random digits table, actually simulate an SRS of 15 students. What is the proportion of students in the sample who leave their locker closed but unlocked? Line 123 54580 81507 27102 56027 55892 33063 41842 81868