1. Lecture # 6:Designing samples or sample survey Important vocabulary Experimental Unit: An individual person,animal object on which the variables of interest is measured. Population: The entire group of units about whom information is desired Sample: A representative part of the population selected to be measured or observed in order to gather information about the population.

2. Example: A forester is interested in determining total number of trees on tree farms in Montana. He divides all such farms into 4 classes depending on size. From each class he selects a sample of 15 farms. He counts and records the number of trees in the selected farms. Population: All tree farms in Montana Sample: the 4 X 15 selected variable measured: The number of trees in each farm

3. Two types of study Observational, Experimental Observational Study: We just observe the response, do not try to influence or manipulate the responses in any way. Experimental Study: Deliberately assign some treatments on subjects and observe their responses and try to see a causal relationship among the treatment and the response. Possible lurking variables may confound the causal relationship, even if it exists in an observational study.

4. Example: To determine whether a review session will improve scores, an instructor randomly divides his class into two groups and makes one group attend a study session. He compares the scores of the two groups. : Designed Experiment The instructor announces study session to all the students, makes a list of those who attend and compare the scores of those who attend with those who do not.: Observational Lot of other variables: motivation, schedule

5. Sampling Designs We choose a sample to draw conclusions on a larger population. Poor sample designs lead to inferior conclusions. Example:Call-in opinion polls, only very strongly opinionated group spend money and time to respond, not a fair representation of the actual population.

6. Bad Sampling schemes Voluntary response sampling: People choose to respond to a general appeal, only strongly opinionated (usually negative about the proposition) respond. Convenience Sampling: Sample individuals easiest to reach. E.g.,To know consumer behaviour, interview local mall shoppers, mall shoppers are not a fair representation of the entire consumer society.(they are rich and in typical age groups usually!).

7. Sampling Bias If the sampling design favors certain part of the population, it introduces a systematic error in your inference procedures. If the design of a study favors certain outcomes relative to others, it is called biased. To give useful conclusions the sample must be an adequate representation of the population.

8. Simple Random Sample (SRS) To give equal chance to every unit in the population for being included in the sample. Definition: A SRS of size n consists of n individuals from the population chosen such that every set of n individuals has an equal chance of being selected. It is like mixing names in a hat and selecting a handful of n names.

9. Random Number Table (B) A string of digits Each digit has equal chance to be any of the digits from 0 to 9. The entries are independent Every pair has equal chance of being one of 00,01,….,99. Every triplet has equal chance of being one of 000,001,….,999.

10. How to choose an SRS using Table B The stat department wants to review its Ph.D exam system by interviewing 5 students from the following list of 16 senior Ph.D students: Agarwal, Anderson, Baxter,Cross,DeCruz, Gomez,Kim,Maron, Neter,Pliego, Puri, Richards, Shen, Tyson, Tsai, Wang

11. Attach labels to the subjects in the population, 01,…..16 serially. Use any line say line 101 of table B.it says: 19223 95034 05756 28713 96409 ….. So the first 10 two digit groups are: 19 22 39 50 34 05 75 62 87 13 96 40 …. Select the first 5 two digited numbers falling within your range of labels 01,..,16. So the first unit selected is unit 05 (Decruz), second unit 13(Shen) and so on. You will discard all two-digit groups not in your label range for example 19,22,39 and so on.

12. You will ignore any repetitions of a number you have already selected as you cannot choose the same subject twice. This is actually simple random sample without replacement. We will learn how to choose a random sample using Excel’s sampling function.

13. Other sampling Designs: Probability Sampling: Each member of the population has a pre-specified chance of being selected (SRS is a special case with this chance being equal for all individuals) Stratified Random Sampling:Divide the population into strata, each stratum consisting of similar units, choose a SRS within each strata, combine all the samples to form your full sample.

14. Caution about Sample survey Undercoverage: Telephone surveys missing 6% american households without residential telephone, sampling households misses homeless people, shelters, dorms. Nonresponse: People chosen can not be reached or refuses to co-operate. US census suffers greatly due to non- response, specially in big metropolitan areas

15. Other causes of Bias Deliberate lies on sensitive issues from the respondent Faulty memory if asked about past events Confusing framing of questions Questions designed to influence responses

16. Statistical Inference The result obtained from a sample comes with a margin of error. It is variable as if you choose a different sample you will get a different answer. How reliable or how close is the sample results to the true population. We will use probability laws to make a statement about how large an error we are likely to make. Larger samples give better answers than smaller samples.