Table of Random Digits

Transcription

1 Table of Random Digits A table can be given that represents a list of completely random digits it is essentially like picking from a hat Each entry is equally likely to be any digit The entries are independent of each other one does not influence the other

2 Using Table B Method 1 Assign a number to everyone in your population. Make sure each number is equally likely to come up. For 25 subjects: assign them each a number OR For 225 subjects: assign them each a number or What is more effective, assigning numbers alphabetically or by rows of desks?

3 Using Table B ctd Pick a line on the table to start with Note that the lines are numbered 101 and up, but do NOT use those numbers It does not matter what row you choose to start with Start underlining numbers of however many digits are appropriate one at a time Circle the first number you get to that is also one of your subjects. Continue along the line until you have filled all the spots that you need.

4 Use Table B to come up with a SRS of 5 students from a group of 50.

5 Using Table B Method 2 Assign a random number to everyone in your population. Sort the numbers in ascending order. The first n numbers will be in your sample.

6 Use Table B to come up with a SRS of 5 students from a group of 50.

7 Sampling Plan 1: Give each person a card from a standard deck of cards. The first 10 cards from another deck of cards will be the sample chosen to take the survey. Sampling Plan 2: Each person will roll a die. The first 10 people to roll a 6 will be the sample chosen to take the survey.

8 Other Sampling Designs Probability Sample: sample chosen by chance does not have to be equal chances for each sample Essential piece is that chance is used to select the sample Ex. Roll a die for each subject, if they get a 1, they are chosen to be in the study

9 Stratified Random Sample: (used only in surveys or studies) 1. Divide the population into groups or strata that are homogenous with respect to a pre-determined (possible lurking) variable. 2. Choose a separate SRS from each strata Stratified can often be a better choice than SRS because it can sort out lurking variables and give a basis for comparison

10 Ex. I want to study the expenditure per student for high school in CT. What are some possible variables on which to stratify?

11 Cluster Sampling: the population is divided into groups(clusters) and some clusters are randomly selected with everyone in the cluster being in the sample. Ex. You want to know the % of students who think they have enough time to finish the SAT math. You cluster students by high school, then randomly select high schools and survey every student that took the SAT in that school.

12 Quota Sample: use randomness to begin selecting your sample. Continue selecting individuals until you have reached your predetermined sample size. Ex. Flip a coin as people come in the room. If they flip heads they are in the sample. Stop after 10 individuals have been chosen. Systematic Sampling: using a list of the population choose every k th member of the population. Ex. On a street, pick a random house to start, and choose every 10 th house after that.

13 Ex. Each of the 29 NBA teams has 12 players. A sample of 58 players is the be chosen as follows. Each team will be asked to place 12 cards with its players names into a hat and randomly draw out two names. The two names from each team will be combined to make up the sample. What type of sample is this?

14 Ex. To find the occupancy size of rented apartments in a building, researchers wish to pick a sample of 10 apartments. Since there are 12 floors with 10 apartments on each floor, the researcher decides to randomly select one floor and will survey each apartment on this floor. What type of sample is this?

15 Cautions With Sample Surveys Most sampling plans for surveys usually have some inherent flaw that will introduce some sort of bias. Sampling biases: a systematic error in a sampling method that leads to an unrepresentative sample Other biases (nonsampling biases) can result from how the survey is conducted even from an SRS or stratified random sample.

16 1. Undercoverage (Sampling Bias) Occurs when some groups in the population are left out in the process of selecting the sample. Ex. For each of the following, discuss who is being left out and how this might affect the results 1. A surveyor randomly calls 100 households to ask what the highest degree the head of household has.

17 2. Nonresponse Bias (nonsampling) An individual chosen for the sample can t be contacted or does not respond Could result in bias if the people who are not responding share some variable in common. Most obvious example is hang-ups in phone surveys or simply not answering Nonresponse is NOT voluntary response.

18 3. Response bias (nonsampling) Occurs when the respondent lies or the interviewer unintentionally biases the response Ex. A female interviewer asking males about their opinions on females in the workplace Memory questions often result in response bias for example being asked how many times you have had fast food in the past 4 months.

19 4. Wording of Question Bias (nonsampling) Results from inflammatory or leading wording as well as confusing questions. Ex. Since the start of the war in Iraq, over 3000 soldiers have been killed, are you in favor of sending more troops? Ex. Does it seem possible or does it seem impossible to you that the Nazi extermination of the Jews never happened? This question resulted in 22% saying it was possible, when worded properly, only 1% believed the Holocaust never happened

20 5. Inference about the population Sample surveys only provide an estimate of a population All surveys include a margin of error which does not account for poor sampling! To increase your accuracy, increase your sample size but too many can also be a problem

21 List the many things that are wrong with this situation and suggest some ways to improve it: 100 people were randomly dialed from an automatic dialer. They were asked by a female interviewer: Do you agree or disagree that women should not be considered qualified for the presidency?