Notes 6.1: Sampling
Learning Target Identify the benefits and bias of different sampling methods.Population: The entire group of interest.Sample: A part of the group of interest.Data: Information that collected to be examined and used to help make decisions.Census: Data gathered from the entire population.This is difficult and expensive if the population is large.Survey: Data gathering from part of the population.This is easier (smaller sets of data and less time consuming). It needs to be done carefully to make sure the data you get is a good representation of the population.Parameter: What data is called that is obtained from a census (from the entire population)Statistic: What data is called that is obtained from a survey (from a sample).?I can identify a population and a sample in given situations?Example 1: Identify the population and a sample in the following examples, and then determine whether the data collected is a parameter or a statistic:Asking theater goers what they thought about a new release.Population: ask everyone in the theater (parameter)Sample: ask a few people in the theater (statistic)Asking who Americans will vote for in the presidential election.Population: ask every American (parameter)Sample: ask your parents, friends, and teachers (statistic)Determining how many defective computer chips have been manufacturedPopulation: check every chip (parameter)Sample: check a few chips every day (statistic)Bias: Systematic deviation from the actual value.Bias influences results and creates values that are in favor of or against one thing, person, or group compared with another, usually in a way considered to be unfair. Bias in sampling methods can cause results that are far from the actual population. The goal is for the sample to be a good representation of the population. (No bias) This is usually easier said than done…. There are many forms of bias:Sampling Bias: The way the sample is obtained is not a good representation of the population.Voluntary Response: Sample obtained by people “choosing” to participate will influence resultsOnly opinionated people will choose to respondExample: Ask people to call a given number and answer questions about animal rightsConvenience Sample: Sample obtained by asking participants that are easy to ask.Example: Ask friends (or family), “safe” people, or the first people you see.Response Bias: The way answers are obtained is not representative of the population. Response bias includes:Under coverage or Non-Response: Too small of a number of enough people were asked (or agreed to participate) will influence resultsAt least 30 responses and up to 10% of the population)Example: A sample of 2 people will not give you much informationTo avoid: ask more people than you needWording: The way questions are worded will influence resultsA confusing question or leading question can lead to certain answersExample: Asking a question such as “Do you think there should be stricter gun control laws since firearms are the leading cause of accidental deaths in the U. S.?” To avoid: have someone proof read your questions to make sure they make sense and are not misleadingUntruthful Answers: People lie when answering questions will influence results. Usually occurs when they are not taking the questions seriously or they are asked controversial questions and are afraid they will be judged by their answer (if survey is not anonymous). Some people answer what they think you want to hear (or what they want to be)Example: Asking a question such as “Do you believe that abortion is a good form of birth control?” or “How much do you exercise every week?”To avoid: good luck!?I can recognize forms of bias (voluntary response, wording, under coverage, etc.) ?Example 2: Identify the type of bias that has occurred in the following situations:Surveying shoppers at the mall and asking the first 40 people you see. Convenience SampleAn online poll asks if female athletes should be paid the same as male athletes. To answer the question you need to call (you will be charged $1 for the phone call). Voluntary Response SampleA surveyor asks a man the question “Would you marry the same person if you had to do it all over again?” in front of his wife. Untruthful Answer (possibly)A surveyor goes door to door, visiting homes between 9 AM and 4 PM . Under coverageA survey includes the following “The government should force you to pay higher taxes”. WordingOther questions to consider when looking for bias:Who sponsored? Do they have an interest in getting a certain resultHow was sample selected? Make sure it wasn’t convenience or voluntaryHow large is the sample? It should be at least 30 (or 10% of the population)What is the response rate? If they asked 30 people but 2 responded there is an issueHow were results obtained? Were they anonymous, were they interviewed in personWhat were the exact questions asked? Make sure the wording is appropriateAny result that is not a good representation of the entire population is considered bias. Sampling Methods: The way that a sample is obtained. If done correctly, these methods can help reduce bias. Any non-biased method will use some sort of random selection!Simple Random Sample (SRS): Every individual in the population has the same chance of being selected as everyone else.This is the most preferred way of sampling, but it is difficult to do because it requires a complete list of every individual in the population.Examples of SRS include: Drawing names from a hat, dealing out cards, pulling popsicle sticks, calculator, and Random Number Table (we will be learning how to do the last two). Systematic Sampling: Every kth person is selected. This incorporates randomness and reduces the bias of a convenience sample.Example of systematic sampling: Ask every 10th person you see. Cluster Sampling: Divides the population into groups usually by location (called clusters). The clusters are randomly selected and everyone in that cluster is chosen.Example of cluster sampling: Randomly select a few classrooms and then ask every student in those rooms.Stratified Sampling: Divides the population into groups with similar characteristics (called strata). A sample is then taken from each group using either random or systematic.Example of stratified sampling: Separate students by grade and then randomly choose 25 freshmen, 25 sophomores, 25 juniors and 25 seniors.?I can identify appropriate sampling methods (SRS, Stratified, Cluster, and Systematic) ?Example 3: Identify the sample method utilized in each description.A student randomly selects a few tables every lunch and asks everyone at the selected tables.ClusterA student gets a list of teachers and categorizes them by the department they teach in (math, science, etc.) Then they randomly choose 2 teachers from every department.StratifiedA student asks every 20th student that walks into the lunch room.SystematicA student writes everyone’s name on a piece of paper (all the same size), puts them in a container. A name is drawn, one at a time, remixing after every selection until the number of participants has been selected.Simple Random SampleThe best method of sampling is a SRS. To select an SRS, use a calculator (random number generator) or a random digit table.?I can use a calculator and a random digit table to select a SRS?Calculator46685209715500Calculator steps:Step 1: Select:MATHPROBrandInt(Step 2: randInt(minimum value , maximum value)…. the range.Step 3: Press ENTER and the calculator will select one random number at a time.53454309525000Step 4: (Optional) randInt( minimum , maximum , number of values you want chosen all at once)40119306159500Example 4: Choose 3 numbers between 1 and 25 one at a timerndInt ( 1, 25) then push Enter 3 timesExample 5: Choose 3 numbers between 1 and 25 at the same timerndInt( 1, 25 , 3 )If a random number is selected and then calculator selects it again, you must ignore the number (skip it) and move on to the next random number. These numbers represent people and you should not select the same person twice (sample without replacement). 333565525971500Example 6: In this example, there are only 4 numbers selected since the second 10 must be ignored (it is a repeated number).The numbers selected are 14, 17, 10, and 6.Seed a Calculator: Calculators (and computers) are not capable of creating "truly random" numbers.? They create what are called "pseudo-random" numbers, meaning they use a formula to create the values.? To engage this formula, the calculator uses a starting value, called a "seed," and then creates the random numbers based upon this seed.? If two calculators start with the same seed value, they will generate the same sequence of random values.To seed a calculator: Type the seed number STO> MATH PROB rand ENTERSeeds can be used to get the same answers as everyone else (not random at all, but a way to make sure you are using the calculator and not making upa number).42970455905500Example 7: Seed calculator to 123 and then find 4 numbers from 1-50.123 rand then randInt ( 1 , 50 , 4 )Since there were repeats in the first set of numbers, the 4 random numbers chosen are 36, 14, 24, 23. Everyone should have the exact same values.Seeds can also be used to get different answers (more practical).Seed the calculator to a number of your choice (not the same as anyone else). Possibilities are endless but could include the last 4 digits of your phone number, your birthday, etc. The goal is to seed your calculator with a different number than anyone else so you will get completely different random numbers.Example 8: Seed calculator to a number of your choice then find 5 random numbers from 1- 100. Write down your results:Share your results with the class (everyone should get different values).Random Number Table (or Table of Random Digits): This contains the digits 0 through 9 occurring in a random pattern. They are organized by groups of 5 in rows (that are numbered for reference) and columns. To use a table:Step 1: Number the individuals in the population. For consistency, these numbers should consist of the same number of digits (and the smallest number of digits possible)Step 2: Choose a random starting point (close your eyes and point). Sometimes you are given the starting point, which means your answer will NOT be random, but it is used to check if you are using the table properly (and not just randomly making up answers, not that you would ever do that).Step 3: Read through the table in chunks equal to the number of digits of your sample size. Skip repeats and numbers that do not correspond to any individual in the population. If you run out of numbers, continue to the next line.Example 9: There are 50 items in our population, start on Line 108 and select 5. Use 2 digit numbers: 01, 02, 03, ……, 49, 50 to number the population Start at Line 108 (given) and read 2 digit number across: 60940 72024 17868 24943 6179060 (skip), 94 (skip), 07, 20, 24, 17, 86 (skip), 68 (skip), 24 (skip already used), 94 (skip), 36The 5 numbers chosen are: 7, 20, 24, 17, and 36.Example 10: There are 100 items in our population, start on Line 145 and select 4:100 can still be represented as 2 digit numbers: 00, 01, 02, ….., 98, 99 Start at Line 145 and read 2 digit numbers across: 19687 12633 57857 95806The 4 numbers chosen are: 19, 68, 71, 26 Example 11: From 250 items, choose 3 starting on a random line of your choice:Use 3 digit numbers 001, 002, …., 249, 250Ignore any number from 251 – 999 (and repeats)Since you start at a line of your choice, there will not be similar answers (these will actually be random numbers)Example 12: Five teachers were nominated to win “Outstanding Math Teacher Award” and it was decided the winner would be chosen randomly. The teachers nominated were:BoguesDuBayPeriorRauppTimmonsUse Line 148 to determine who wins.Assign digits to teachers. Since there are 5 teachers: Bogues = 1, DuBay = 2, ….., Timmons = 5.Line 148: 00694 0 (skip) 0 (skip) 6 (skip) 4. 4 is chosen = Raupp (CONGRATULATIONS!!) ................
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