5.3: SAMPLING

Errors in Sampling Sampling Errors- Errors caused by the act of taking a sample. Makes sample results inaccurate. Random Sampling Error Errors caused by the chance in selecting a random sample. Nonsampling Error Errors not related to the act of selecting a sample from the population. They can even be present in a census.

Sampling Frame: Individuals from the population from which the sample can be obtained from. Not always the whole population. EX: A political group interested in how people in the state feel about budget cuts takes a sample of 1000 people from registered voter lists.

SAMPLING ERRORS: Undercoverage When some groups of the population are left out of the sample On purpose or by accident Examples: Call-in poll, stopping mall, mailings, standing by back door of school, etc.

Processing Errors * Mistakes * Examples: - doing arithmetic wrong - typos - recording wrong numbers/info - losing data NONSAMPLING ERRORS:

Response Error * When subjects give an incorrect response * Examples: - lying (especially with sensitive questions) - remembering info incorrectly - don’t understand question - etc.

Nonresponse Error * Failure to obtain data from an individual in the sample * Happens b/c subjects refuse to respond or can’t be contacted * Examples: - not answering phone/ hanging up phone - not sending back mailing - absent on day of poll - refuse to write answers on a survey

Wording of questions * When a question: - is confusing - uses big words or technical language that most people don’t understand - uses a word that has more than one meaning and doesn’t clarify - ARE SLANTED towards one response (based on the question alone or a statement with the question * Usually non-sampling error

What to do about these errors: * For nonresponse… just select another individual * Weight the responses based on who responds Example: If twice as many rural homes respond than urban homes, give more weight to the responses from the urban.

Complete the book problems: p. 242 #56 p. 246 #64 p. 252 #75

p. 242 #56 56) (a) non-sampling (response error) (b) non-sampling (processing error) (c) sampling (undercoverage, not everyone gets the paper) 64) 50% in favor was for the question worded “protecting the life of the unborn child” 29% in favor was for the question “prohibiting abortions” p. 246 #64

p. 252 #75 75) (a) sampling error (undercoverage on those not in the phone book) (b) non sampling error (nonresponse) (c) sampling error (convenience sample, voluntary response sample)

Other types of samples…

Review: Take an SRS of 5 people from the following list. Number the people down the columns, starting with 1. Start at line 124 in the Table of Random Digits. JohnChristineRobert SueMatthewStacy LaurenAndreaMegan JimChrisPatrick MarieGretchenAlison JakeJenniferJeffrey KarenFrankAnnie

Other ways to take samples Example: At a university, there are 1500 professors. However, 1000 are male and 500 are female. To take an accurate sample of the university faculty’s opinions, we decide to take a sample of 100 male professors and 50 female. Their total sample is these 150 professors. Why is this not an SRS? What was their process? Why is this sampling method better than just an SRS?

Stratified Random Sample: (NOT simple random sample) 1)Divide population into groups with something in common (called STRATA) Example: gender, age, etc. 2) Take separate SRS in each strata and combine these to make the full sample - can sometimes be a % of each strata

Try p. 246 #62 Basketball: Wade Carter Miller Stoudamire Gasol Farmar Billups Golf: (line 140)

Try p. 247 #68 (a) First separate the faculty into the 2000 males and 500 females Next, assign the males the #0001 – 2000, and assign the females #001 – 500. For the males, read across the table every 4 digits starting at line 122. Ignore #2001 – 9999, 0000 and repeats. First 200 numbers are our sample For the females, read across the table every 3 digits starting at a different line (maybe line 145). Ignore #501 – 999, 000 and repeats. First 200 numbers are our sample. The total 400 faculty selected are our sample

Probability Sample: * Chosen by chance * Give a chance to each individual, but not always an equal chance. * We must know what chance each sample has Example: The lottery

Systematic Sample: * Randomly picking a first individual, and then selecting every ____ person after that. * Example: Interview every 5 th person that walks thru the back door of CB South in the morning. * Example: Write down the type of car in every 3 rd spot in the CB South parking lot.

Cluster Sample Pick a certain area/part of the population. Try to get every individual in that selection Example: select one lunch period, and talk to everyone at that lunch Census Sample everyone in the entire population.

EXAMPLE: We need to survey a random sample of 30 passengers on a flight from San Francisco to Tokyo. Name each sampling method described below: Pick every 10 th passenger that boards From the boarding list, randomly choose 5 people flying first class, and 25 of the other passengers Randomly generate 30 seat numbers and survey the passengers who sit there Randomly select a seat position (right window, left window, right aisle, etc.) and survey all people in those seats

Questions to ask before you believe a poll: p. 249

Random Rectangles Activity!

Try the following: p. 253 – 256 #77, 78, 80, 83

77) (a) Biased because of undercoverage. You are not able to sample the most expensive seats (b) Sampling error, because it was an error in the WAY you collected your sample 78) # 19, 26, 06,09 Rodriguez, Montoya, Fernandez, Castillo

80) (a) the population is all American college students (b) the list of 340 PSY 001 students (c) If he is trying to conclude about ALL college students, you should not just sample from students in PSY 001. (d) Yes, it is slanted. “fair price to pay” (e) He did not ask students about whether they were in favor of TV commercials. He asked them if they thought commercials were a fair price to pay for watching TV. (f) No, not relevant. The sampling frame does not represent the population.

Try p. 255 #81, 86

81) (a) – give each student a number - randomly select 250 students to interview (b) - Randomly choose a number from 1 thru once you have that number (like 7 for example), take every 10 th person from that (like 17 th, 27 th, 37 th, etc.) (c) Separate into bussed and live nearby. Give every student in the bussed category a #, and then randomly select 200. Then give every student in the live nearby category a number, and randomly select 50. You total of 250 is your sample. (d) stratified. It is a more accurate representation of the population.