Statistics Sampling https://www.123rf.com/photo_6622261_statistics-and-analysis-of-data-as-background.html

Sampling You want to have a sample that closely resembles your population – a representative sample

Is it a representative sample? population Sampling IN-CLASS PROBLEM Is it a representative sample? population sample Vfrench, 2010

Sampling How do you make sure your sample statistic is close to your population parameter? http://us.cdn2.123rf.com/168nwm/ajn/ajn0901/ajn090100009.jpg

Sampling Your sample will RARELY be exactly the same as your population

Sampling Make sure that every element/subject in the population has an equal chance of being in the sample a RANDOM sample

Sampling How do you make sure your sample statistic is close to your population parameter?

Sampling Take the BIGGEST sample you can the LAW OF LARGE NUMBERS

Which school has the more believable results? Sampling IN-CLASS PROBLEM Which school has the more believable results? Favorite Class School A # of Students School B English 11 3 Math 7 4 Science 12 Social Studies 10 2 Computer Science 13 Music/Art 14 Physical Education 15 Foreign Language 6 1

Sampling The number in your sample is called the “sample size” It is usually called “n”

Sampling The population also has a size (probably really REALLY huge, and also probably unknown) called: “N”

Sampling How do you make sure your sample statistic is close to your population parameter?

Sampling Sampling errors can lead to results which have a specific bias or are only relevant to a specific subgroup

Sampling Suppose that you want to find out how successful ($) a film will be Suppose your film only appeals to a certain audience

What will you deduce from this sample? Sampling IN-CLASS PROBLEM Bad luck sample: What will you deduce from this sample? Vfrench, 2010

What will you deduce from this sample? Sampling IN-CLASS PROBLEM Unbiased sample: What will you deduce from this sample? Vfrench, 2010

Sampling IN-CLASS PROBLEM How do you make sure your sample statistic is close to your population parameter?

How To Lie With Statistics #1 Truman vs Dewey 1948 Why did they make the wrong forecast?    What would you do differently to get an accurate forecast?   http://www.theipinionsjournal.com

Questions?

Observational Surveys can be used to answer research questions

Types of Survey Research: Interrogation Surveys Ethnology Observation Observational Types of Survey Research: Interrogation Surveys Ethnology Observation

Surveys Are non-experimental, descriptive research methods Involve asking questions of respondents Are useful to collect data on something that cannot be directly observed (like opinions)

Observational For a survey, the whole group you are interested in finding out something about is called the population

You instead survey only a portion of the population - a Observational You instead survey only a portion of the population - a sample

Observational You do this because you do not have the resources to survey the entire population

Observational A sample is representative when it is an accurate reflection of the population under study ?

Observational No sample is ever a perfect representation of the population of interest ?

Questions?

Sampling A census is a “sampling” of “all” the members of a population

Sampling A description of all the members of a population is called a frame

Sampling Random Sampling Each member of the population has an equal chance of being included in the sample

How could you take a random sample? SAMPLING IN-CLASS PROBLEM How could you take a random sample? 1 Alabama 2  Alaska 3  Arizona 4  Arkansas 5  California 6  Colorado 7  Connecticut 8  Delaware 9  Florida 10  Georgia 11  Hawaii 12  Idaho 13  Illinois 14  Indiana 15  Iowa 16  Kansas 17  Kentucky 18  Louisiana 19  Maine 20  Maryland 21  Massachusetts 22  Michigan 23  Minnesota 24  Mississippi 25  Missouri 26  Montana 27  Nebraska 28  Nevada 29  New Hampshire 30  New Jersey 31  New Mexico 32  New York 33  North Carolina 34   North Dakota 35  Ohio 36  Oklahoma 37  Oregon 38  Pennsylvania 39  Rhode Island 40  South Carolina 41  South Dakota 42  Tennessee 43  Texas 44  Utah 45  Vermont 46  Virginia 47  Washington 48  West Virginia 49  Wisconsin 50  Wyoming

Will this be representative? SAMPLING IN-CLASS PROBLEM Will this be representative? 1 Alabama 2  Alaska 3  Arizona 4  Arkansas 5  California 6  Colorado 7  Connecticut 8  Delaware 9  Florida 10  Georgia 11  Hawaii 12  Idaho 13  Illinois 14  Indiana 15  Iowa 16  Kansas 17  Kentucky 18  Louisiana 19  Maine 20  Maryland 21  Massachusetts 22  Michigan 23  Minnesota 24  Mississippi 25  Missouri 26  Montana 27  Nebraska 28  Nevada 29  New Hampshire 30  New Jersey 31  New Mexico 32  New York 33  North Carolina 34   North Dakota 35  Ohio 36  Oklahoma 37  Oregon 38  Pennsylvania 39  Rhode Island 40  South Carolina 41  South Dakota 42  Tennessee 43  Texas 44  Utah 45  Vermont 46  Virginia 47  Washington 48  West Virginia 49  Wisconsin 50  Wyoming

Sampling Stratified Sampling Divide the population into non-overlapping groups (strata) Each member of a strata has an equal chance of being included in the sample

You need three random samples SAMPLING IN-CLASS PROBLEM 1  Connecticut 2  Delaware 3  Illinois 4  Indiana 5  Iowa 6  Maine 7  Maryland 8  Massachusetts 9  Michigan 10  Minnesota 11  Montana 12  New Hampshire 13  New Jersey 14  New York 15   North Dakota 16  Ohio 17  Pennsylvania 18  Rhode Island 19  South Dakota 20  Vermont 21  Wisconsin You need three random samples 1  Alaska 2  Arizona 3  California 4  Colorado 5  Hawaii 6  Idaho 7  Nevada 8  New Mexico 9  Oklahoma 10  Oregon 11  Utah 12  Washington 13  Wyoming 14  Kansas 15  Missouri 16  Nebraska 1 Alabama 2  Arkansas 3  Florida 4  Georgia 5  Kentucky 6  Louisiana 7  Mississippi 8  North Carolina 9  South Carolina 10  Tennessee 11  Texas 12  Virginia 13  West Virginia

Will this be representative? SAMPLING IN-CLASS PROBLEM 1  Connecticut 2  Delaware 3  Illinois 4  Indiana 5  Iowa 6  Maine 7  Maryland 8  Massachusetts 9  Michigan 10  Minnesota 11  Montana 12  New Hampshire 13  New Jersey 14  New York 15   North Dakota 16  Ohio 17  Pennsylvania 18  Rhode Island 19  South Dakota 20  Vermont 21  Wisconsin Will this be representative? 1  Alaska 2  Arizona 3  California 4  Colorado 5  Hawaii 6  Idaho 7  Nevada 8  New Mexico 9  Oklahoma 10  Oregon 11  Utah 12  Washington 13  Wyoming 14  Kansas 15  Missouri 16  Nebraska 1 Alabama 2  Arkansas 3  Florida 4  Georgia 5  Kentucky 6  Louisiana 7  Mississippi 8  North Carolina 9  South Carolina 10  Tennessee 11  Texas 12  Virginia 13  West Virginia

Sampling Systematic Sampling Selects every “kth” member from the population (from a random starting point)

Sampling We need 10 observations in our sample That will be every 5th member of the population Pick a random starting place 1-5

SAMPLING IN-CLASS PROBLEM 1 Alabama 2  Alaska 3  Arizona 4  Arkansas 5  California 6  Colorado 7  Connecticut 8  Delaware 9  Florida 10  Georgia 11  Hawaii 12  Idaho 13  Illinois 14  Indiana 15  Iowa 16  Kansas 17  Kentucky 18  Louisiana 19  Maine 20  Maryland 21  Massachusetts 22  Michigan 23  Minnesota 24  Mississippi 25  Missouri 26  Montana 27  Nebraska 28  Nevada 29  New Hampshire 30  New Jersey 31  New Mexico 32  New York 33  North Carolina 34   North Dakota 35  Ohio 36  Oklahoma 37  Oregon 38  Pennsylvania 39  Rhode Island 40  South Carolina 41  South Dakota 42  Tennessee 43  Texas 44  Utah 45  Vermont 46  Virginia 47  Washington 48  West Virginia 49  Wisconsin 50  Wyoming

Will this be representative? SAMPLING IN-CLASS PROBLEM Will this be representative? 1 Alabama 2  Alaska 3  Arizona 4  Arkansas 5  California 6  Colorado 7  Connecticut 8  Delaware 9  Florida 10  Georgia 11  Hawaii 12  Idaho 13  Illinois 14  Indiana 15  Iowa 16  Kansas 17  Kentucky 18  Louisiana 19  Maine 20  Maryland 21  Massachusetts 22  Michigan 23  Minnesota 24  Mississippi 25  Missouri 26  Montana 27  Nebraska 28  Nevada 29  New Hampshire 30  New Jersey 31  New Mexico 32  New York 33  North Carolina 34   North Dakota 35  Ohio 36  Oklahoma 37  Oregon 38  Pennsylvania 39  Rhode Island 40  South Carolina 41  South Dakota 42  Tennessee 43  Texas 44  Utah 45  Vermont 46  Virginia 47  Washington 48  West Virginia 49  Wisconsin 50  Wyoming

Sampling Cluster Sampling Randomly select a group of members from the population

Pick a starting place: SAMPLING IN-CLASS PROBLEM 1 Alabama 2 Alaska 3  Arizona 4  Arkansas 5  California 6  Colorado 7  Connecticut 8  Delaware 9  Florida 10  Georgia 11  Hawaii 12  Idaho 13  Illinois 14  Indiana 15  Iowa 16  Kansas 17  Kentucky 18  Louisiana 19  Maine 20  Maryland 21  Massachusetts 22  Michigan 23  Minnesota 24  Mississippi 25  Missouri 26  Montana 27  Nebraska 28  Nevada 29  New Hampshire 30  New Jersey 31  New Mexico 32  New York 33  North Carolina 34   North Dakota 35  Ohio 36  Oklahoma 37  Oregon 38  Pennsylvania 39  Rhode Island 40  South Carolina 41  South Dakota 42  Tennessee 43  Texas 44  Utah 45  Vermont 46  Virginia 47  Washington 48  West Virginia 49  Wisconsin 50  Wyoming

Will this be representative? SAMPLING IN-CLASS PROBLEM Will this be representative? 1 Alabama 2  Alaska 3  Arizona 4  Arkansas 5  California 6  Colorado 7  Connecticut 8  Delaware 9  Florida 10  Georgia 11  Hawaii 12  Idaho 13  Illinois 14  Indiana 15  Iowa 16  Kansas 17  Kentucky 18  Louisiana 19  Maine 20  Maryland 21  Massachusetts 22  Michigan 23  Minnesota 24  Mississippi 25  Missouri 26  Montana 27  Nebraska 28  Nevada 29  New Hampshire 30  New Jersey 31  New Mexico 32  New York 33  North Carolina 34   North Dakota 35  Ohio 36  Oklahoma 37  Oregon 38  Pennsylvania 39  Rhode Island 40  South Carolina 41  South Dakota 42  Tennessee 43  Texas 44  Utah 45  Vermont 46  Virginia 47  Washington 48  West Virginia 49  Wisconsin 50  Wyoming

Questions?

Bias If your sample is not representative of the population, the sample is biased

Bias Sources of bias: sampling bias (bad-luck sample) nonresponse bias (Reps respond, Dems don’t) response bias (crummy survey questions) inaccurate data entry

Questions?