MDM 4UI – Selecting Samples

Put your stuff IN the desks

Get into 4 groups.

One group – 10 people

One group – 8 people

Two groups – 6 people each

So this chapter is pretty boring ….

The StoryIn a very remote part of Canada there is a town of 30 people. They are organized into 4 very distinct groups. While the groups live and work in harmony they have different beliefs on many topics. The diversity in the beliefs of the townsfolk conveniently reflects the diversity of beliefs in Canada.

Boris the Pirate has recently been hired by the Canadian Government to visit the town and conduct a survey on the town’s opinion of pirates. The Government will use this information to draw conclusions about Canada’s opinions of pirates.

The TownspeopleActors & Actresses

Rachel McAdamsEvagenline LillyElisha CuthbertKim CatrellCarey Ann MossMichael J. FoxJim CarreyKeanu ReevesRyan RenoldsWilliam Shattner

Athletes

Hayley Wickenheiser

Tessa VirtuePerdita FelicienCatriona Le May Doan

Sidney CrosbyJoey VottoSimon WittfieldSteve Nash

Monsters & Aliens

GodzillaJabberwockKing KongDraculaAlien from Alien Movies

The Balrog

Politicians

Sir John A. Macdonald

Pierre TrudeauTommy DouglasKim CampbellAlexa McDonoughElizabeth May

The government requires that Boris survey approximately half the townspeople.

Attempt 1

Boris arrives in the town early in the morning and asks the first 15 people he finds on Main Street to complete his pirate survey. They all say yes.

Rachel McAdamsEvagenline LillyElisha CuthbertKim CatrellCarey Ann MossMichael J. FoxJim CarreyRyan Renolds

Hayley WickenheiserTessa VirtuePerdita FelicienCatriona Le May DoanSidney CrosbyJoey Votto

Kim Campbell

Shockingly the government asked him to do it again….

Attempt 2Boris writes down a list of everyone in town in alphabetical order and then finds asks every other person on his list to do the survey. They all say yes.

Alexa McDonoughAlien from Alien Movies

Carey Ann MossCatriona Le May Doan

DraculaElisha CuthbertElizabeth May

Evagenline LillyGodzilla

Hayley WickenheiserJabberwockJim CarreyJoey Votto

Keanu ReevesKim Campbell

Kim CatrellKing Kong

Michael J. FoxPerdita FelicienPierre Trudeau

Rachel McAdamsRyan RenoldsSidney CrosbySimon Wittfield

Sir John A. MacdonaldSteve Nash

Tessa VirtueThe Balrog

Tommy DouglasWilliam Shattner

Boris gives up quickly …

Attempt 3Boris just decides to ask everyone in two of the four groups. 2 out of 4 is half. (right?) They all say yes.

Government still not happy …

Attempt 4Boris decides to ask half of each group at random. They say yes again. !!

Athletes

Hayley WickenheiserSidney CrosbyJoey VottoSimon Wittfield

Monsters & Aliens

GodzillaKing KongDracula

Politicians

Sir John A. MacdonaldPierre TrudeauElizabeth May

Actors & Actresses

Kim CatrellCarey Ann MossKeanu ReevesRyan RenoldsWilliam Shattner

? ?

The End?After 4 attempts everyone in town has been asked, except for the Alien from the movie Alien. (No one knows where it came from anyways) Poor Joey Votto has had to complete the survey 4 times!! The government decides to recall Boris. Since Boris asked 29 of the 30 “people” in town he has actually completed a census of the town and gained valuable information on Canadians opinions on pirates.

Unfortunately to complete the census and ask (almost) everybody Boris wasted a lot of money. Suppose Boris had only done the survey once. Which method would have been best?

The AnswerIt depends….

Perhaps the question was trivial enough that it didn’t really matter who he asked. A quick random survey would have been sufficient.

Perhaps the question was so important that he should have done a census from the beginning. Does this ever happen in Canada?

Organizing everyone in an alphabetic list was time consuming, but what if he had done it by street addresses or used the phone book. That would have saved time but he still might have asked 83% of the monsters and 20% of the actors.

Asking whole groups certainly was quick because Boris waited until each group was assembled. Whole segments of the population were ignored. Picking all the people on half the streets would have been better but still there are no guarantees that it would have generated a representative sample.

Asking the same percentage of each group seemed like the best idea but due to random chance it still created an over 2 to 1 gender imbalance.

The Answer part 2

Techniques for picking a sample that accurately represents the population are very advanced mathematics.

Techniques for determining how accurately a sample represents a population are also very advanced mathematics.

You need to have an understanding of some introductory techniques and be able to evaluate their pros and cons.

MDM 4UI – Selecting Samples

In a census every member of a population is surveyed. This is expensive and generally unnessary. Only used when asking everyone is important or required.

In general a sample or portion of the population is surveyed. The conclusions generated from the sample are used to draw conclusions about the whole population.

There are 2 ways to study a sample studied in this course.

Cross-section: Study a cross section of the population at an instant in time.

Longitudinal: Study the same sample several times over a period of time. (Eg: drug trials)

MDM 4UI – Selecting Samples

There are 6 sampling methods we study in the course.

Simple Random: Randomly pick people to survey.

Systematic: Put people in order (somehow) and survey every nth (eg. 5th) person

Stratified: Put people in groups then survey the same percentage in each group. (all groups, some members)

Clustered: Put people in groups then survey the some whole groups and ignore others. (some groups, all members)

Multi-stage: Put people in groups then pick some of the groups and survey the same percentage in the groups that are chosen. (some groups, some members)

Destructive: A method where the sample is destroyed as part of the survey.(Good for light bulbs, not so much for people)