"In earlier times they had no statistics, and so they had to fall back on lies. Hence the huge exaggerations of primitive literature - giants or miracles.

"In earlie

r times they had

nostatistics, and so th

ey

had to fall back on lie

s.

Hence the huge

exaggerations of

primitiv

e literature -

giants or miracles or

wonders! They did it with

lies and we do it with

statistics; but it is all th

e

same."

Stephen LeacocK (1869-

1944)

Facts are stubborn,

but statistics are more pliable."

Mark Twain (1835-1910)“POLLS ARE FOR DOGS”John G. Diefenbaker

(13th Prime Minister of Canada)

What is Statistics?

Statistics is the gathering, organizing, analyzing, and presenting of numerical information.

The data gathered by statistical studies are used to guide decisions, explain events, predict future courses of action, or provide the basis for a solution to a problem.

Population vs. SampleOnce you have decided on the topic you wish to study, the first major step of your study involves gathering the data. From whom you are going to gather the data is your first decision.

Population

all individuals who belong to a group being studied

Group being studied

Sample

a selection of individuals taken from a population

People that are actually asked or polled

Identify the population for each of the following questions

a) Whom do you plan to vote for in the next Ontario election?

_____________________________

b) Do women prefer to wear ordinary glasses or contact lenses?

_______________________________

All Canadian Citizens that live in Ontario of voting age

Women who require corrective eyewear

Determine if the following is a sample or a population

a) A representative from each hockey team is asked to complete a survey on game times__________________

b) Canada census survey__________________

c) One in every 10 bottles of pop are tested for defects in a factory________________________

Sample

Population

Sample

Types of Data and Sampling

Once you have determined the population that you are considering for your study. The next step in completing your study is obtaining a sample that best represents your population.

Sample selection is one of the key factors that will determine if your survey is valid and will produce legitimate conclusions

Types of DataRaw Data

This is the name given to data that has not yet been analyzed, only collected.

Discrete Data

There is a limit to the categories that data can be placed in. Ex. The soft drink size at the movie theatre

There are only the 4 categories and it is not possible to go in between them.

Continuous Data

All rational values.

The data can take on any value, particularly decimal values of infinite place value.

Population numbers

Counts of physical objects where fractions don’t make sense (people)

Time ( can win a race in 3 seconds or 3.4 seconds or 3.148 etc..)

Length

Mass

Discrete Data Continuous Data

4 Types of Data

Nominal DataOrdinal Data

Interval Data

Ratio Data

This is data that can be linked into categories but those categories can not be ranked or quantified

Ex: if a survey asks what type of food you prefer: Chinese, Italian, American or Indian.

Nominal Data Discrete

Data is organized into rankings.

Ex: Rank your top five favourite movies. Matrix = 1

Batman Begins = 2 etc…

The order doesn’t matter as long as the data can be ranked the way that you want it to be.

Ex: Matrix = 100Batman Begins = 300

Ordinal DataDiscrete

Data is categorized into numerical groupings in which the distance between these groupings is the same

The initial or zero point is arbitrary

Ex: Intervals 2006-2007 is the same as 2005-2006

Ex: IQ intervals

Interval Data Discrete

All continuous data is Ratio Data.

The name ratio comes from Rational, the number system which contains decimal values

Ex: Your time in the 100 m dash

Ratio DataContinuous

Sampling The method used to collect sample

data from a population is very important and can mean the difference between a credible conclusion or a biased one

Simple Random Sampling

Gives all the elements of the population an equal chance of being a part of the sample.

Must be as impartial as possible and not favouring one over the other

Systematic Sample

Selecting a sample from a population is done systematically or through a constant counting process

Ex: picking every 100th person from a phone book

To determine if you should choose ever 5th or 100th item find the ratio of the population and sample

If you wanted a tenth of the population then select every 10th item.

Ex: A telephone company is planning a marketing survey of its 760 000 customers. For budget reasons, the company wants a sample size of about 250.

a) Determine the interval that should be used for a systematic sample.

Therefore the company should be selecting every 3040th customer for their survey

population sizeinterval =

sample size

760000

250 3040

Stratified Sample Takes into account that a population

is made up of many demographics that tend to react differently

If a population of turtles has more females than males, then if the sample is purposely weighted with more females than males in a proportional number to the population, it is stratified sample.

To determine how many subjects from each subgroup to select determine the percent of that subgroup is in the population and multiply by the number desired in the sample

##

subgroupsample

population

Ex: Before booking bands for the school dances, the students’ council at Statsville H.S. wants to survey the music preferences of the student body. The following table shows the enrolment at the high school

a) Design a stratified sample for a survey of 25% of the student body

Grade # Students

9 255

10 232

11 209

12 184

Total 880

25% of the student body is

880 x 0.25 = 220

Complete this step for each grade and you should get that there should be:• 64 gr 9’s• 58 gr 10’s• 52 gr 11’s• 46 gr 12’s

##

255220

880

63.75

= 64 gr 9's should be selected

subgroupsample

population

To check they should add up to 220

Cluster Sample Takes advantage of groups that have

similar characteristics of other similar groupings

Randomly selecting whole classes assuming they are random

Multi-Stage Sample

Uses compound randomization

A study that determines passenger safety in cars randomly picks a car manufacturer (stage 1), then randomly picks a vehicle type like a van, compact, truck (stage 2), then randomly picks a type of car in that class (stage 3).

Ex: Suppose that your population consisted of all Ontario households. How would you create a Multi-Staged Sample?

You could first randomly select from the different towns/cities in Ontario

Then randomly select a sample of blocks or subdivision within the selected cities

Finally you could then select from individual homes on that block

Voluntary-Response Sample

Depends on the initiative of the sample itself

Internet and mail polls

Elements selected for the sample may or may not respond

This creates a potential bias

Convenience Sample

Samples local elements that are nearby or elements that are accessible with little or no cost

Telephone or internet

Homework

Pg 117 #4,6,8,9,11Pg 123 # 1-6