chapter 1 jan. 8, 20081 chapter 1 where do data come from?

Chapter 1 Jan. 8, 2008

1

Chapter 1

Where Do Data Come From?


2

Thought Question 1

From a recent study, researchers concluded that high levels of alcohol consumption resulted in lower graduation rates at colleges. How do you think this study was carried out in order to get these results? Do you think the conclusion is correct? Is there a more reasonable conclusion?


3

Thought Question 2

It is popular knowledge that for similar jobs men earn more money on average than women, and yet there are cases where some women make more money than some men. Therefore, to determine if men really do earn more, you would need to sample many people of each sex. Suppose we also want to know if, on average, men stay at their current jobs for a longer time period than women. How could you go about trying to determine this? Would it be sufficient to collect data for one member of each sex?... two members of each sex? What information about men’s and women’s measurements would help you decide how many people to measure?


4


5

What is STATISTICS ?

Using “data” to draw a conclusion about something unknown.

Decision making in the presence of uncertainty.


6

Statistics- Meaning ?

Method of analysisa collection of methods for planning experiments

or observational studies, obtaining data, and

then organizing, summarizing, presenting,

analyzing, interpreting, and drawing conclusions

based on the data.


7

Statistics- Meaning ?

Our Book:

Statistics is the science (or ‘art’) of data.


8

Common Language


9

Population The complete collection of all subjects or

objects (scores, people, measurements, and

so on) that are being studied.

The collection is complete in the sense that it

includes all subjects to be studied.


10

Census: The collection of data from every element in a population.

Sample : A subset of elements drawn from a population from which we collect data.

The sample must be a good representative of the entire population.


11

Population

individuals


12

Sampling Frame

Individuals that could possibly be selected for the sample (not necessarily the same as the population)


13

List of Individuals123456789

1011121314151617

Census

1

9

23 4 5 6

78

10

17161513

14

1211

1

9

23 4 5 6

78

10

17161513

14

1211

Census


14

Sampling Frame

1

9

23 4 5 6

7810

17161513

14

1211

List of Individuals123456789

1011121314151617

Sample


15

Example

Suppose we are interested in the average age of all Malaspina students.

The relevant population is all Malaspina students (including students in all campuses).

Sampling Frame: List of Malaspina students at the Nanaimo campus.


16

Example Cont.

A sample can be students in this Math 161 class, or, 50 randomly selected Malaspina students at the Nanaimo campus.

If we use the ages of all Malaspina students, then we have a census.


17

_____________________________________

______________________________________

______________________________________

What is Statistics?


18

Descriptive & Inferential StatisticsDescriptive & Inferential Statistics

StatisticalMethods

DescriptiveStatistics

InferentialStatistics

StatisticalMethods

DescriptiveStatistics

InferentialStatistics


19

Descriptive Statistics

Consists of the collection, organization,

summarization, and presentation of

data.


20

Inferential Statistics

Consists of generalizing from samples

to populations, performing estimations

and hypothesis tests, determining

relationships among variables, and making

predictions.


21

What Is “Data”?(better: What are “data”?)

?

Pieces of information.

Numbers.

The above are data only if the information has a meaning attached.


22

Data

Data are observations that have been collected. The observation may be numerical (example: age, height, GPA) or non-numerical (example: gender, eye colour, province of residence)

The Nature of DataThe Nature of Data


23

Two Types of Data

Quantitative or Numeric Data

Numbers representing counts or measurements.

Qualitative or Categorical Data Data can be separated into different categories that are distinguished by some non-numeric characteristics.

The Nature of DataThe Nature of Data


24

ExamplesQuantitative (numerical) data

the ________________ of college graduates

the ________________ between home and school

Qualitative (or categorical) data

the ___________ of college graduates (F, M)

the ___________ of a product (best, good, bad)


25

Two Types of Quantitative Data

Discrete: Data values that can be counted such as 0, 1, 2, 3, . . .

Example: Number of students in a Stat. class.

Continuous: Data that can assume an infinite number of values between any two specific values. - Usually results from measurements.

22 33


26

Classify as discrete or continuous:

1. The number of eggs that hens lay;

for example, 3 eggs a day________.

Examples

2. The height of College students.

___________________


27

C a te go rica l

D isc re te C o ntin uo us

N u m e rica l

D a ta


28

1. Nominal: characterized by data that

consist of names, labels, or categories only.

The data cannot be arranged in an ordering

scheme (such as low to high)

Example: Survey responses may be yes, no,

or undecided. Eye colour, gender etc.

Levels of Measurements


29

2. Ordinal: involves data that may be

arranged in some order, but differences

between data values either cannot be

determined or are meaningless

Example: Course grades: A, B, C, D, or F

Dress size: small, medium, large, XL


30

3. Interval: like the ordinal level, with the

additional property that the difference between

any two data values is meaningful. However,

there is no natural zero starting point (where

none of the quantity is present)

Example: Years 1000, 2000, 1776, and 1492

Temperature in 0C - 0 0C does not mean no

temperature.


31

4. Ratio: the interval level modified to

include the natural zero starting point (where

zero indicates that none of the quantity is

present). For values at this level, differences

and ratios are meaningful.

Example: Prices of college textbooks.


32

Levels of Measurement_________________ - categories only

_________________- categories with some order

_________________- differences but no natural

starting point

_________________- differences and a natural

starting point


33

Summary

DataData

CategoricalCategorical NumericalNumerical

NominalNominal OrdinalOrdinal IntervalInterval RatioRatio


34

How Data are Obtained Observational Study

– Observes individuals and measures variables of interest but does not attempt to influence the responses.

– Describes some group or situation.– Sample Surveys are a type of observational

study.

Experiment– Deliberately imposes some treatment on

individuals in order to observe their responses.– Studies whether the treatment causes change in

the response.


35

Experiments vs. observational studies

for comparing the effects of treatments: Experiment

– experimenter determines which units receive which treatments (ideally using some form of random allocation)

Observational study– compare units that happen to have received each of the

treatments

– often useful for identifying possible causes of effects, but cannot reliably establish causation

Only properly designed and executed experiments can reliably demonstrate causation.


36

Data SourcesData Sources

DataSources

Primary Secondary

Experiment Survey Observation


37

Case Study

The Effect of Hypnosison the

Immune System

reported in Science News, Sept. 4, 1993, p. 153


38

Case Study


Immune System

Objective:To determine if hypnosis strengthens thedisease-fighting capacity of immune cells.


39

Case Study 65 college students.

– 33 easily hypnotized– 32 not easily hypnotized

white blood cell counts measured

All students viewed a brief video about the immune system.


40

Case Study

Students randomly assigned to one of three conditions– subjects hypnotized, given mental exercise– subjects relaxed in sensory deprivation

tank– control group (no treatment)


41

Case Study

white blood cell counts re-measured after one week

the two white blood cell counts are compared for each group

Results– hypnotized group showed larger jump in white

blood cells– “easily hypnotized” group showed largest immune

enhancement


42

Case Study


Immune System

What is the population?

What is the sample?


43

Case Study


Immune System

What data werecollected?

Easy or difficult to achieve hypnotic trance

Group assignment Pre-study white

blood cell count Post-study white

blood cell count


44

Case Study


Immune System

Is this an experimentor

an observational study?


45

Case Study


Immune System

Do hypnosis and mental exercise affect the immune system?


46

Case Study

Weight Gain SpellsHeart Risk for Women

“Weight, weight change, and coronary heart disease in women.” W.C. Willett, et al., vol. 273(6), Journal of the American Medical Association, Feb. 8, 1995.

(Reported in Science News, Feb. 18, 1995, p. 108)


47

Case Study


Objective:To recommend a range of body mass index (a function of weight and height) in terms of

coronary heart disease (CHD) risk in women.


48

Case Study

Study started in 1976 with 115,818 women aged 30 to 55 years and without a history of previous CHD.

Each woman’s weight (body mass) was determined.

Each woman was asked her weight at age 18.


49

Case Study

The cohort of women were followed for 14 years.

The number of CHD (fatal and nonfatal) cases were counted (1292 cases).

Results were adjusted for other variables.


50

Case Study

Results: compare those who gained less than 11 pounds from age 18 to current age to the others.– 11 to 17 lbs: 25% more likely to develop

heart disease– 17 to 24 lbs: 64% more likely– 24 to 44 lbs: 92% more likely– more than 44 lbs: 165% more likely


51

Case Study


What is the population?

What is the sample?


52

Case Study


What data werecollected?

Age in 1976 Weight in 1976 Weight at age 18 Incidence of coronary

heart disease Other: smoking, family

history, menopausal status, post-menopausal hormone use


53

Case Study


Is this an experimentor

an observational study?


54

Case Study


Does weight gain in women increase their risk

for CHD?


55

Key Concepts Knowing about statistical methods will

have practical consequences in your everyday lives.

Experiment versus Observational Study. Common Terms:

– Individuals, Population, Sampling Frame, Sample, Sample Survey, Census, Variable.


56

ConclusionConclusion Defined statistics. Distinguished between descriptive &

inferential statistics. Summarized the sources of data. Described the types of data & scales. Common Terms: Population, Sampling

frame, Census, Sample, Individuals, Variables etc.

chapter 1 jan. 8, 20081 chapter 1 where do data come from?

Documents

sample slide

census slide

common language slide

collection of data

population individuals

list of malaspina students

selected malaspina students

art of data