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Statistical Reasoning

Real Estate Statistics

- From Scottsdale Real Estate Report

What is statistics?

- Statistics is the science of collecting,

organizing, and interpreting data. - Statistics are the data that describe or

summarize something.

Fundamentals of Statistics

- Suppose that you want to know which candidate is

most popular choice for the upcoming presidential

election. - How might you get some find some data?
- CNN/Opinion Research Corporation Poll. Oct.

12-14, 2007. N485 registered voters nationwide

who are Democrats or independents who lean to the

Democratic Party. MoE 4.5.

PollingReport.com

- "Please tell me which of the following people you

would be most likely to support for the

Democratic nomination for president in the year

2008 . . . ." - 10/12-14/07
- Hillary Clinton 46
- Barack Obama 17
- Al Gore 14
- John Edwards 12
- Bill Richardson 3
- Joe Biden 1
- Christopher Dodd 1
- Mike Gravel 1
- Dennis Kucinich 1
- Unsure 4

Definitions

- Population - the complete set of people or things

being studied. - What is the population in our political poll?
- Sample - the subset of the population from which

your data is obtained. - What is the sample in our political poll?
- Population parameters - the characteristics about

the population that we want to learn about. - What parameters are we interested in with our

political poll? - Sample statistics - raw data consolidated into a

set of numbers that characterize the data. - What sample statistic are given from our poll?

Statistical Study

start

1. Identify goals

2. Draw from a population

population

sample

3. Collect raw data and summarize

5. Draw conclusions

4. Make inferences about population

Sample statistics

Population parameters

Choosing a sample

- Want to find a representative sample - one in

which the sample members match those of the

population. - Sampling methods
- Simple random sampling - choose in a way that

every sample of a given size has an equal chance

of being chosen. - Systematic sampling - use a simple system for

choosing the sample. - Convenience sampling - choose a sample based on

convenience - Stratified sampling - use when we are interested

in the difference between different subgroups - How would we find a representative sample for our

political poll?

Sampling Methods

- Which type of sampling is used in each of these

cases? - You are conducting a survey of students in a

dormitory. You choose your sample by knocking on

every 10th door. - To survey opinions on a possible property tax

increase, a research firm randomly draws the

addresses of 150 homeowners from a public list of

all homeowners. - Agricultural inspectors for Jefferson County

check the levels of residue from three common

pesticides on 25 ears of corn from each of the

104 corn producing farms in the county. - Anthropologists determine the average brain size

of early Neanderthals in Europe by studying

skulls found at three sites in southern Europe.

Bias

- Bias refers to any problem in the design or

conduct of a statistical study that tends to

favor certain results. - How might bias be introduced in our political

poll?

Types of studies

- Observational study - researchers attempt to

observe or measure characteristics of the sample,

but do not try to influence these

characteristics. - Experiment - researchers apply a treatment to

some or all of the sample members, then look to

see whether the treatment has any effect

Experimental studies

- Suppose you want to test whether high doses of

vitamin C can help prevent colds. Researches

must ask some people in the sample to take the

high dose of vitamin C - we call this the

treatment group, and we compare to a control

group who does not take vitamin C - Both the treatment group and the control group

must be chosen randomly and must be alike in all

respects except for the treatment.

Placebo effect and Blinding

- What is the Placebo effect?
- A placebo lacks the active ingredients of a

treatment being tested in a study, but is

identical in appearance to the treatment.

Participants dont know if they are getting the

treatment or not. - In statistical terms, keeping people in the dark

about whether they are receiving the treatment is

called blinding. - Single blind participants dont know if they

are receiving the treatment or the placebo. - Double blind the researchers dont know who is

getting the treatment and who is getting the

placebo.

Case control studies

- Observational studies that look like experiments

because the sample naturally divides into groups. - Consider that you want to study how alcohol

consumed during pregnancy can be harmful to the

baby. Obviously you couldnt set this up as an

experiment since you know that alcohol can cause

harm, instead you might look for participants

who engage in the behavior under study and they

form cases. The participants who dont engage in

the behavior are the control group.

Margin of error

- Surveys and opinion polls usually include a

margin of error. - The margin of error is used to describe the

confidence interval that is likely to include the

true population parameter. The confidence

interval is - (sample statistic - margin of error) to (sample

statistic margin of error)

Should you believe a statistical study?

- 8 guidelines
- Identify goal, population, type of study
- Consider the source
- Look for bias in the sample
- Look for problems in defining or measuring the

variables of interest - Watch out for confounding variables
- Consider the setting and the wording in surveys
- Check that results are presented fairly
- Stand back and consider the conclusions

Should you believe these studies?

- Spend time working on the worksheet

Statistical Tables and Graphs

- Think about the grade distribution from our last

exam. How was the data presented? - Suppose the grades on the exam were
- 57, 63, 94, 68, 88, 86, 73, 91, 83, 84, 79, 59,

72, 75, 96, 81, 76, 89, 75, 78 - What are some things you could do with this data

to get a better feel for how your score compares

to the rest of the class?

Frequency Table

- A frequency table has two columns
- The first column lists all the categories of data
- The second column lists the frequency of each

category

Another way to look at the data

Quantitative vs. Qualitative data

- Suppose that the tests were given a letter grade

instead of an score - this is called qualitative

data because it describes the quality of the data

(Aexcellent, Bgood, Csatisfactory,) - The score is quantitative data. It is a measure

of what percentage of the work was correct.

Quantitative data is always in the form of a

number, but data in the form of numbers is not

always quantitative. - For example, film reviewers might rate a new

movie on a scale of 1 to 5 stars. This is a

number rating, but the numbers represent

subjective opinions.

Carbon Dioxide Emissions

- Carbon dioxide is released into the atmosphere

primarily by the combustion of fossil fuels (oil,

coal, natural gas). The following table lists

the 8 countries that emit the carbon dioxide each

year.

Bar Graphs

A bar graph with the bars in descending order is

often called a Pareto chart.

- Why might you want to display the bars in

descending order?

- Why are the countries in a different order in the

two charts displayed here?

Pie Chart

-What stands out on the pie chart?

-Why might you choose to represent the data in a

pie chart rather than a bar graph?

Histogram and Line Charts

Histograms and Line charts are used when the

categories are quantitative.

Time series diagram

A time series diagram is a line chart where the

horizontal axis is time.

- The following data shows how a state lottery

distributed its 2.1 million proceeds in the year

2000. - Draw two graphs. One should support the argument

that too much money from the state lottery went

toward education. The other should support the

counter argument, too little money from the state

lottery went toward education. - Choose a side to the above argument, either pro

or con. Write a paragraph defending your

argument, citing social, political, ethical

and/or religious facts.

Graphics in the Media

- Multiple bar graphs
- Stack Plots
- Geographical data
- Contour maps
- 3 dimensional data

Contour Map of Temperature

Median Age by State

Cautions about Graphics

- Perceptual distortion
- Watch the scales

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