Statistics Lecture 2 Notes

7/29/2019 Statistics Lecture 2 Notes

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MATH 1050Y

A Non-Calculus Based Introduction toProbability & Statistical Methods

Section A

FW 2012-13

Instructor: Jaclyn Semple

MATH 1050Y-A (FW 2012-13) 1 -37

Recap of Last Class

MATH 1050Y-A (FW 2012-13)

1. A sample of 50 patients is selected fromall the patients admitted to the ER at ahospital, and it is found that 28% have nohealth insurance. The value 28% is a:

A. Parameter

B. Statistic

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Recap of Last Class

MATH 1050Y-A (FW 2012-13)

2. Telephone area codes best fits the datacategory of:

A. Qualitative, nominalB. Qualitative, ordinalC. Quantitative, discrete, ratioD. Quantitative, discrete, intervalE. Quantitative, continuous, ratio

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Recap of Last Class

MATH 1050Y-A (FW 2012-13)

3. Annual incomes of nurses best fits the datacategory of:

A. Qualitative, nominalB. Qualitative, ordinalC. Quantitative, discrete, ratioD. Quantitative, continuous, intervalE. Quantitative, continuous, ratio

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Recap of Last Class

MATH 1050Y-A (FW 2012-13)

4. A pollster in Saskatchewan surveys 200people and asks them their preference ofpolitical party. She codes the responses as 0

(for Green), 1 (for Liberal), 2 (for NDP), 3 (forConservative). She then calculates theaverage and gets 1.78. How can this valuebe interpreted?

Discuss with your neighbour

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Chapter 1Introduction to Statistics

1-1 Overview

1-2 The Nature of Data

1-3 Uses and Abuses of Statistics

1-4 Design of Experiments


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Abuses of Statistics

Data can often be presented in ways that maybe misleading.

Some abuses of statistics are unintentional,

such as people who are ignorant or careless. In other cases, the abuses of statistics are

intentionally in order to support personalobjectives.

We should learn to distinguish betweenstatistical conclusions that are likely to bevalid and those that are seriously flawed.

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Bad Samples

A major source of deceptive statistics isinappropriate methods of collecting data.

One very common sampling method allows

the sample subjects to decide for themselveswhether to be included.

A self-selected sample is one in which therespondents themselves decide whether to beincluded.

In this case, valid conclusions can be madeonly about the specific group of people whoagree to participate and not about thepopulation.

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Small Samples

We will see later that small samples are notnecessarily a bad thing. However, smallsamples are sometimes used as a form ofstatistical lying.

Example: The preferences of only 10 dentistsshould not be used as a basis for a generalizedclaim such as Colgate toothpaste isrecommended by 7 out of 10 dentists.

Samples small or large must be unbiasedand representative of the population from whichit comes.

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Precise Numbers

Sometimes the numbers themselves can bedeceptive. A very precise figure can often bemisinterpreted as being accurate.

Example: A sample of 2500 students from aCanadian university produced an average salaryof $25,542.64.

A precise figure can be an estimate (samplestatistic) rather than a population parameter.When it is an estimate, this fact should beemphasized to avoid confusion.

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Guesstimates

Some estimates are really just guesses and canbe in error by substantial amounts.

As such, it is important for us to consider the

source of the estimate and how it wasdeveloped.

Example: Your friend asks you How manypeople were at the party on Saturday? Youanswer, About 30 people. However, you didntactually count the number of people at the party.Also, you were only there for one hour and theparty lasted for six hours.

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Distorted Percentages

Misleading or unclear percentages aresometimes used.

Example: An airline ran full-page ads boasting

that, with respect to lost baggage, they hadimproved 100% in the last six months. Manypeople would incorrectly interpret this to meanthat now no baggage is being lost.


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Partial Pictures

Data can be presented in such a way as to omitan important piece of information.

Example: In the 1950s, Camel brand cigarettes

aired a commercial indicating that they askedthousands of doctors the question Whatcigarette do you smoke, Doctor? Based on theanswers to this question, they were able to claimMore doctors smoke Camels than any otherbrand of cigarette. What they failed to mentionis what percentage of doctors in their sampleactually smoked cigarettes or didnt respond.

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Partial Pictures contd

Example: A car company advertises that Ninetypercent of all our cars sold in this country in thelast ten years are still on the road. BUT they

didnt mention that almost all of those cars hadbeen sold within just the last three years!

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Deliberate Distortion

Some studies or surveys are distorted onpurpose. The distortion can occur within thecontext of the data, the source of the data, thesampling method, or the conclusions.

Example: A website catering to dog ownersposts an online survey to determine the mostpopular type of pet.

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Loaded Questions

If survey questions are not worded carefully, theresults of a study can be misleading. Surveyquestions can be loaded or intentionallyworded to elicit a desired response.

Example: The percentage of people who agreewith the statement Too little money is beingspent on welfare. would tend to be much lowerthan the percentage who agree with thestatement Too little money is being spent onassistance to the poor.

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To correctly interpret a graph, you must analyze thenumerical information given in the graph, so as notto be misled by the graphs shape. Read labels andunits on the axes!

Misleading Graphs

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Diagram (b) is designed to exaggerate the difference byincreasing each dimension in proportion to the actualamounts of oil consumption.

Pictographs


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Pause & Practice

1. Youve been hired to research recognition of theRoots brand name, and you must conduct atelephone survey of 1500 customers in Canada.

This is an example of:

A. Distorted percentages

B. Guesstimates

C. Bad sample

D. Precise numbers

E. Misleading graphs

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Pause & Practice

2. A report sponsored by British Columbia fruitfarmers concluded that cholesterol levels can belowered by eating fruit products. Do you trust this

conclusion?

A. Yes

B. No

Discuss with your neighbour why this conclusionmight be suspect.

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Pause & Practice

3. Sixty-eight percent of those who responded to aToronto Star poll question said that the provincialgovernment should change the law to make iteasier to get squeegee kids off the streets. Doyou think this result valid?

A. Yes

B. No

Discuss the validity of this result with yourneighbour.

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Pause & Practice

4. An East Coast newspaper claims that pregnantmothers can increase their chances of havinghealthy babies by eating lobster. That claim isbased on a study showing that babies born tolobster-eating mothers have fewer healthproblems than babies born to mothers who donteat lobsters. Do you find anything wrong with thisclaim?

A. Yes

B. No

Discuss with your neighbour.

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Pause & Practice

5. A researcher at the Sloan-Kettering CancerResearch Center was once criticized for falsifyingdata. Among his data were figures obtained from

6 groups of mice, with 20 mice per group. Thefollowing values were given for the percentage ofsuccesses in each group: 53%, 58%, 63%, 46%,48%, 67%. Whats wrong here?

Discuss with your neighbour

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Coming up

MATH 1050Y-A (FW 2012-13)

Assignment #1 is posted Due Sept. 18th in seminar

Reminder: seminar hours start tomorrow No quiz this week

Next class: 1-4 Design of Experiments

Documents

Statistics Lecture 2 Notes