1 MATB344 Applied Statistics Introduction to newbies in Statistics.

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MATB344 Applied StatisticsMATB344 Applied Statistics

Introduction toIntroduction to

newbies in Statisticsnewbies in Statistics

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What is Statistics?What is Statistics?• Statistics is encountered in our daily life. Statistics is encountered in our daily life.

Unavoidable.Unavoidable.• Involves gathering, analysis and presentation of dataInvolves gathering, analysis and presentation of data

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What does a Statistician do?What does a Statistician do?• Collects numbers or data

• Systematically organizes or arranges the data

• Analyzes the data…extracts relevant information to provide a complete numerical description

• Infers general conclusions about the problem using this numerical description

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Uses of StatisticsUses of Statistics• Satistics - a branch of mathematics that

have applications in daily life• Statistics – like a “new language” to you.• Usage:

– a theoretical discipline in its own right – a tool for researchers in other fields– a general tool to draw general conclusions in a

large variety of applications

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• In PoliticsIn Politics– Forecasting and predicting winners of elections– Where to concentrate campaign appearances,

advertising and $$…• In Industry

– To market product…– Eg: to predict the average length of life of a

light bulb– Cannot test all the bulbs, so choose some

sample to obtain the statistics.

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CASE 1: OPINION POLLSCASE 1: OPINION POLLS

Do you think that the United States war on terrorism will Do you think that the United States war on terrorism will spread to countries other than Afghanistan?spread to countries other than Afghanistan?

YES 64%YES 64% NO 34%NO 34%

Do you think that the United States should be directly Do you think that the United States should be directly involved in negotiating peace agreements in other parts of involved in negotiating peace agreements in other parts of the world?the world?

YES 62%YES 62% NO 31%NO 31%

Do you think that the United States war on terrorism will Do you think that the United States war on terrorism will spread to countries other than Afghanistan?spread to countries other than Afghanistan?

YES 64%YES 64% NO 34%NO 34%

Do you think that the United States should be directly Do you think that the United States should be directly involved in negotiating peace agreements in other parts of involved in negotiating peace agreements in other parts of the world?the world?

YES 62%YES 62% NO 31%NO 31%

THE WAR ON TERRORISMTHE WAR ON TERRORISM

How do we get the poll? Ask everyone? Is it possible?

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Common Problem in StatisticsCommon Problem in Statistics• We are interested in the conclusion and prediction about the

whole body of measurements, eg: Malaysian citizens . • The set of the whole body of measurements of interest is

called POPULATION.POPULATION.• But we cannot survey on them all.• Sometimes, a the whole body of measurements is large and

cannot be totally enumerated.• Solution: Use a smaller set of measurement to represent the

whole body of measurements. • The smaller set of measurements that will (hopefully) be

representative of the larger set is called the SAMPLE.SAMPLE.

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ExamplesExamples• To predict the average length of life of a light

bulb - to enumerate the population is destructive. We

cannot take all light bulb and test.- So, select a smaller number of light bulb as a sample

• To forecast the winner of an election- population of the whole country is too big and

people do change their mind- So, select a group of people in certain location to be

the sample.

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What’s common in What’s common in “Sample” and “Population”“Sample” and “Population”

• We distinguish between set of objects on which we take measurements and the measurements themselves.

- Experimental Units:Experimental Units: The items or objects on which measurements are taken

- Sample (or Population):Sample (or Population): the set of measurements taken on the experimental units.

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ExamplesExamples

• Light bulbs

–Experimental unit = bulbExperimental unit = bulb

• Opinion polls

–Experimental unit = personExperimental unit = person

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Descriptive StatisticsDescriptive Statistics

• Used to describe sets of measurements.

• Example : Bar charts, pie charts, line charts etc.

• Suitable for entire population.

• DESCRIPTIVE STATISTICS DESCRIPTIVE STATISTICS consists of procedures used to summarize and describe the set of measurements.

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Inferential StatisticsInferential Statistics

• Used to describe / make inferences about a population based on statistics of the sample.

• Used when we cannot enumerate the whole population

• INFERENTIAL STATISTICS:INFERENTIAL STATISTICS: Procedures used to draw conclusions or inferences about the population from information contained in the sample.

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Objective of Inferential StatisticsObjective of Inferential Statistics

• To make inferences about a population– draw conclusions– make prediction– make decision

from information contained in a sample.• The statistician’s job is to find the best

way to do this.

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But, …But, …

• How can be sure that the poll result is reliable?

• We need a measure of reliability.

Who makes the best burgers? Votes Percent

McDonalds 123 Votes 13%

Burger King 384 Votes 39%

Wendy’s 304 Votes 31%

All three have equally good burgers 72 Votes 7%

None of these have good burgers 98 Votes 10%

Our conclusions could be incorrect…Our conclusions could be incorrect…consider this internet opinion poll…consider this internet opinion poll…

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Summary: Steps in Inferential StatisticsSummary: Steps in Inferential Statistics

• Define the objective of the experimentobjective of the experiment and the population of interest

• Determine the design of the experimentdesign of the experiment and the sampling plan to be used

• CollectCollect and analyzeanalyze the data• Make inferencesMake inferences about the population from

information in the sample• Determine the goodnessgoodness or reliabilityreliability of the

inference.

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• Define the objective of the experimentobjective of the experiment and the population of interest


• CollectCollect and analyzeanalyze the data• Make inferencesMake inferences about the population from


inference.

Example : In Presidential ElectionObjective : To determine Who will get the most votesPopulation: Set of all votes (from all registered voters)Sample : Sample voters from each states in USA.

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• Define the objective of the experiment and the population of interest


• Collect and analyze the data• Make inferences about the population from

information in the sample• Determine the goodness or reliability of the

inference.

• To decide how to select sample.

• How big a sample to select.

• How much will it cost if the sample is selected.

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• Determine the design of the experiment and the sampling plan to be used

• CollectCollect and analyzeanalyze the data• Make inferences about the population from


inference.

• Collect information from the sample

• Use appropriate method of analysis

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• Collect and analyze the data• Make inferencesMake inferences about the population from


inference.

• Use information from the analysis to make inference

• Many methods but only one is the most accurate. Choose the best.

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• Collect and analyze the data• Make inferences about the population from


inference.

• Inference might be wrong because we’re not looking at the whole population.

• Need to have measure of reliability

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Conclusion: Learn to View Conclusion: Learn to View Statistics CriticallyStatistics Critically

• Why? Because Statistics can lie.• According to people against statistics - there

are three kinds of lies…..– LiesLies– Damn LiesDamn Lies– StatisticsStatistics

• Be positive!!!You need to make statistics work for you, not lie for you!

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How to make statistics work for How to make statistics work for you and give reliable inference?you and give reliable inference?

• Use software tools to help perform the procedures.

• List of Softwares:

– MINITABMINITAB

– SPSSSPSS

– Microsoft EXCELMicrosoft EXCEL

– Java applets.Java applets.

1 MATB344 Applied Statistics Introduction to newbies in Statistics.

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