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Introduction to Statistics

Chapter 1MSIS 111 Prof. Nick Dedeke

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Objectives

Define statisticsDifferentiate between descriptive and inferential statisticsDefine statistical variablesClassifying numbers

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What is Statistics?

A general way to view statistics is as follows: it is a language and the set of rules that enables us to make sense of data about events, people, places and things.

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Valid Statistic?: Example 1An online survey conducted recently led some to the conclusion that Apple’s iphone product will not succeed in the U.S. market. 75% of the men and 89% of the women surveyed answered “never” when asked the question: Would you buy an ipod?

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Valid Statistic?: Example 2When you vote consider this information. A mail survey showed that in the years when Democrats controlled the Congress, U.S. had a higher number of destructive, level 5 hurricanes. In the years that the Republicans controlled Congress, the U.S. have more days with extremely cold and extremely hot days.

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Valid Statistic?: Example 3If you are seeking to have a job quickly after you graduate, do not wear a clothing with a white color during your interview. A recent phone survey of fifty human resources managers at the top 10 retail firms in America revealed that only 2% of them wear white clothing to work.

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FactsThere is such a thing as bad statistics Poor methods, sample, and/or

interpretation

You can always make bad statistics say anything you want it to sayThe cure for bad statistics is good statistics

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Do we really need statistics?

Imagine a government never gathers data about population growth. Imagine a hospital that never stores data about patient data and care Imagine a car firm that never analyzes data about vehicle rolloversImagine an insurance firm that never interprets the causes for the increases in health care costs

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Definition of statistics?Statistics is a science dealing with the collection, organization, analysis, interpretation and presentation of quantitative and qualitative data.

Statistics is a means to an end. The objective is not statistics for its own sake, it is the effective use of statistics for decision-making that matters for firms.

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Challenge of statistics?Statistics has two primary challenges: Describing a group of entities using a segment

of the group. For example, we have over 300 million U.S. citizens. I have the question to answer. How tall are Americans? This kind is called descriptive statistics. FOCUS – Present or Past

Generating conclusions about future trends of a large group of data using smaller set from the same or related group. For example, I have the question: At which rate are we depleting fishes in our rivers? This kind is called inferential statistics. FOCUS – Present or Future

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Terminologies in statistics?

Census: Gathering of data from every member of a group or population, e.g. all voters in a presidential election, all subscribers to cable TV

Sample: A randomly sampled set of members of a population (fraction of the size of a census)

Variable: Attribute of interest of each member of group

Observation or measurement: The value of a variable for a member of a group (population or sample)

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Exercise 1:

How many members are in this sample?

Bill, Marty, Mary, Sue, Buba, Dub, Anne, Ali Baba, Jane, Phil, Don, Monki

If I were interested in the physical attributes of the members, which two variables will I survey?If I were interested in the opinions of the sample which two variables will I survey?If I were interested in the identity of the members, which two variables will I survey?

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Exercise 1 Responses

How many members are in this sample (data

set)? 12

Physical attributes: height, weight, hair color, genderOpinion: political affiliation, political worldview,Identity: last name, nationality, ID number, Soc. Sec.No.

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Exercise 2

For each of the underlined variables write down an example of what the observation (responses to survey) would be when you survey a member of the population.

Physical attributes: height, weight, hair color, genderOpinion: political affiliation, political worldview,Identity: last name, nationality, ID number, Soc. Sec.No.

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Exercise 2 Responses

Weight: 200 poundsGender: FemalePolitic. affiliation: Republican Political view: LiberalNationality: NigerianSoc.Sec: 123974

Numerical dataNumerical data: Permit the use of arithmetical operations

Categorical dataCategorical data: Permit only the building of subgroups

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Data Measurement

The question that one puts on a survey determines how a variable is measured. Consider the following questions: How much income do you make per year (in

thousand $)? Do you make more than the US national

average of $30,000 per year?[Yes] [No]

How much income do you make per year?[Below $10k] [$10k to $30k] [$30k to $50k] [$50k to $70k] [above $70k]

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Data MeasurementMany variables could be measured at different levels.

Do you make more than the US national average of $30,000 per year?[Yes] [No] Nominal levelNominal level.. Grouping only and ranking not Grouping only and ranking not advisable/ permissibleadvisable/ permissible

How much income do you make per year?[Below $10k] [$10k to $30k] [$30k to $50k] [$50k to $70k] [above $70k] Ordinal levelOrdinal level. Absolute zero not emphasized and . Absolute zero not emphasized and ranking possibleranking possible

How much income do you make per year (in thousand $)? Ratio levelRatio level.. Absolute zero and ratio of Absolute zero and ratio of numbers are meaningful. Arithmetical operations numbers are meaningful. Arithmetical operations possiblepossible

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Exercise 3: Data Measurement

What is the level of measurements of the following observations: 1980: date of birth Social security number Temperature, e.g. 90 degrees Fahrenheit Age: 19 years old Rating of customer service: Excellent (7)

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Exercise 3: ResponsesWhat kind of level of measurements are the following observations: 1980: date of birth [ORDINAL] Social security number [NOMINAL] Temperature, e.g. 90 degrees Fahrenheit

[INTERVAL] Age: 19 years old [RATIO] Rating of customer service: Excellent (7)

[ORDINAL]

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Analyzing Data

Nonparametric statistics [ORDINAL] Nonparametric statistics [NOMINAL] Parametric statistics [INTERVAL] Parametric statistics [RATIO]

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Data Measurement: Examples

Two respondents: $20,000 and $ 40,000 income/yr. Many variables could be measured at different levels.

Do you make more than the US national average of $30,000 per year?[Yes] [No] Nominal levelNominal level.. Grouping only and ranking not advisable/ Grouping only and ranking not advisable/ permissible. permissible. Analyses:Analyses: Income class of B ranks higher than A.Income class of B ranks higher than A. Difference in incomes = ??; ratio of income of class?? Not possible.Difference in incomes = ??; ratio of income of class?? Not possible.

How much income do you make per year?[Below $10k] [$10k to $30k] [$30k to $50k] [$50k to $70k] [above $70k] Ordinal levelOrdinal level.. Absolute zero not emphasized and ranking Absolute zero not emphasized and ranking possible. possible. Analyses:Analyses: Income class of B ranks higher than A.Income class of B ranks higher than A. Difference in income classes = ranges from $1-$40,000; ratio of Difference in income classes = ranges from $1-$40,000; ratio of income of class?? Not possible.income of class?? Not possible.

If you divide your salary by $20,000 per year, what do you get?[¼] [½ ] [¾ ] [1] [1¼] [1½ ] 1¾ ] [2] [2¼] [2½ ] [2¾] Interval levelInterval level.. Absolute zero is convenient and ratio of numbers Absolute zero is convenient and ratio of numbers are meaningful. are meaningful. Analyses:Analyses: Income B ranks higher than A.Income B ranks higher than A. Difference between consecutive income classes =$5,000; ratio of Difference between consecutive income classes =$5,000; ratio of income of B twice as high as A (2 divided by 1).income of B twice as high as A (2 divided by 1).

How much income do you make per year (in thousand $)?___________ $ thousandsRatio levelRatio level.. Absolute zero and ratio of numbers are meaningful. Absolute zero and ratio of numbers are meaningful. Analyses:Analyses: Income B ranks higher than A.Income B ranks higher than A. Difference in income Difference in income =$20,000; income of B twice as high as A (40,000/20,000).=$20,000; income of B twice as high as A (40,000/20,000).