STAT 111PRINCIPLES OF STATISTICSYASAR UNIVERSITY2010-2011 FallAssist. Prof. Dr. R. Serkan Albayrakserkan.albayrak@yasar.edu.trhttp://yasaruniversity.yahooboard.net/

Brief Introduction Syllabus Course Materials Grading-Next Slide Etc.

Previously in Principles of Statistics…2007

A A- B+ B B- C+ C C- D+ D F

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Previously in Principles of Statistics…2008

CHAPTER 1

What is Statistics Statistics can be thought of as a whole

subject or discipline ... It can be thought of as the methods used

to collect, process and/or interpret data ... It can be thought of as the collections of

data gathered by those methods ... It can also be thought of as a specially

calculated figures (e.g. averages) to characterize collection ...

What is Statistics Statistics are like a bikini; What is

revealed is interesting; What is concealed is crucial. - R. Taylor

Statistics is the science and art of making decisions based on quantitative evidence.

Liber de Ludo Aleae “The most fundamental

principle of all in gambling is simply equal conditions, e.g. of opponents, of bystanders, of money, of situation, of the dice box, and of the die itself. To the extent to which you depart from that equality, if it is in your opponent’s favor, you are a fool, and if in your own, you are unjust.”

Girolamo Cardano1501 – 1576

De Ratiociniis in Ludo Aleae PROPOSITION IV

“Suppose now that I am playing against someone with the agreement that the first of us to win three times will take the stake. And suppose that I have already won twice and my opponent has already won once. I want to know how much of the money should fall to me if we do not wish to continue the game, but rather to divide equitably the money we are playing for.” Christiann Huygens

1629 – 1695

Branches of StatisticsDescriptive

Statistics Involves organizing,

summarizing, and displaying data.

Inferential Statistics Involves using sample data to draw conclusions about a population.

Branches of Statistics The objective of descriptive statistics

methods is to summarize a set of observations.

The objective of inferential statistics methods is to make inferences (predictions, decisions) about population based on information contained in a sample, and to quantify the level of uncertainty in our decisions.

Example: Descriptive and Inferential StatisticsDecide which part of the study represents

the descriptive branch of statistics. What conclusions might be drawn from the study using inferential statistics?

A large sample of men, aged 48, was studied for 18 years. For unmarried men, approximately 70% were alive at age 65. For married men, 90% were alive at age 65.

Solution: Descriptive and Inferential StatisticsDescriptive statistics involves statements such as “For unmarried men, approximately 70% were alive at age 65” and “For married men, 90% were alive at 65.”

A possible inference drawn from the study is that being married is associated with a longer life for men.

PLAN We will follow

Logic Statistics (Descriptive) Probability Statistics (Inferential)

Valid Rules of Reasoning An ARGUMENT is a sequence of

statements, one of which is called the CONCLUSION. The other statements are PREMISES (assumptions). The argument presents the premises—collectively— as evidence that the conclusion is true.

Example: If A is true then B is true. A is true. Therefore, B is true.

If A is true then B is true. A is true. Therefore, B is true.The CONCLUSION is that B is true. The PREMISES are If A is true then B

is true and A is true. The premises support the conclusion that B is true. The word "therefore" is not part of the conclusion: It is a signal that the statement after it is the conclusion.

The words thus, hence, so, and the phrases it follows that, we see that, and so on, also flag conclusions. The words suppose, let, given, assume, and so on, flag premises.

A concrete argument of the form just given might be: If it is sunny, I will wear sandals. It is sunny. Therefore, I will wear

sandals. Here, A is "it is sunny" and B is "I will wear sandals." We usually omit the words "is true." So, for example, the previous

argument would be written If A then B. A. Therefore, B. The statement not A means A is false.

Validity & SoundnessAn argument is VALID if the conclusion must

be true whenever the premises are true.If an argument is valid and its premises are

true, the argument is SOUND.Cheese more than a billion years old is

stale. The Moon is made of cheese. The Moon is more than a billion years old. Therefore, the Moon is stale cheese.

VALID but NOT SOUND!

Some Valid Rules of Reasoning A or not A. (LAW OF THE EXCLUDED MIDDLE) Not (A and not A). A. Therefore, A or B. A. B. Therefore, A and B. A and B. Therefore, A. Not A. Therefore, not (A and B). A or B. Not A. Therefore, B. (DENYING THE DISJUNCT) Not (A and B). Therefore, (not A) or (not B). (DE MORGAN) Not (A or B). Therefore, (not A) and (not B). (DE MORGAN) If A then B. A. Therefore, B. (AFFIRMING THE PRECEDENT, MODUS

PONENDO PONENS, "affirming by affirming") If A then B. Not B. Therefore, not A. (DENYING THE CONSEQUENT,

MODUS TOLLENDO TOLLENS, "denying by denying")

Common Formal Fallacies A or B. Therefore, A. A or B. A. Therefore, not B. (AFFIRMING THE DISJUNCT) NOT BOTH A AND B ARE TRUE. NOT A. THEREFORE, B. IF A THEN B. B. THEREFORE, A. IF A THEN B. NOT A. THEREFORE, NOT B. IF A THEN B. C. THEREFORE, B. IF A THEN B. NOT C. THEREFORE, NOT A. IF A THEN B. A. THEREFORE, C. IF A THEN B. NOT B. THEREFORE, NOT C.

AD HOMINEM (PERSONAL ATTACK) NANCY CLAIMS THE DEATH PENALTY IS A GOOD THING. BUT

NANCY ONCE SET FIRE TO A VACANT WAREHOUSE. NANCY IS EVIL. THEREFORE, THE DEATH PENALTY IS A BAD THING.

THIS ARGUMENT DOES NOT ADDRESS NANCY'S ARGUMENT, IT JUST SAYS SHE MUST BE WRONG (ABOUT EVERYTHING) BECAUSE SHE IS EVIL. WHETHER NANCY IS GOOD OR EVIL IS IRRELEVANT: IT HAS NO BEARING ON WHETHER HER ARGUMENT IS SOUND.

THIS IS A FALLACY OF RELEVANCE: IT ESTABLISHES THAT NANCY IS BAD, THEN EQUATES BEING BAD AND NEVER BEING RIGHT. IN SYMBOLS, THE ARGUMENT IS IF A THEN B. A. THEREFORE C. (IF SOMEBODY SETS FIRE TO A VACANT WAREHOUSE, THAT PERSON IS EVIL. NANCY SET FIRE TO A VACANT WAREHOUSE. THEREFORE, NANCY'S OPINION ABOUT THE DEATH PENALTY IS WRONG.)

AD HOMINEM IS LATIN FOR "TOWARDS THE PERSON." AN AD HOMINEM ARGUMENT ATTACKS THE PERSON MAKING THE CLAIM, RATHER THAN THE PERSON'S REASONING. A VARIANT OF THE AD HOMINEM ARGUMENT IS "GUILT BY ASSOCIATION."

BAD MOTIVE BOB CLAIMS THE DEATH PENALTY IS A GOOD THING. BUT

BOB'S FAMILY BUSINESS MANUFACTURES CASKETS. BOB BENEFITS WHEN PEOPLE DIE, SO HIS MOTIVES ARE SUSPECT. THEREFORE, THE DEATH PENALTY IS A BAD THING.

THIS ARGUMENT DOES NOT ADDRESS BOB'S ARGUMENT, IT ADDRESSES BOB'S MOTIVES. HIS MOTIVES ARE IRRELEVANT: THEY HAVE NOTHING TO DO WITH WHETHER HIS ARGUMENT FOR THE DEATH PENALTY IS SOUND.

THIS IS RELATED TO AN AD HOMINEM ARGUMENT. IT, TOO, ADDRESSES THE PERSON, NOT THE PERSON'S ARGUMENT. HOWEVER, RATHER THAN CONDEMNING BOB AS EVIL, IT IMPUGNS HIS MOTIVES IN ARGUING FOR THIS PARTICULAR CONCLUSION.

TU QUOQUE (LOOK WHO'S TALKING) AMY SAYS PEOPLE SHOULDN'T SMOKE

CIGARETTES IN PUBLIC BECAUSE CIGARETTE SMOKE HAS A STRONG ODOR. BUT AMY WEARS STRONG PERFUME ALL THE TIME. AMY IS CLEARLY A HYPOCRITE. THEREFORE, SMOKING IN PUBLIC IS FINE.

THIS ARGUMENT DOES NOT ENGAGE AMY'S ARGUMENT: IT ATTACKS HER FOR THE (IN)CONSISTENCY OF HER OPINIONS IN THIS MATTER AND IN SOME OTHER MATTER. WHETHER AMY WEARS STRONG FRAGRANCES HAS NOTHING TO DO WITH WHETHER HER ARGUMENT AGAINST SMOKING IS SOUND.

TWO WRONGS MAKE A RIGHT YES, I HIT BILLY. BUT SALLY HIT HIM FIRST. THIS ARGUMENT CLAIMS IT IS FINE TO DO SOMETHING

WRONG BECAUSE SOMEBODY ELSE DID SOMETHING WRONG. THE ARGUMENT IS OF THE FORM: IF A THEN B. A. THEREFORE C. (IN WORDS: IF SALLY HIT BILLY, IT'S OK FOR BILLY TO HIT SALLY. SALLY HIT BILLY. THEREFORE, IT'S OK FOR ME TO HIT BILLY.)

GENERALLY, THE TWO-WRONGS-MAKE-A-RIGHT ARGUMENT SAYS THAT THE JUSTIFIED WRONG HAPPENED AFTER THE EXCULPATORY WRONG, OR WAS LESS SEVERE. FOR INSTANCE, SALLY HIT BILLY FIRST, OR SALLY HIT BILLY HARDER THAN I DID, OR SALLY PULLED A KNIFE ON BILLY.

AD BACULUM (APPEAL TO FORCE) IF YOU DON'T GIVE ME YOUR LUNCH MONEY, MY BIG

BROTHER WILL BEAT YOU UP. YOU DON'T WANT TO BE BEATEN UP, DO YOU? THEREFORE, YOU SHOULD GIVE ME YOUR LUNCH MONEY.

THIS ARGUMENT APPEALS TO FORCE: ACCEPT MY CONCLUSION—OR ELSE. IT IS NOT A LOGICAL ARGUMENT. [+17]

NOTE 2-17: BUT IT CAN BE QUITE PERSUASIVE NONETHELESS.

IT IS AN ARGUMENT THAT IF YOU DO NOT ACCEPT THE CONCLUSION (AND GIVE ME YOUR LUNCH MONEY), SOMETHING BAD WILL HAPPEN (YOU WILL GET BEATEN)—NOT AN ARGUMENT THAT THE CONCLUSION IS CORRECT. THE FORM OF THE ARGUMENT IS IF A THEN B. B IS BAD. THEREFORE, NOT A. HERE, A IS "YOU DON'T GIVE ME YOUR LUNCH MONEY," B IS "YOU WILL BE BEATEN UP."

AD MISERICORDIUM (APPEAL TO PITY) YES, I DOWNLOADED MUSIC ILLEGALLY—BUT MY

GIRLFRIEND LEFT ME AND I LOST MY JOB SO I WAS BROKE AND I COULDN'T AFFORD TO BUY MUSIC AND I WAS SO SAD THAT I WAS BROKE AND THAT MY GIRLFRIEND WAS GONE THAT I REALLY HAD TO LISTEN TO 100 VARIATIONS OF SHE CAUGHT THE KATY.

THIS ARGUMENT JUSTIFIES AN ACTION NOT BY CLAIMING THAT IT IS CORRECT, BUT BY AN APPEAL TO PITY: EXTENUATING CIRCUMSTANCES OF A SORT.

AD MISERICORDIUM IS LATIN FOR "TO PITY." IT IS AN APPEAL TO COMPASSION RATHER THAN TO REASON. ANOTHER EXAMPLE:

YES, I FAILED THE FINAL. BUT I NEED TO GET AN A IN THE CLASS OR I [WON'T GET INTO BUSINESS SCHOOL] / [WILL LOSE MY SCHOLARSHIP] / [WILL VIOLATE MY ACADEMIC PROBATION] / [WILL LOSE MY 4.0 GPA]. YOU HAVE TO GIVE ME AN A!

AD POPULUM (BANDWAGON) MILLIONS OF PEOPLE SHARE COPYRIGHTED MP3 FILES

AND VIDEOS ONLINE. THEREFORE, SHARING COPYRIGHTED MUSIC AND VIDEOS IS FINE.

THIS "BANDWAGON" ARGUMENT CLAIMS THAT SOMETHING IS MORAL BECAUSE IT IS COMMON. COMMON AND CORRECT ARE NOT THE SAME. WHETHER A PRACTICE IS WIDESPREAD HAS LITTLE BEARING ON WHETHER IT IS LEGAL OR MORAL. THAT MANY PEOPLE BELIEVE SOMETHING IS TRUE DOES NOT MAKE IT TRUE.

AD POPULUM IS LATIN FOR "TO THE PEOPLE." IT EQUATES THE POPULARITY OF AN IDEA WITH THE TRUTH OF THE IDEA: EVERYBODY CAN'T BE WRONG. FEW TEENAGERS HAVE NOT MADE AD POPULUM ARGUMENTS: "BUT MOM, EVERYBODY IS DOING IT!"

STRAW MAN-BOSTAN KORKULUĞU BOB: SLEEPING A FULL 12 HOURS ONCE IN A

WHILE IS A HEALTHY PLEASURE. SAMANTHA: IF EVERYBODY SLEPT 12 HOURS

ALL THE TIME, NOTHING WOULD EVER GET DONE; THE REDUCTION IN PRODUCTIVITY WOULD DRIVE THE COUNTRY INTO BANKRUPTCY. THEREFORE, NOBODY SHOULD SLEEP FOR 12 HOURS.

SAMANTHA ATTACKED A DIFFERENT CLAIM FROM THE ONE BOB MADE: SHE ATTACKED THE ASSERTION THAT IT IS GOOD FOR EVERYBODY TO SLEEP 12 HOURS EVERY DAY. BOB ONLY CLAIMED THAT IS WAS GOOD ONCE IN A WHILE.

RED HERRING-DİKKATİ BAŞKA YERE ÇEKMEK ART: TEACHER SALARIES SHOULD BE INCREASED TO

ATTRACT BETTER TEACHERS. BETTE: LENGTHENING THE SCHOOL DAY WOULD ALSO

IMPROVE STUDENT LEARNING OUTCOMES. THEREFORE, TEACHER SALARIES SHOULD REMAIN THE SAME.

ART ARGUES THAT INCREASING TEACHER SALARIES WOULD ATTRACT BETTER TEACHERS. BETTE DOES NOT ADDRESS HIS ARGUMENT: SHE SIMPLY ARGUES THAT THERE ARE OTHER WAYS OF IMPROVING STUDENT LEARNING OUTCOMES. ART DID NOT EVEN USE STUDENT LEARNING OUTCOMES AS A REASON FOR INCREASING TEACHER SALARIES. EVEN IF BETTE IS CORRECT THAT LENGTHENING THE SCHOOL DAY WOULD IMPROVE LEARNING OUTCOMES, HER ARGUMENT IS SIDEWAYS TO ART'S: IT IS A DISTRACTION, NOT A REFUTATION.

A RED HERRING ARGUMENT DISTRACTS THE LISTENER FROM THE REAL TOPIC

RED HERRING ARGUMENTS ARE VERY COMMON IN POLITICAL DISCOURSE.

EQUIVOCATION ALL MEN SHOULD HAVE THE RIGHT TO VOTE. SALLY IS

NOT A MAN. THEREFORE, SALLY SHOULD NOT NECESSARILY HAVE THE RIGHT TO VOTE.

THIS IS AN EXAMPLE OF EQUIVOCATION, A FALLACY FACILITATED BY THE FACT THAT A WORD CAN HAVE MORE THAN ONE MEANING.

THIS ARGUMENT USES THE WORD MAN IN TWO DIFFERENT WAYS. IN THE FIRST PREMISE, THE WORD MEANS HUMAN WHILE IN THE SECOND, IT MEANS MALE. GENERALLY, EQUIVOCATION IS CONSIDERED A FALLACY OF RELEVANCE, BUT THIS EXAMPLE FITS OUR DEFINITION OF A FALLACY OF EVIDENCE.

THE LOGICAL FORM OF THIS ARGUMENT IS IF A THEN B. NOT C. THEREFORE, B IS NOT NECESSARILY TRUE.

Others (Generalizability) Trident (4/5)Trident® sugarless gum used to advertise

that "4 out of 5 dentists surveyed recommend Trident® sugarless gum for their patients who chew gum."

Yale University Graduates

Data In its broadest sense, Statistics is the science of

drawing conclusions about the world from data. Data are observations (measurements) of some quantity or quality of something in the world.

"Data" is a plural noun; the singular form is "datum." Our lives are filled with data: the weather, weights, prices, our state of health, exam grades, bank balances, election results, and so on. Data come in many forms, most of which are numbers, or can be translated into numbers for analysis.

There are several important questions to keep in mind when you evaluate quantitative evidence:

Are the data relevant to the question asked?

Was the data collection fair, or might there have been some conscious or unconscious BIAS that influenced the results or made some cases less likely to be observed?

Do the data make sense?

Data ~ Information Qualitative Data : Consists of

attributes, labels, or nonnumerical entries.

Major Place of birth

Eye color

Hot/Warm/Cold Population density: low/medium/high Height: short/medium/tall Young/Middle-aged/Old Social class: lower/middle/upper Family size: fewer than 3, 3–5, 5 or more Rural/Urban area Type of climate Gender Ethnicity Zip code Hair color Country of origin

Data ~ Information Quantitative Data : Numerical

measurements or counts.Age Weight of a

letterTemperature

Temperature in °C Population density: people per square mile Height in inches Height in centimeters Body mass index (BMI) Age in seconds Income in dollars Family size (#people)

Example – Classifying Data by Type The base prices of several vehicles are

shown in the table. Which data are qualitative data and which are quantitative data? (Source Ford Motor Company)

Solution – Classifying Data by Type

Quantitative Data (Base prices of vehicles models are numerical entries)

Qualitative Data (Names of vehicle models are nonnumerical entries)

The fact that a category is labeled with a number does not make the variable quantitative!

The real issue is whether arithmetic with the values makes sense.

Levels of MeasurementNominal level of measurement

Qualitative data only Categorized using names, labels, or qualities No mathematical computations can be made

Ordinal level of measurement• Qualitative or quantitative data• Data can be arranged in order• Differences between data entries is not

meaningful

Example – Classifying data by level Two data sets are shown. Which data

set consists of data at the nominal level? Which data set consists of data at the ordinal level? (Source: Nielsen Media Research)

Solution – Classifying data by level

Ordinal level (lists the rank of five TV programs. Data can be ordered. Difference between ranks is not meaningful.)

Nominal level (lists the call letters of each network affiliate. Call letters are names of network affiliates.)

Levels of MeasurementInterval level of measurement Quantitative data Data can be ordered Differences between data entries is

meaningful Zero represents a position on a scale

(not an inherent zero – zero does not imply “none”)

Levels of MeasurementRatio level of measurement Similar to interval level Zero entry is an inherent zero (implies

“none”) A ratio of two data values can be

formed One data value can be expressed as a

multiple of another

Example – Classifying data by level

Two data sets are shown. Which data set consists of data at the interval level? Which data set consists of data at the ratio level? (Source: Major League Baseball)

Solution – Classifying data by level

Interval level (Quantitative data. Can find a difference between two dates, but a ratio does not make sense.)

Ratio level (Can find differences and write ratios.)

Summary of Four Levels of MeasurementLevel ofMeasurement

Put data in

categories

Arrangedata inorder

Subtractdata

values

Determine if one data value is a

multiple of another

Nominal Yes No No No

Ordinal Yes Yes No No

Interval Yes Yes Yes No

Ratio Yes Yes Yes Yes

Variable, Value & Data One of the most problematic

relationship. What is really a variable? What is value? What is data? How they are related?

GENDERFEMALE

MALEVariable

Values

Theoretical MALE

MALEMALEFEMALE

FEMALE

FEMALE

…

Observed

Data

ExampleVariable: New York Yankees’ World Series VictoriesValues: 1901,1902,…(all possible years)Data: 1923,1927,1928,…