- WELCOME TO AN INTRODUCTION TO STATISTICS.
LIKE MOST PEOPLE, YOU PROBABLY FEEL THAT IT IS IMPORTANT
TO MAKE INFORMED DECISIONS,
BUT WHAT DOES THIS MEAN?
PROBABLY, IT MEANS BEING ABLE TO PROPERLY EVALUATE THE DATA
AND CLAIMS THAT BOMBARD YOU EVERY DAY.
IF YOU CANNOT DISTINGUISH GOOD FROM FAULTY REASONING,
THEN YOU ARE VULNERABLE TO MANIPULATION.
YOU MAY MAKE DECISIONS THAT ARE NOT IN YOUR BEST INTEREST.
STATISTICS PROVIDE TOOLS NEEDED TO REACT INTELLIGENTLY
TO INFORMATION YOU HEAR OR READ.
AS A RESULT, STATISTICS IS AN IMPORTANT TOPIC TO STUDY
AND LEARN.
LET'S LOOK AT SOME COMMON CLAIMS WE MAY HAVE HEARD BEFORE.
I WON'T READ THESE,
BUT YOU MAY WANT TO PAUSE THE VIDEO
TO READ ALL OF THESE CLAIMS.
STATISTICS ARE OFTEN PRESENTED IN AN EFFORT TO ADD CREDIBILITY
TO AN ARGUMENT, ADVICE OR SALES PITCH.
MUCH OF THE INFORMATION PRESENTED
MAY NOT REPRESENT A CAREFUL STATISTICAL ANALYSIS.
THE INFORMATION MAY BE MISLEADING
AND PUSH YOU INTO DECISIONS THAT YOU MIGHT FIND CAUSE REGRET.
AS A RESULT, LEARNING ABOUT STATISTICS IS A STEP TOWARDS
TAKING CONTROL OF YOUR LIFE.
THIS MODULE WILL MAKE YOU A MORE INTELLIGENT CONSUMER
OF STATISTICAL CLAIMS.
JUST AS IMPORTANT AS DETECTING THE DECEPTIVE USE OF STATISTICS
IS THE APPRECIATION OF THE PROPER USE OF STATISTICS.
WHEN A RESEARCH TEAM IS TESTING A NEW TREATMENT FOR DISEASE,
STATISTICS ALLOW THEM TO CONCLUDE,
BASED ON A RELATIVELY SMALL TRIAL,
THAT THERE IS GOOD EVIDENCE THEIR DRUG IS EFFECTIVE.
STATISTICS ALLOWED PROSECUTORS IN THE FIFTIES AND SIXTIES
TO DEMONSTRATE RACIAL BIAS EXISTED IN JURY PANELS.
STATISTICS ARE ALL AROUND YOU--
SOMETIMES USED WELL, SOMETIMES NOT.
BEFORE WE BEGIN GATHERING AND ANALYZING DATA,
WE NEED TO CHARACTERIZE THE POPULATION WE ARE STUDYING.
IF WE WANT TO STUDY THE AMOUNT OF MONEY SPENT ON TEXT BOOKS
BY A TYPICAL FIRST-YEAR COLLEGE STUDENT,
OUR POPULATION MIGHT BE ALL FIRST-YEAR COLLEGE STUDENTS
AT YOUR COLLEGE.
SO THE POPULATION OF A STUDY IS THE GROUP THE COLLECTED DATA
IS INTENDED TO DESCRIBE.
SOMETIMES THE INTENDED POPULATION IS CALLED
THE TARGET POPULATION,
SINCE IF WE DESIGN OUR STUDY BADLY,
THE COLLECTED DATA MIGHT NOT ACTUALLY BE REPRESENTATIVE
OF AN INTENDED POPULATION.
IF WE WERE ABLE TO GATHER DATA
ON EVERY MEMBER OF OUR POPULATION,
SAY, THE AVERAGE AMOUNT OF MONEY SPENT ON TEXTBOOKS
BY EACH FIRST-YEAR COLLEGE STUDENT AT YOUR COLLEGE
DURING THE 2012/2013 ACADEMIC YEAR,
THE RESULTING NUMBER WOULD BE CALLED A PARAMETER.
SO A PARAMETER IS A VALUE CALCULATED USING ALL OF THE DATA
FROM A POPULATION.
WE SELDOM SEE PARAMETERS,
HOWEVER, SINCE SURVEYING AN ENTIRE POPULATION
IS USUALLY VERY TIME CONSUMING AND EXPENSIVE
UNLESS THE POPULATION IS VERY SMALL
OR WE ALREADY HAVE THE DATA COLLECTED.
AND A SURVEY OF AN ENTIRE POPULATION IS CALLED A CENSUS.
SINCE SURVEYING AN ENTIRE POPULATION IS OFTEN IMPRACTICAL,
WE USUALLY SELECT A SAMPLE TO STUDY,
WHERE A SAMPLE IS A SMALLER SUBSET OF THE ENTIRE POPULATION,
IDEALLY, ONE THAT IS FAIRLY REPRESENTATIVE
OF THE WHOLE POPULATION.
WE WILL DISCUSS SAMPLING METHODS IN GREATER DETAIL
IN THE NEXT LESSON.
FOR NOW, LET'S ASSUME THE SAMPLES ARE CHOSEN
IN AN APPROPRIATE MANNER.
IF WE SURVEY A SAMPLE OF 100 FIRST-YEAR STUDENTS
AT YOUR COLLEGE,
I'D FIND THE AVERAGE AMOUNT OF THE MONEY SPENT
BY THESE STUDENTS ON TEXTBOOKS.
THE RESULTING NUMBER IS CALLED A STATISTIC,
WHERE A STATISTIC IS A VALUE
CALCULATED USING THE DATA FROM THE SAMPLE.
SO AGAIN, A PARAMETER IS A VALUE CALCULATED USING ALL THE DATA
FROM THE ENTIRE POPULATION,
AND A STATISTIC IS A VALUE CALCULATED USING THE DATA
FROM A SAMPLE OF THE POPULATION.
LET'S TAKE A LOOK AT SOME EXAMPLES.
A POLITICAL SCIENTIST SURVEYS
39 OF THE CURRENT 152 REPRESENTATIVES
IN A STATE'S CONGRESS.
WHAT IS THE SIZE OF THE SAMPLE,
AND WHAT IS THE SIZE OF THE POPULATION?
WELL, THE SAMPLE WOULD BE THE 39 REPRESENTATIVES
THAT WERE SURVEYED,
AND THE SIZE OF THE POPULATION WOULD BE
ALL OF THE 152 REPRESENTATIVES.
NOW, FOR THE NEXT THREE QUESTIONS,
THE SITUATION WILL BE THE SAME, BUT THE QUESTION WILL CHANGE.
THE CITY OF PRESCOTT HAS 8,800 REGISTERED VOTERS.
THERE ARE TWO CANDIDATES FOR CITY COUNCIL
IN AN UPCOMING ELECTION,
BROWN AND FELICE.
THE DAY BEFORE THE ELECTION,
A TELEPHONE POLL OF 600 RANDOMLY-SELECTED
REGISTERED VOTERS WAS CONDUCTED.
206 SAID THEY'D VOTE FOR BROWN, 350 SAID THEY'D VOTE FOR FELICE,
AND 44 WERE UNDECIDED.
DESCRIBE THE POPULATION
THE SURVEYS ARE REALLY INTERESTED IN,
AND WE HAVE A LIST TO SELECT FROM.
WE HAVE ALL CITIZENS OF PRESCOTT,
ALL REGISTERED VOTERS IN PRESCOTT,
ALL REGISTERED VOTERS WITH TELEPHONES IN PRESCOTT,
THE 600 VOTERS SURVEYED,
THE 206 VOTERS WHO SAID THEY'D VOTE FOR BROWN,
AND THE LAST CHOICE IS NONE OF THE ABOVE.
GOING BACK UP TO THE GIVEN INFORMATION,
THEY CONDUCTED A POLL OF 600
RANDOMLY-SELECTED REGISTERED VOTERS FROM WITHIN PRESCOTT.
SO THE POPULATION THEY'RE REALLY INTERESTED IN
WOULD BE ALL REGISTERED VOTERS IN PRESCOTT,
WHICH WOULD BE THIS OPTION HERE.
NOW, FOR THIS QUESTION, THE GIVEN INFORMATION IS THE SAME,
BUT NOW WE WANT TO DESCRIBE THE POPULATION
THE SURVEYORS ACTUALLY REPRESENTED BY THIS SURVEY.
AND THE KEY HERE IS THAT IT WAS A TELEPHONE POLL,
SO THE SURVEY ACTUALLY ONLY WOULD REPRESENT
THE REGISTERED VOTERS WITH TELEPHONES IN PRESCOTT.
IF A REGISTERED VOTER DID NOT HAVE A TELEPHONE,
THEY WOULD NOT HAVE A CHANCE TO PARTICIPATE IN THE POLL.
AND THEN FINALLY,
WE WANT TO DESCRIBE THE SAMPLE OF THIS SURVEY,
AND THE SAMPLE WOULD BE THE 600 VOTERS
THAT WERE ACTUALLY SURVEYED.
NOW, ONCE WE HAVE GATHERED DATA FROM A SURVEY,
WE MIGHT WISH TO CLASSIFY IT.
ROUGHLY SPEAKING, DATA COULD BE CLASSIFIED AS CATEGORICAL DATA
OR A QUANTITATIVE DATA.
CATEGORICAL OR A QUANTITATIVE DATA ARE PIECES OF INFORMATION
THAT ALLOW US TO CLASSIFY THE OBJECTS UNDER INVESTIGATION
INTO VARIOUS CATEGORIES,
WHILE QUANTITATIVE DATA ARE RESPONSES
THAT ARE NUMERICAL IN NATURE
AND WITH WHICH WE CAN PERFORM
MEANINGFUL ARITHMETIC CALCULATIONS.
SO EVEN IF THE DATA IS NUMERICAL,
IT STILL WOULD BE CATEGORICAL OR QUALITATIVE
IF THE ARITHMETIC CALCULATIONS WERE NOT MEANINGFUL.
LET'S LOOK AT SOME EXAMPLES.
HERE ARE THREE EXAMPLES OF CATEGORICAL
OR A QUANTITATIVE DATA.
FAVORITE MOVIES OR FAVORITE CAR WOULD OBVIOUSLY BE CATEGORICAL,
BUT NOTICE HOW EVEN ZIP CODES WOULD BE CONSIDERED CATEGORICAL
OR QUALITATIVE,
BECAUSE EVEN THOUGH ZIP CODES ARE NUMERICAL,
IF WE FOUND THE SUM OR FOUND THE AVERAGE OF ZIP CODES,
IT WOULD NOT BE MEANINGFUL,
AND THEREFORE, ZIP CODES WOULD STILL BE CATEGORICAL.
AND SOME QUANTITATIVE EXAMPLES WOULD BE AGE, WEIGHT,
COMMUTE TIME, IDEAL TEMPERATURES AND SO ON.
NOTICE FOR THIS QUALITATIVE DATA,
FOR EXAMPLE, IF WE WERE TO FIND THE AVERAGE,
THE CALCULATION WOULD BE MEANINGFUL.
OKAY. WE'RE GOING TO STOP HERE FOR THIS INTRO VIDEO.
I HOPE YOU FOUND THIS HELPFUL.