Stat 31, Section 1, Last Time

• Correlation

• Linear Regression– Idea – graphics– Computation– Interpretation

Midterm I

Coming up: Tuesday, Feb. 15

Material: HW Assignments 1 – 4

Extra Office Hours:

Mon. Feb. 14, 8:30 – 12:00, 2:00 – 3:30

Bring Along:

1 8.5” x 11” sheet of paper with formulas

(front & back OK, but no newspapers)

Chapter 3: Producing Data

(how this is done is critical to conclusions)

Section 3.1: Statistical Settings

2 Main Types:

I. Observational Study

Simply “see what happens, no intervention”

(to individuals or variables of interest)

e.g. Political Polls, Supermarket Scanners

Producing Data

2 Main Types:

I. Observational Study

II. Experiment

(Make Changes, & Study Effect)Apply “treatment” to individuals & measure

“responses”

e.g. Clinical trials for drugs, agricultural trials

(safe? effective?) (max yield?)

Producing Data

2 Main Types:

I. Observational Study

II. Experiment

(common sense)

Caution: Thinking is required for each.

Both if you do statistics & if you need to understand somebody else’s results

Producing Data

2 Main Types:

I. Observational Study

II. Experiment (common sense)

Caution: Thinking is required for each

Both if you do statistics & if you need to understand somebody else’s results

Helpful Distinctions(Critical Issue of “Good” vs. “Bad”)

I. Observational Studies:

A. Anecdotal Evidence

Idea: Study just a few cases

Problem: may not be representative

(or worse: only considered for this reason)

e.g. Cures for hiccups

Key Question: how were data chosen?(early medicine: this gave crazy attempts at cures)

Helpful DistinctionsI. Observational Studies:

B. Sampling

Idea: Seek sample representative of population

HW:

(old) 3.1, 3.3, 3.5, 3.7

Challenge: How to sample?

(turns out: not easy)

How to sample?History of Presidential Election Polls

During Campaigns, constantly hear in news “polls say …” How good are these? Why?

1936 Landon vs. Roosevelt Literary Digest Poll: 43% for R

Result: 62% for R

What happened?Sample size not big enough? 2.4 million

Biggest Poll ever done (before or since)

Bias in SamplingBias: Systematically favoring one outcome

(need to think carefully)

Selection Bias: Addresses from L. D.

readers, phone books, club memberships

(representative of population?)

Non-Response Bias: Return-mail survey

(who had time?)

Bias in Sampling1936 Presidential Election (cont.)

Interesting Alternative Poll:

Gallup: 56% for R (sample size ~ 50,000)

Gallup of L.D. 44% for R ( ~ 3,000)

Predicted both correct result (62% for R),

and L. D. error (43% for R)!

(what was better?)

Improved SamplingGallup’s Improvements:

(i) Personal Interviews

(attacks non-response bias)

(ii) Quota Sampling

(attacks selection bias)

Quota SamplingIdea: make “sample like population”

So surveyor chooses people to give:i. Right % male

ii. Right % “young”

iii. Right % “blue collar”

iv. …

This worked well, until …

How to sample?1948 Dewey Truman sample size

Crossley 50% 45%

Gallup 50% 44% 50,000

Roper 53% 38% 15,000

Actual 45% 50% -

Note: Embarassing for polls, famous photo of Truman + Headline “Dewey Wins”

What went wrong?Problem: Unintentional Bias

(surveyors understood bias,

but still made choices)

Lesson: Human Choice can not give a Representative Sample

Surprising Improvement: Random Sampling

Now called “scientific sampling”

Random = Scientific???

Random SamplingKey Idea: “random error” is smaller than

“unintentional bias”, for large enough sample sizes

How large?

Current sample sizes: ~1,000 - 3,000

Note: now << 50,000 used in 1948.

So surveys are much cheaper

(thus many more done now….)

Random Sampling

How Accurate?

• Can (& will) calculate using “probability”

• Justifies term “scientific sampling”

• 2nd improvement over quota sampling

Random SamplingWhat is random?

Simple Random Sampling:

Each member of population is

equally likely to be in sample

Key Idea: Different from “just choose some”

Random SamplingAn old (but still fun?) experiment:

Choose a number among 1,2,3,4

Old typical results: about 70% choose “3”

(perhaps you have seen this before…)

Main lesson: human choice does not give “equally likely” (i.e. random sample)

Random Sampling

How to choose a random sample?

Old Approaches:

– Random Number Table

– Roll Dice

Modern Approach:

– Computer Generated

Random SamplingEXCEL generation of random samples:

https://www.unc.edu/~marron/UNCstat31-2005/Stat31Eg15.xls

Goal 1: Generate Random Numbers

EXCEL approaches:

• RAND function

• Tools Data Analysis Random

Number Generation

EXCEL Random SamplingGoal 2: Randomly Reorder List

EXCEL approach:

• Highlight block with list & random num’s

• Sort whole thing on numbers

Goal 3: Random Sample from List

• Choose 1st subset from random re-order

• Since, each equally likely in each spot

EXCEL DetailsRAND:

• Not available among “Statistical” functions

• But can find on “All” menu

• Note no (explicit) inputs

• Just put in desired cell

• Drag downwards for several random #s

• Caution: these change on each re-comp.

• Thus not recommended for this

EXCEL DetailsTools Data Analysis Random Number

Generation :• Set: # Variables: 1

Distribution: Uniform (over [0,1])

• Generates Fixed List

(doesn’t change with re-computation)

(note entries are “just numbers”)• Thus stable for later interpretation• Recommended for random sample choice

EXCEL DetailsSorting Lists:

• Highlight Block with Both:

– Names to sort

– Random numbers

• Data Sort Choose Column

• Result is random re-ordering of List

Random Sampling HWHW:

C8: For the letters A – L, use EXCEL to:

(a) Put in a random order.

(b) Choose a random sample of 6.

(Hints: for (a), want each equally likely,

for (b), reorder, and choose a subset)

Random Sampling HWInteresting Question:

What is the % of Male Students at UNC?

(Your chance of date,

or take 100% - to get your chance)

HW:

C9: Print Class Handouthttps://www.unc.edu/~marron/UNCstat31-2005/Stat31HWC9.doc

Random Sampling HWNotes on HW C9:• 3 dumb ways to sample, 1 good one• Goal is to learn about sampling,

Not “get right answer”• Part 1, put symbol for yourself, Ms and Fs

for others• Put both count & % (%100 x count / 25)• Part 2, “tally” is:• Part 4, student phone directory available

in Student Union?

Random Sampling HWNotes on HW C9,

• Hints on Part 4:– For each draw, first draw a “random page”– Tools Data Analysis Random Number

Generation Uniform is one way to do this– In “Uniform”, you need to set “Parameters”, to

0 and “number of pages”.– This gives a random decimal, to get an

integer, round up, using CEILING– In CEILING, set “significance” to 1.

Random Sampling HWNotes on HW C9,

• Hints on Part 4 (cont.):– Next Choose Random Column– Next Choose Random Name– Caution: Different numbers on each page.– Challenge: still make equally likely– Approach: choose larger number.– Approach: when not there, just toss it out– Approach: then do a “redraw”– Also redraw if can’t tell gender

More On SurveysMore Common Sense:

How you ask the question

makes a big difference

HW:

3.55,

3.57