Communicating Quantitative Information

SpreadsheetsContinue with measures of centrality. High

Stakes [Educational] TestingMale vs. Female

Homework: Continue postings.Complete spreadsheet assignment, if you

didn't…

Spreadsheet

• To show formulas, use ` and Ctrl. The ` is called grave

• Different situations call for different graphs.– Pie: parts of a whole– Bar (or column): individual, distinct quantities. Can be

time– Line: Time based or other continuous quantities– X-Y: chart 2 related values

Spreadsheet

• Use HELP• Caution: formulas use = equal sign• Formulas can contain numbers and cell

references• Copy-and-paste makes relative

addressing– Always check if okay

• Apply general rule(s) of proof-read, edit, enhance, print,…proof-read

News

• How was it to vote in primary?

• What happened in the primary? How was it communicated? How could it have been better?

• Other news?

Postings• Start to think about how information could have

been better presented– including missing information

• Stories:– Hottest summer– Emergency room– Drinking– Immigration– Tax cuts– G-7 countries debt levels

Testing: preview

• Inspired by posting in previous class• Not enough to note how many people died

by given treatment• How many would have died without

treatment?• Check out articles on depression

medications causing suicides– Initial effect of making people more

energetic…

Testing terminology

• Control group versus test/condition group– Careful in assignments

• Double blind: neither subject nor evaluator knows who is in what group– Not always possible

• Most likely not possible in surgery example

• Placebo effect– Take medicine that [you] believe will do you good

may, by itself, make you feel better• Hawthorne effect

– Being studied improved workers

General comments on education

My view, but it is an informed view!• Efforts should be made to improve

schools, that is, make them better.• It is not clear that they were much better in

the past.– Different populations, different requirements,

different outcomes for people who dropped out.

• Think about last week's 'story': self-selected group versus everyone taking the PSAT

Posting topics

• What was k-12 school drop out rate in 1950s, 1960s, 1970s, 1980s, 1990s, now?– or go further back

• When did the GED begin? What are the current absolute numbers and proportions of GED diplomas?

• How did your k-12 school district do recently in the NCLB testing? Regents?

…and educational testingProblems with 'high stakes' testing• too much time devoted to testing, not teaching and

learning• the multiple choice/multiple guess format of most tests

'dumbs down' curriculum– rote grading of essays also can discourage thinking

• encourages corruption– weaker students shuffled around– plain lies at all levels

One positive aspect of NCLB is that the rules distinguished different groups of students and required improvement in each category.– but this also could lead to corruption.

Race to the Top: claim to evaluate on improvements.

Normal Distribution• Recall: mean = mode = median. • Standard deviation: 68% of entries within 1 sd of

mean, 95% within 2, 99% within 3.

6 Sigma• … name of quality in manufacturing

campaign with goal to get 99% (6 standard deviations—3 on each side) into acceptable range.– Manufacture good things almost all the time

• Usually increasingly difficult to get last amount

Inoculation campaign

• Campaign to give children in Africa polio shots.

• Estimate made: $3 to get 90% of children.

• Students in prior class said: why can’t [UN, NGO] pay the $3 for the remaining 10%?

• Answer?

Interlude: discrete vs continuous

• The graph showing normal distribution represented continuous function. This is approached by large number of data points.

• Need to understand for a given application/situation, are there– a) finite number of measurements?– b) is there something that forces the readings

to be rounded off and/or only take certain values—quantized effect?

More on normal

• Big standard deviation says that the data is spread out

• Small standard deviation says that most of the data is close to the mean– preferred situation with manufacturing: 6

sigma movement.

Male vs Female Math. ability issue

• What did the president of Harvard say? Not clear, but one transcript of remarks referred to the variance

• male innate ability is more spread out: more in the 'outliers', at both ends

• Draw this!

Answer

Why is variance relevant?

• The Summers issue was why there are so few female tenured professors in the sciences at Harvard– This concerns the [upper] outliers, not the

mean.

Harvard president comments, cont.

• Good article about this in 1/24/05 New York Times. Included comments:– social forces dwarf the innate differences, if

they exist– hard work dwarf innate differences: the Asian-

American (parent) phenomenon

Why focus on the normal distribution?

• Many things 'in nature' are normal.

• A normal distribution can be something dependent on many discrete events– binomial tends to normal

Coin toss

• Example (the example) of bi-nomial: two choices.– fair coin means chances equally likely. Binomial also

can refer to situations in which chances are not equal.• Each toss is independent!• Calculate P for probability of sequences by

multiplying– Head Head has P of (1/2) * (1/2) = ¼– Head Tail has P of (1/2) * (1/2) = ¼– Tail Head has P of (1/2)* (1/2) = ¼– Tail Tail has P of (1/2)*(1/2) = ¼

= 1

Binomial Distribution• Note: when flipping coins, any single sequence

of heads and tails is equally likely!– H H H H H H H H H H– H T H T H T H T H T

• There are more sequences with 5 heads and 5 tails than any other combination– will return to this topic later. Extra credit to make a

posting explaining the formula.

• When flipping coins in a sequence (assuming a fair coin), the odds of heads on the next flip is ½ no matter what the sequence has been.

Class Exercise

• Flip a coin 10 times. Record number of heads. – What are possible values?

• I will record data points and we will see the distribution evolving…

Data collection

• Each of you will gather more data than I will collect…– H, T, T, H, ….. T– count heads, count tails. Check if these two

numbers add up to 10– Report to me how many heads.

Binomial….

• with more and more values will resemble normal– asymptotic….tending towards

1 1 ½ heads ½ tails

1 2 1 ¼ 2 heads, 2/4 1 head&1 tail, ¼ 2 tail

1 3 3 1

1 4 6 4 1

1 5 10 10 5 1

1 6 15 20 15 6 1

Not everything is normally distributed….

• Some distributions are not normal, so need to be aware of them, also.– mean, mode, median, standard deviation,

range still have meaning.

– bimodal, multi-modal can arise when there are 2 or more distinct populations….

Uniform distribution

• Equal number of occurrences of each/all values in a range– 20, 20, 20, 21, 21, 21, 22, 22, 22, 23, 23, 23,

24, 24, 24, 25, 25, 25– Range is 20 to 25– What is mean? What is mode?

• Can you generalize for uniform distributions?

Gauss story

• Karl Gauss (1777-1855), was in a class with the assignment: add up the numbers 1 to 100.

• What is the mean? For this uniform distribution, the mean is the mean of the lowest and the biggest numbers: 1 and 100. Mean is 101/2 is 50.5

• The sum of all the numbers is the same as if they were each the mean: 100 * 50.5 is 5050.

Gauss story: another way

• Here are the numbers: 1, 2, 3, 4, …. 98, 99, 100

• Group numbers high and low

• 1 and 100, 2 and 99, 3 and 98, … There are 50 pairs. Each pair adds to 101 (the same thing!). 50 * 101 is (also) 5050.

Bi-modal

• or multi-modal. You really have two (or more) distinct and dissimilar populations

• Consider a Purchase class attracting mainly dance majors and football players. Measure weight!

Correlation• Correlation: the degree to which measurements/variables are

related.• Can compute Pierson correlation coefficient: -1 to 1. 0 is no

correlation. Nearer to 1 or -1 shows correlation.• Correlation coefficient values below are 1, .85, -.94, .17

http://www.psychstat.smsu.edu/introbook/sbk17.htm

But…

• Correlation is not causality.– Comment made about smoking and cancer,

but it has been proven that smoking causes cancer by population studies and biological studies.

• The damage to lungs is visible

– The cause isn't absolute—some people do not get cancer…..

Puzzle

• 32 cards are dealt from a well-shuffled deck of 52 cards. The deck contains 26 red and 26 black cards. What is the difference between the number of black cards among the 32 dealt and the red cards remaining in the deck?

Homework

• Keep up on postings.– can go back to old[er] topics

• We will cover mortgages, subprime crisis

• We will cover polls

• Evaluate sources

• Start to decide on topics for – diagram project– presentation projects