class 6, 10/14/13intro to statistical

analysis

research is• systematic self-critical inquiry made public

(Lawrence Stenhouse, 1981)• challenging accepted or “received” knowledge

(Alfred North Whitehead)• figuring out what the devil people think they

are up to (Geertz)• copy from one, it’s plagiarism; copy from

many, it’s research (Wilson Mizner)

dimensions of researchproximity• face-to-face………………………….…….

……...distancedduration• intermittent…….……………….….

…………..field-baseddescription• measurement…….……………….

…………………narrativetheory• building……………………………….…...

…………..…..testing

preferences cont.

• Inventor Thomas Edison had a simple test he used to measure the “unexpectedness quotient” of prospective employees. He would invite a candidate to lunch and serve a bowl of soup. He would then watch to see whether the person salted his soup before tasting it. If he did, he wouldn't be offered the job. Edison felt that people are more open to different possibilities if they don't salt their experience of life before tasting it.

(Von Oech, Roger. (2002). Expect the unexpected or you won't find it. San Francisco, CA: Berrett-Koehler)

an introduction to statistics

brief history• statistics: from the same root as state• first use of statistics was descriptive—counting

matters of importance to the State, e.g., census

• inferential statistics began with the study of probabilities– once people understood probabilities of an

event given certain conditions, they began to realize that they could make inferences from a sample to population

computational shortages and bottlenecks across time (in the West)

• paper: mathematicians learned to develop shortcuts, complex algorithms

• Roman numerals: incredibly clumsy • CXCVIII + XLIV =

• no zero• time (pre-calculating machines): development

of more shortcuts and algorithms

• time (hand calculating machines)• computer speed, memory, money

(mainframes): algorithms and clever ways to “trick” computers

• clumsy software, memory, speed (first PCs)• imagination: with fast computers and

unlimited memory, only constraint is how to use them

some people in the history of statistics• Karl Pearson (1857-1936)• Ronald Fisher (1890-1962)• William Gosset (“Student”) (1876-1937)• Prasanta Chandra Mahalanobis (1893-1972)• Andrei Kolmogorov (1903-1987)• John Tukey (1915-2000)• Jerzy Neyman (1894-1981)• Gertrude Cox (1900-1978)• F(lorence) N(ightingale) David (1909-1995)

some moments in history of statistics• 1908: Student’s t-test• 1915: distribution of the correlation coefficient

(Fisher)• 1925: Statistical methods for research workers

(Fisher)• 1931: Indian Statistical Institute (Mahalanobis)• 1934: proof of the central limit theorem (Levy,

Lindeberg)• 1935: The design of experiments (Fisher)

• 1945: nonparametric tests (Wilcoxon)• 1947: Mann-Whitney formulation of

nonparametric tests• 1959: definitive formulation of hypothesis

testing (Lehmann)• 1970: Games, gods, and gambling (F. N.

David)• 1977: Cox’s formulation of significance testing• 1977: Exploratory data analysis (Tukey)

Pearson’s 4 parameters• mean• standard deviation• symmetry• kurtosis

Parameters are not numbers like measurements. They can never be observed but can be inferred by how the measurements scatter. From the Greek for “almost measurements.”

(Salsburg, D. (1981). The lady tasting tea. New York, NY: Henry Holt.)

normal distribution (bell-shaped curved)

• many things in the world distributed normally

• many statistics distributed normally• in normal distributions only 2 parameters• mathematically, normal distributions,

compared to many other distributions, easy to work with

Krathwohl, ch 17: descriptive statisticsdescription by measurement• nominal

• 1 = freshman, 2=sophomores etc• ordinal

• 1 = Gretsky; 2=Howe, 3=Hull, 4 = Crosby, etc

• interval• fahrenheit scale

• ratio• metric scale, eg, distance

graphic representation of data

• “to convey the greatest number of ideas in the shortest time with the least ink in the smallest space”

measures of central tendency• mode: measure that appears most often

– e.g., survey of favorite restaurants• median: middle score

– e.g., baseball players salaries• mean: average

– “well behaved data”

skewness: asymmetry in distribution• tail to right: positive skew (mean largest,

then median, then mode)– can be due to floor effect

• tail to left: negative skew (mean smallest, then median, then mode)– can be due to ceiling effect

measures of dispersion & variability

• range: distance from highest to lowest• standard deviation and variance: average

distance of each observation from mean (and average distance squared)

standard score (z-score): raw score translated into distance from mean in SD units

derived (scale) score: translates standard scores into scale where all scores positive

stanine (standard nine): half a SD

in a normal distribution

• 68.26% of cases within 1 SD either side of the mean

• 95.44% within 2 SDs • 99.74% within 3SDs

measures of relationships• correlation (Pearson product-moment):

strength of relationship, -1 to 1– positive: as one measure gets larger (or

smaller), so does the other– negative: as one measure gets smaller,

other gets larger (or vice versa)• effect of outliers (figure 17.9)• effect of range (figures 17.10, 17.11)• effect of nonlinearity (figures 17.9,17.12)

alwaysplot

your data!!then, look at the plot

most carefully

correlation and causation• no statistical relationship necessarily implies

causationother correlations for special conditions

(beyond the scope of this course)treatment of outliers• be careful and be honest

interpreting statistics• were analyses appropriate• were assumptions underlying analyses met• was sample representative• look carefully at data and what underlies

them

exploratory data analysis (Tukey, 1977)• perfectly legitimate, and important, but

conclusions or hypotheses that result should be tested with another data set

reaction time speed .7 1.43 .8 1.25 .9 1.11 1.0 1.0 1.1 .91 1.2 .83 1.4 .71 1.5 .67 1.6 .62 10.0 .10 20.0 .05

M: 3.65 .79

Zuger: A Crash Course in Playing the Numbers Wheelan, C. (2013). Naked statistics.

• staying well all about probability and risk• is it mean or median survival you’re looking

at• studies that show a drug works get published,

studies that show it doesn’t, don’t• Wheelan has propped the factory gates wide

open. Take his tour

Sieber & Tolich: Communicating Informed Consent and Process Consent

• informed: what a reasonable person would want to know

• process consent: ongoing• letter seeking consent: 12 items on p. 117

– piloting– ensure comprehension– adequacy of decision making (see p. 120)

• delivery (recruiting)• internet research• hard-to-reach subjects (sampling discussion)• letter example pp. 130-131• gatekeepers

– description, pp. 132-133, useful (except 3rd person)

• assent and consent • when signed consent not needed (pp. 135-

136)• research without consent (pp. 137-138)• subject’s right to withdraw at any time

Becker ch 3• [Researchers] have to organize their material,

express an argument clearly enough that readers can follow their reasoning and accept the conclusions. They make this job harder than it need be when they think that there is only One Right Way to do it, that each paper has a preordained structure they must find. They simplify their work, on the other hand, when they recognize that there are many effective ways to say something and that their job is only to choose one and execute it so that readers will know what they are doing. (p. 43)

some writing tips• write introductions last (p. 50)• put the conclusion at the beginning (p. 52)• evasive vacuous sentences a good way to

begin early drafts• any sentence can be changed, rewritten, or

contradicted—you can write anything at all (p. 54)

• begin with a “spew” draft (p. 55)• give thoughts a physical embodiment—get

them on paper (p. 56)

• outlines can help, but not if you begin with them (p. 60)

• do what is easiest first (p. 60)• talking about them, instead of just wishing

them away, solves all sorts of scientific problems, not just those of writing (p. 64)

tips not from Becker• write conclusion first• never start a paper at the beginning• writing not a linear process

APA heading levels (62-63)

1. Centered, Bold, Upper, Lower2. Flush Left, Bold, Upper, Lower3. Indented, bold, lower paragraph

heading ending with period.4. Indented, bold, italics, lower paragraph

heading ending with period.5. Indented, italics, lower paragraph heading

ending with period.

Contemporary Realities (1) Cronbach (1975) observed, “It is the special task of the social scientist in each generation to

pin down contemporary facts…[and] to realign culture’s view of [people] with present realities” (p. 126). Educational researchers study people interacting in culture. The realities we encounter daily continually change. . . .

Other People’s Children (2) The most salient contemporary reality affecting early education and care in contemporary post-

industrial societies is that increasingly large segments of these societies have given over the raising of their young children, from an increasingly early age, to others. At one time, only the rich did not raise their own children. Now, the large majority of children are being raised by others. Giving one’s children to others to raise is a new phenomenon for the working and middle classes.

Increasing numbers. (3) According to the US Department of Education National Center for Education Statistics, 57% of children age 3-5 in the US are in some kind of institutional early childhood care and education program. For children of mothers with college degrees or higher, the percentage rises to 73%. The percentage of children from 3-5 in at least one “weekly non-parental care arrangements,” which includes, in addition to institutional care, informal out-of-the-home care, for example, with baby sitters or relatives, or children in unlicensed day cares, rises to 73%.

Institutional care. (4) Children in institutional care range . . . .

comma (78-80)• between elements in a series (3 or more)—

before and or or (Harvard comma)– the height, width, and depth

• to set off nonessential or nonrestrictive clause– John, who loved his wife, was the key

informant.• to separate 2 independent clauses joined by a

conjunction (e.g., but, and, for, yet etc)– John loved Angela, but Angela loved

Rashad.

• to set off year in exact dates– April 18, 1992, Masatoshi left . . .– April 1992 Masatoshi left . . .

• to set off year in citations (in parens)– (Hatano, 1998)

• in numbers 1,000 or more

do not use commas• to separate compound verbs

– I hit the ball, and ran to first base. (wrong)– I hit the ball and ran to first base. (correct)– I hit the ball, and I ran to first base.

• to separate the subject from the verb– The young woman in the second row in the blue

dress and red hat, raised her hand to ask a question. (wrong)

– Miranda, who was sitting in the second row and was wearing a blue dress and red hat, raised her hand. (correct)

Vogt• nominal scale• operational definition• outlier• parsimony• path diagram• practical significance• Pygmalion effect

more goods• good free music

– Krannert Uncorked, most thursdays, 5pm– student and faculty performances, Smith Hall and

Krannert (see Inside Illinois)• good place to prepare for Hallowe’en

– Dallas & Company, 1st & University, C• good used book stores

– Jane Addams, 208 N. Neil C– Old Main Book Shop, 116 N Walnut C– Priceless Books, 108 W Main U

Asian grocery stores• Lee’s, next to IGA on Kirby, C• Far East, 5th St south of University, C• AmKo, 1st and Springfield, C • Green Onion, 2020 S. Neil, C

directions to Homer Lake• take Washington in Urbana east. • a few miles east of Urbana, road will end. Turn right,

then the first left.• a few more miles road will jog right then left• a few more miles, road will turn into county highway.

continue east.• about 15 miles out, you will see wooded area to

right, housing development to left.• cross bridge over a channel—bit of lake to right, • continue a few hundred yards to first paved road to

right—small sign: Salt Fork Forest Preserve• turn right, continue about ¼ mile—entrance to

Homer Lake.

free and cheap• under construction