class 6, 10/14/13 intro to statistical analysis
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Transcript of class 6, 10/14/13 intro to statistical analysis
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class 6, 10/14/13intro to statistical
analysis
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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)
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dimensions of researchproximity• face-to-face………………………….…….
……...distancedduration• intermittent…….……………….….
…………..field-baseddescription• measurement…….……………….
…………………narrativetheory• building……………………………….…...
…………..…..testing
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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)
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an introduction to statistics
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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
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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
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• 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
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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)
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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)
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• 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)
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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.)
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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
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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
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graphic representation of data
• “to convey the greatest number of ideas in the shortest time with the least ink in the smallest space”
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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”
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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
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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)
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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
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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
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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)
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alwaysplot
your data!!then, look at the plot
most carefully
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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
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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
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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
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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
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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)
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• 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
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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)
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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)
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• 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
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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.
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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 . . . .
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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.
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• 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
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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)
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Vogt• nominal scale• operational definition• outlier• parsimony• path diagram• practical significance• Pygmalion effect
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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
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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
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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.
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free and cheap• under construction