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Descriptive statistics


									class 6, 10/10/11
intro to statistical
research is
• 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 research
• face-to-face……………………...distanced
• sampling………….………………..field-based
• measurement…….…………………narrative
• 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 t. San Francisco: Berrett-Koehler.
an introduction to
brief history
• statistics: from the same root as state
• first use of statistics was descriptive—to
  describe by 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
• time (clumsy calculating machines)
• computer speed, memory, money
  (mainframes): algorithms and clever ways
  to “trick” computers
• clumsy software, memory, speed (first
• 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-
• Andrei Kolmogorov (1903-1987)
• John Tukey (1915-2000)
• Jerzy Neyman (1894-1981)
• Gertrude Cox (1900-1978)
• F(lorence) N(ightingale) David (1909-
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: Founding of 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.
• 1977: Cox’s formulation of
  significance testing
• 1977: Exploratory data analysis
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. Parameter
    comes from the Greek for “almost
        Salsburg, D. (1981). The lady tasting tea. New
         York: Henry Holt.)
normal distribution (bell-shaped curved)
• many things in the world distributed
• 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 statistics
description by measurement
• nominal
     • 1=freshman, 2=sophomores etc
• ordinal
     • 1=Gretsky; 2=Howe, 3=Hull, 4=Richard
• 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
   – e.g., survey of favorite restaurants
• median: middle score
   – e.g., professional athletes’ 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
• standard deviation and variance:
  average distance of each observation
  from mean (and average distance
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 the 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,
     the other gets larger (or vice versa)
      • effect of outliers (see figure 17.9)
      • effect of range (see figure 17.10.
      • effect of nonlinearity (see figures
        17.9 & 17.12)
your data
 look at the plot
  most carefully
correlation and causation
• no statistical relationship necessarily
  implies causation
other correlations for special
  conditions (beyond the scope of this
treatment of outliers
• be careful and be honest
interpreting statistics
• were analyses appropriate
• were assumptions underlying analyses met
• was sample representative
• look carefully at the 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                   .10
  20                   .05

M: 3.65                       .79

Sieber, ch. 5: Privacy
• privacy
• confidentiality
• anonymity
• the subtlety of privacy issues
5.3 the right to privacy
• Hatch Act
5.4 behavioral definition of privacy
5.5 privacy and informed consent
5.6 sensitivity
• ask someone who works with
• ask researchers who work with
• ask member of population
5.7 brokered data
                  APA hints
heading levels (62-63)

1.      Centered, Bold, Upper, Lower
2. Flush Left, Bold, Upper, Lower
3.    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
   – John, who loved his wife, was the key
• to separate 2 independent clauses joined
  by a conjunction (e.g., but, and, for, yet
   – John loved Angela, but Angela loved
• 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 comma
• to separate compound verbs
  – Megan intercepted the pass and skated up
    the ice.
• to separate the subject from the verb
  – Jeremy’s passion for continuous movement
    sports like soccer and ice hockey resulted in
    impatience with football.
• when you feel like it
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)
tips cont.
• 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
                more bests
• best free music
  – Krannert Uncorked, most thursdays, 5pm
  – student and faculty performances, Smith
    Hall and Krannert (see Inside Illinois)
• best place to prepare for Hallowe’en
  – Dallas & Company, 1st & University, C
• best used book stores
  – Jane Addams, 208 N. Neil C
  – Old Main Book Shop, 116 N Walnut C
  – Priceless Books, 108 W Main U
more good reasonably cheap food
• pizza: Papa Murphy’s (by Schnuck’s, U,
  1753 W. Kirby, C)
• Mexican: Dos Reales, 1407 N Prospect,
  C; 1106 W University, U
• Barbeque: Black Dog Smoke and Ale
• Chinese: Golden Harbor, C
this week free and cheap
• under construction
directions to Homer Lake
• take Washington in U 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
• turn right, continue about ¼ mile—entrance to
  Homer Lake.
In the middle of the ocean, there is a
special place, which is a Dragon Gate. It has
this wonderful property: Any fish that
swims through it immediately turns into a
dragon. However, the Dragon Gate does not
look any different from any other part of
the ocean. So you can never find it by
looking for it. The only way to know where
it is is to notice that the fish who swim
through it become dragons. However, when
a fish swims through the Dragon Gate and
becomes a dragon, it doesn’t look any
different. It just looks like the same fish
it was before. So you can’t tell where the
Dragon Gate is by looking closely to find
just where the change takes place.
Furthermore, when fish swim through the
Dragon Gate and become dragons, they
don’t feel any different, so they don’t
know that they have changed into dragons.
They just are dragons from then on.
You could be a dragon!

   (Howard Becker, 1998, pp. 218-219)

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