class 6, 10/10/11
intro to statistical
methods
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
proximity
• face-to-face……………………...distanced
duration
• sampling………….………………..field-based
description
• measurement…….…………………narrative
theory
• 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
statistics
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
algorithms
• time (clumsy 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 (18931972)
• Andrei Kolmogorov (1903-1987)
• John Tukey (1915-2000)
• Jerzy Neyman (1894-1981)
• Gertrude Cox (1900-1978)
• F(lorence) N(ightingale) David (19091995)
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.
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. Parameter
comes from the Greek for “almost
measurements.”
Salsburg, D. (1981). The lady tasting tea. New
York: 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 statistics
description by measurement
• nominal
• 1=freshman, 2=sophomores etc
• ordinal
• 1=Gretsky; 2=Howe, 3=Hull, 4=Richard
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., 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
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 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.
17.11)
• effect of nonlinearity (see figures
17.9 & 17.12)
always
plot
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
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 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
.7
.8
.9
1.0
1.1
1.2
1.4
1.5
1.6
10
20
M: 3.65
thinking
speed
1.43
1.25
1.11
1.0
.91
.83
.71
.67
.62
.10
.05
.79
Ethics
Sieber, ch. 5: Privacy
5.1
• privacy
• confidentiality
• anonymity
5.2
• 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
population
• ask researchers who work with
population
• 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
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 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
House
• 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
Preserve
• turn right, continue about ¼ mile—entrance to
Homer Lake.
Research
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)