inf 397c introduction to research in library and information science spring, 2005 day 2
DESCRIPTION
INF 397C Introduction to Research in Library and Information Science Spring, 2005 Day 2. Standard Deviation. Ļ = SQRT( Ī£ (X - Āµ) 2 /N) (Does that give you a headache?). USA Today has come out with a new survey - apparently, three out of every four people make up 75% of the population. - PowerPoint PPT PresentationTRANSCRIPT
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R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | [email protected] 1
i
INF 397CIntroduction to Research in Library and
Information Science
Spring, 2005
Day 2
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R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | [email protected] 2
iStandard Deviation
Ļ = SQRT(Ī£(X - Āµ)2/N)
(Does that give you a headache?)
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R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | [email protected] 3
iā¢ USA Today has come out with a new
survey - apparently, three out of every four people make up 75% of the population. ā David Letterman
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R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | [email protected] 4
iā¢ Statistics: The only science that enables
different experts using the same figures to draw different conclusions. ā Evan Esar (1899 - 1995), US humorist
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R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | [email protected] 5
iHow to talk about a set of #s?
Name M/F B'day Fing.
lgth MLB
gms Q
Alex J. M 9-Nov 5 2 4
Ben B. M 19-Dec 7 0 3
Brazos P. M 5-Sep 8 6 4
Derek N. M 5-Aug 8 12 4
Hans H. M 24-Jan 7.4 0 4
Jay Y. M 2-Jul 7.5 3 4
Mike Z. M 10-Feb 7.3 0 5
Randolph B. M 16-Jan 7.1 43 5
Terry V. M 10-Oct 7 4 5
Will M. M 31-Oct 7.7 50 4
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iName M/F
B'day
Fing lgth.
MLB gms.
Q
Hans H. M 24-Jan 7.4 0 4
Mike Z. M 10-Feb 7.3 0 5
Ben B. M 19-Dec 7 0 3
Alex J. M 9-Nov 5 2 4
Jay Y. M 2-Jul 7.5 3 4
Terry V. M 10-Oct 7 4 5
Brazos P. M 5-Sep 8 6 4
Derek N. M 5-Aug 8 12 4
Randolph B. M 16-Jan 7.1 43 5
Will M. M 31-Oct 7.7 50 4
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R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | [email protected] 7
iHistograms
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R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | [email protected] 8
iPercentiles/Deciles
ā¢ The cumulative percentage for any given score is the āpercentileā for that score.
ā¢ The decile is one-tenth of the percentile (usually rounded to the nearest whole number).
ā¢ So, in our finger example, 7.7 cm was the 80th percentile, or the 8th decile.
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R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | [email protected] 9
iScales
ā¢ The data we collect can be represented on one of FOUR types of scales:ā Nominal ā Ordinalā Intervalā Ratio
ā¢ āScaleā in the sense that an individual score is placed at some point along a continuum.
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R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | [email protected] 10
iNominal Scale
ā¢ Describe something by giving it a name. (Name ā Nominal. Get it?)
ā¢ Mutually exclusive categories.ā¢ For example:
ā Gender: 1 = Female, 2 = Male
ā Marital status: 1 = single, 2 = married, 3 = divorced, 4 = widowed
ā Make of car: 1 = Ford, 2 = Chevy . . .
ā¢ The numbers are just names.
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iOrdinal Scale
ā¢ An ordered set of objects. ā¢ But no implication about the relative
SIZE of the steps.ā¢ Example:
ā The 50 states in order of population: ā¢ 1 = Californiaā¢ 2 = Texasā¢ 3 = New York ā¢ . . . 50 = Wyoming
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iInterval Scale
ā¢ Ordered, like an ordinal scale.ā¢ Plus there are equal intervals between each
pair of scores.ā¢ With Interval data, we can calculate means
(averages).ā¢ However, the zero point is arbitrary.ā¢ Examples:
ā Temperature in Fahrenheit or Centigrade.ā IQ scores
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R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | [email protected] 13
iRatio Scale
ā¢ Interval scale, plus an absolute zero.
ā¢ Sample:ā Distance, weight, height, time (but not years
ā e.g., the year 2002 isnāt ātwiceā 1001).
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R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | [email protected] 14
iScales (contād.)
Itās possible to measure the same attribute on different scales. Say, for instance, your midterm test. I could:
ā¢ Give you a ā1ā if you donāt finish, and a ā2ā if you finish.
ā¢ ā1ā for highest grade in class, ā2ā for second highest grade, . . . .
ā¢ ā1ā for first quarter of the class, ā2ā for second quarter of the class,ā . . .
ā¢ Raw test score (100, 99, . . . .).ā (NOTE: A score of 100 doesnāt mean the person
āknowsā twice as much as a person who scores 50, he/she just gets twice the score.)
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R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | [email protected] 15
iScales (contād.)Nominal Ordinal Interval Ratio
Name = = =
Mutually-exclusive
= = =
Ordered = =
Equal interval
=
+ abs. 0Gender, Yes/No
Class rank, ratings
Days of wk., temp.
Inches, dollars
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R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | [email protected] 16
iCritical Skepticism
ā¢ Remember the Rabbit Pie example from last week?
ā¢ The ācritical consumerā of statistics asked āwhat do you mean by ā50/50āā?
ā¢ Letās look at some other situations and claims.
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R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | [email protected] 17
iCompany is hurting.
ā¢ Weād like to ask you to take a 50% cut in pay.
ā¢ But if you do, weāll give you a 60% raise next month. OK?
ā¢ Problem: Base rate.
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iSale!
ā¢ āSave 100%ā
ā¢ I doubt it.
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iProbabilities
ā¢ āItās safer to drive in the fog than in the sunshine.ā (Kinda like āMost accidents occur within 25 miles of home.ā Doesnāt mean it gets safer once you get to San Marcos.)
ā¢ Navy literature around WWI:ā āThe death rate in the Navy during the Spanish-
American war was 9/1000. For civilians in NYC during the same period it was 16/1000. So . . . Join the Navy. Itās safer.ā
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R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | [email protected] 20
iAre all results reported?
ā¢ āIn an independent study [ooh, magic words], people who used Doakes toothpaste had 23% fewer cavities.ā
ā¢ How many studies showed MORE cavities for Doakes users?
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R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | [email protected] 21
iSampling problems
ā¢ āAverage salary of 1999 UT grads ā ā$41,000.ā
ā¢ How did they find this? Iāll bet it was average salary of THOSE WHO RESPONDED to a survey.
ā¢ Whoās inclined to respond?
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R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | [email protected] 22
iCorrelation ā Causation
ā¢ Around the turn of the century, there were relatively MANY deaths of tuberculosis in Arizona.
ā¢ Whatās up with that?
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R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | [email protected] 23
iRemember . . .
ā¢ I do NOT want you to become cynical.
ā¢ Not all āmedia biasā is intentional.
ā¢ Just be sensible, critical, skeptical.
ā¢ As you āconsumeā statistics, ask some questions . . .
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R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | [email protected] 24
iAsk yourself. . .
ā¢ Who says so? (A Zest commercial is unlikely to tell you that Irish Spring is best.)
ā¢ How does he/she know? (That Zest is āthe best soap for you.ā)
ā¢ Whatās missing? (One year, 33% of female grad students at Johns Hopkins married faculty.)
ā¢ Did somebody change the subject? (āCamrys are bigger than Accords.ā āAccords are bigger than Camrys.ā)
ā¢ Does it make sense? (āStudy in NYC: Working woman with family needed $40.13/week for adequate support.ā)
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R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | [email protected] 25
iQuote on front of Huff book:
ā¢ āIt aināt so much the things we donāt know that get us in trouble. Itās the things we know that aināt so.ā Artemus Ward, US author
ā¢ Being a critical consumer of statistics will keep you from knowing things that aināt so.
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R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | [email protected] 26
iClaims
ā¢ āBetter chance of being struck by lightening than being bitten by a shark.ā
ā¢ Tom Brokaw ā Tranquilizers.
ā¢ What are some claims you all heard/read?
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R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | [email protected] 28
iBefore the break . . .
ā¢ We learned about frequency distributions.
ā¢ I asserted that a frequency distribution, and/or a histogram (a graphical representation of a frequency distribution), was a good way to summarize a collection of data.
ā¢ Thereās another, even shorter-hand way.
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R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | [email protected] 29
iMeasures of Central Tendency
ā¢ Modeā Most frequent score (or scores ā a
distribution can have multiple modes)
ā¢ Medianā āMiddle scoreāā 50th percentile
ā¢ Mean - Āµ (āmuā)ā āArithmetic averageāā Ī£X/N
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R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | [email protected] 30
iLetās calculate some āaveragesā
ā¢ From old data.
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R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | [email protected] 31
iA quiz about averages1 ā If one score in a distribution changes, will the mode change?__Yes __No __Maybe
2 ā How about the median?__Yes __No __Maybe
3 ā How about the mean?__Yes __No __Maybe
4 ā True or false: In a normal distribution (bell curve), the mode, median, and mean are all the same? __True __False
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R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | [email protected] 32
iMore quiz5 ā (This one is tricky.) If the mode=mean=median, then the distribution is
necessarily a bell curve?__True __False
6 ā I have a distribution of 10 scores. There was an error, and really the highest score is 5 points HIGHER than previously thought.a) What does this do to the mode?
__ Increases it __Decreases it __Nothing __Canāt tellb) What does this do to the median?
__ Increases it __Decreases it __Nothing __Canāt tellc) What does this do to the mean?
__ Increases it __Decreases it __Nothing __Canāt tell
7 ā Which of the following must be an actual score from the distribution?a) Meanb) Medianc) Moded) None of the above
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R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | [email protected] 33
iOK, so which do we use?
ā¢ Means allow further arithmetic/statistical manipulation. But . . .ā¢ It depends on:
ā The type of scale of your dataā¢ Canāt use means with nominal or ordinal scale dataā¢ With nominal data, must use mode
ā The distribution of your dataā¢ Tend to use medians with distributions bounded at one
end but not the other (e.g., salary). (Look at our āNumber of MLB gamesā distribution.)
ā The question you want to answerā¢ āMost popular scoreā vs. āmiddle scoreā vs. āmiddle of the
see-sawāā¢ āStatistics can tell us which measures are technically
correct. It cannot tell us which are āmeaningfulāā (Tal, 2001, p. 52).
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R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | [email protected] 34
iHave sidled up to SHAPES of distributions
ā¢ Symmetrical
ā¢ Skewed ā positive and negative
ā¢ Flat
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R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | [email protected] 35
iWhy . . .
ā¢ . . . isnāt a āmeasure of central tendencyā all we need to characterize a distribution of scores/numbers/data/stuff?
ā¢ āThe price for using measures of central tendency is loss of informationā (Tal, 2001, p. 49).
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R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | [email protected] 36
iNote . . .
ā¢ We started with a bunch of specific scores.ā¢ We put them in order.ā¢ We drew their distribution.ā¢ Now we can report their central tendency.ā¢ So, weāve moved AWAY from specifics, to a
summary. But with Central Tendency, alone, weāve ignored the specifics altogether.ā Note MANY distributions could have a particular
central tendency!ā¢ If we went back to ALL the specifics, weād be
back at square one.
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R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | [email protected] 37
iMeasures of Dispersion
ā¢ Range
ā¢ Semi-interquartile range
ā¢ Standard deviationā Ļ (sigma)
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R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | [email protected] 38
iRange
ā¢ Like the mode . . .ā Easy to calculateā Potentially misleadingā Doesnāt take EVERY score into account.
ā¢ What we need to do is calculate one number that will capture HOW spread out our numbers are from that Central Tendency.ā āStandard Deviationā
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R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | [email protected] 39
iBack to our data ā MLB games
ā¢ Letās take just the men in this class, since N = 10, and itāll be easy to do the math..
ā¢ xls spreadsheet. ā¢ Measures of central tendency.ā¢ Go with mean.ā¢ So, how much do the actual scores
deviate from the mean?
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R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | [email protected] 40
iSo . . .
ā¢ Add up all the deviations and we should have a feel for how disperse, how spread, how deviant, our distribution is.
ā¢ Letās calculate the Standard Deviation.
ā¢ Ļ = SQRT(Ī£(X - Āµ)2/N)
ā¢ Ī£(X - Āµ)
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R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | [email protected] 41
iDamn!
ā¢ OK, so mathematicians at this point do one of two things.
ā¢ Take the absolute value or square āem.
ā¢ We square āem. Ī£(X - Āµ)2
ā¢ Then take the average of the squared deviations. Ī£(X - Āµ)2/N
ā¢ But this number is so BIG!
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R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | [email protected] 42
iOK . . .
ā¢ . . . take the square root (to make up for squaring the deviations earlier).
ā¢ Ļ = SQRT(Ī£(X - Āµ)2/N)
ā¢ Now this doesnāt give you a headache, right?
ā¢ I said ārightā?
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R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | [email protected] 43
iHmmm . . .
Mode Range
Median ?????
Mean Standard Deviation
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R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | [email protected] 44
iWe need . . .
ā¢ A measure of spread that is NOT sensitive to every little score, just as median is not.
ā¢ SIQR: Semi-interquartile range.
ā¢ (Q3 ā Q1)/2
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R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | [email protected] 45
iTo summarize
Mode Range -Easy to calculate.-Maybe be misleading.
Median SIQR -Capture the center.-Not influenced by extreme scores.
Mean
(Āµ)
SD
(Ļ)
-Take every score into account. -Allow later manipulations.
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R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | [email protected] 46
iGraphs
ā¢ Graphs/tables/charts do a good job (done well) of depicting all the data.
ā¢ But they cannot be manipulated mathematically.
ā¢ Plus it can be ROUGH when you have LOTS of data.
ā¢ Letās look at your examples of claims.
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R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | [email protected] 47
iSome rules . . .
ā¢ . . . For building graphs/tables/charts:ā Label axes.ā Divide up the axes evenly.ā Indicate when thereās a break in the rhythm!ā Keep the āaspect ratioā reasonable.ā Histogram, bar chart, line graph, pie chart,
stacked bar chart, which when?ā Keep the user in mind.
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R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | [email protected] 48
iWho wants to guess . . .
ā¢ . . . What I think is the most important sentence in S, Z, & Z (2003), Chapter 2?
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R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | [email protected] 49
ip. 19
ā¢ Penultimate paragraph, first sentence:
ā¢ āIf differences in the dependent variable are to be interpreted unambiguously as a result of the different independent variable conditions, proper control techniques must be used.ā
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R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | [email protected] 50
iā¢ http://highered.mcgraw-hill.com/sites/007
2494468/student_view0/statistics_primer.html
ā¢ Click on Statistics Primer.
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R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | [email protected] 51
iHomework
ā¢ LOTS of reading. See syllabus.
ā¢ Send a table/graph/chart that youāve read this past week. Send email by noon, Friday, 2/4/2005.
See you next week.