Intro to Stats

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Intro to Stats

• Lecture Notes
• November 25, 2008
• R. Sinn

2
Joker and Jody

• The notorious river boat gambler Joker McGants
• was plying his trade a bit too well in the ATL
  one
• April night. Sitting amidst a pile of chips,
  bills and
• booze, Joker realized that Bugsy Haygood was
• downright ill-tempered, ill-mannered and ill-
• equipped to restrain his erupting anger.
• Youre using loaded dice, mug, Bugsy accused.

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Joker and Jody

• Joker donned a look so innocent it was worthy of
• the seraphim, as well it should have been. Joker
• had practiced in front of a mirror for hours upon
• hours for just such occasions. Given that
  Bugsys
• stock and trade involved 9mm projectiles aimed by
• the hoarse whispers of his family, the sweat
  that
• rolled icily down Jokers spine was
  understandable.
• Youre welcome to perform any test you wish
• on these dice, sir, Joker agreed.

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Joker and Jody

• Bugsy performed the various test gamblers use
  to ascertain
• that the dice are true. No shaved corners, no
  weighted
• imbalances, no signs of any alterations. Joker
  smiled his
• winsome best. Bugsy was not amused.
• Just as Joker was judging the possibilities of
  a live-to-
• gamble-another-day escape, the cocktail waitress
  Jody
• DeLong offered a suggestion. Im taking a
  statistics course
• at North Georgia, and I know a way to tell if
  those dice are
• loaded. We can use chi-square.

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Joker and Jody

• Both Joker and Bugsy agreed, although a debate
  quickly ensued
• I prefer using a .01, Joker suggested.
  Dont want any Type I
• errors, you know.
• I disagree, Bugsy told him. I think an a .1
  would better control
• that insidious Type II error. We do want as much
  power as
• possible, dont we?
• Jody did not like the evil glint in Bugsys eye
  nor the way his hand
• inched toward the coat pocket that bulged
  noticeably.

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Chi-Square Tests

• Jody, as bright as she was beautiful, just rolled
  her eyes,
• Everyone knows that a has to be .05. Duh.

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Chi-Square Goodness of Fit

• Compare Expected vs. Actual Counts
• Expected Counts
• Proportions predicted by probability theory or a
  hypothesis stated by the researcher(s)
• Actual Counts
• Proportions that actually occurred during data
  collection

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Were the Jokers Dice Wild?

• The die was cast 600 times, and the following
  frequencies were recorded

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Two Types of ?2 Tests

• Goodness of Fit
• Probability-Based Investigations
• Las Vegas Games
• Must know theoretical counts
• MMs Problem
• Prototype
• Are there enough RED MMs in my bag?

• 2 Categorical Variables
• 2-Way Table
• Compare Rows
• Do columns (groups) influence row totals?
• Religious Affiliations Problem
• Prototype
• Does sect or denomination influence drinking,
  drug use or divorce?

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Examples of ?2 2-Way Tables

• Course Grades one math professor gives only 5
  As and 25 Bs. The rest of the department
  gives 15 As and 30 Bs. Is this professor
  off the reservation?
• Preventing Colds does vitamin C prevent colds?
  A control group takes no additional vitamin C.
  One research group drinks 3 6-oz. glasses of
  orange juice daily. A second research group
  takes 1000 mg vitamin C supplement daily. During
  one cold season, the percentages of colds in each
  group is calculated.

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Examples of ?2 Goodness of Fit

• Genetics the probability of offspring having
  certain inherited traits are well known. If two
  Dobermans are bred, we can verify hypotheses
  about dominant vs. recessive traits by comparing
  expected counts (based on the model) to actual
  counts (based on counting the pups).
• Fair Casino? a roulette wheel has three colors
  red, black and green. Compare 500 spins of the
  wheel to see if wheel is fair given that
  Black-Red-Green theoretically occur in a 18-18-2
  ratio.

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Example 1

• Dobermans can be bred in 4 colors black, red,
  blue and fawn, all of which have rust colored
  highlights. If a black male Doberman (hetero
  dominant allele) and a fawn female Doberman (homo
  recessive allele) were bred, on average half
  their pups would be black, a quarter blue and the
  remaining quarter fawn. Given these parameters,
  suppose over the course of several years, 28 pups
  was born 11 black, 11 blue and 6 fawn.
• Test the hypothesis that the predicted
  proportions are accurate at the .1 level of
  significance (by hand). This situation meets the
  model assumptions for this test.

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Example 2

• A certain color of cars stolen more often than
  others? Of all cars manufactured, 15 are white,
  15 blue, 35 red, 30 black and 5 other, then
  test the hypothesis that a certain color is
  stolen more often at an appropriate level of
  significance. Of 830 stolen vehicle reports, 140
  were white, 100 blue, 270 red, 230 black and 90
  others.

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Final Clicker Exam

• Two types of questions
• High Risk (50)
• High Reward (50)

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Question 1

• The following is an example of which type of
  chi-square test?
• Preventing Colds does vitamin C prevent colds?
  A control group takes no additional vitamin C.
  One research group drinks 3 6-oz. glasses of
  orange juice daily. A second research group
  takes 1000 mg vitamin C supplement daily. During
  one cold season, the percentages of colds in each
  group is calculated.
• Chi-Square 2-way Tables (Test for Independence)
• Chi-Square Goodness of Fit

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Question 2

• The greatest Christmas CD ever recorded was made
  by
• Nickelback
• Mannheim Steamroller
• Trans Siberian Orchestra
• Kenny G

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Question 3

• A fair way to alpha in the activity was to
• Set it high innocent until proven guilty
• Set it low innocent until proven guilty

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Question 4

• The way we ACTUALLY set alpha in the activity
  was
• Medium (.05) tryin not flunk here!
• High (0.10) hang that SOB
• Low (0.000001) blatantly kissin butt hopin
  for an A and a final exam exemption despite a 42
  class average
• Whats alpha again?

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Question 5

• The alternative hypothesis for ANOVA is most
  accurately described by which of the following?
• All the group means are different
• Some of the group means are different
• All the group means are the same
• At least one of the group means is different than
  the others
• Some of the group means are the same

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Question 6

• ANOVA is short for
• A Nocturnal Observation of Villainous Activity
• Analysis of Variance