Intro to Stats

1
Intro to Stats

• Lecture Notes
• March 31, 2009
• R. Sinn

2
Estimates vs. Comparisons

• Confidence Intervals
• Used to estimate population mean
• Accuracy stated as confidence
• T-Test (and occasionally z-test)
• Use to compare sample to population mean
• Accuracy stated as significance

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Pre-Test Post-Test Designs

• A common research design does a blood pressure
  drug work?
• Find 40 people with high blood pressure
• Take their blood pressure (Pre)
• Dose them with experimental drug for 2 months
• Take their blood pressure again (Post)
• Problem 2 samples
• We have 2 groups of scores, but our methods (so
  far) only can handle 1 sample at a time
• What can we do?

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Slick Trick T-Test

• Pre-Test Post-Test Design
• Administer Test
• Perform Experiment
• Administer Same Test
• Check for Improvement (Change)
• Trick
• Subtract 1st score from 2nd (Post Pre)
• Positive Number Score Increased
• Negative Number Score Decreased

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Example 1

• The table on the next slide gives the pretest and
  posttest scores for 20 high school Spanish
  teachers who attended an intensive summer course
  and then took a listening test.
• Did the course improve their listening skills?
• Use an a .05 level of significance

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Data Set 1
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2 Sample Group Comparisons

• 2 Sample T-Tests
• Collect two data lists
• 2 Samples
• Compare 2 sample means to each other
• Compare two research groups
• Treatment vs. Control
• Pretest vs. Posttest
• Demographics comparisons

• 1 Sample T-Tests
• Collect one data list
• 1 Sample
• Compare sample mean to population mean
• Compare sample group to population
• State (GA) vs. USA
• County vs. State
• USA vs. World

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2 Sample Tests 2 Types

• Independent Samples
• Data Lists Unrelated
• Demographic Comparisons
• Treatment vs. Control
• Samples MAY BE DIFFERENT SIZE

• Dependent Samples
• Data Lists Related
• Pretest-Posttest
• Twins, parent-child, husband-wife
• Called Matched-Pairs Data
• Data List MUST BE SAME SIZE

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Example 2

• Is the following research data dependent samples
  or independent samples?
• A pediatrician measured cholesterol in her young
  patients discovering surprisingly high levels.
  Ten such patients were randomly selected to
  participate in a research study. A treatment was
  performed for 2 months. The cholesterol was then
  re-measured for all ten participants.
• Clickers
• Dependent Samples t-test
• Independent Samples t-test

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Example 3

• Dependent samples or independent samples?
• A researcher is comparing the average number of
  miles driven by households. A sample of 14
  Midwestern households (with an average of 16,229
  miles) is compared to a sample of 15 Southern
  households (with an average of 17,689).
• Clickers
• Dependent Samples t-test
• Independent Samples t-test

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Example 4

• Dependent samples or independent samples?
• Dr. Sinn is comparing the mathematics
  self-confidence of White teenagers (n 61) with
  that of Black teenagers (n 43).
• Clickers
• Dependent Samples t-test
• Independent Samples t-test

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Example 5

• Dependent samples or independent samples?
• A general contractor wishes to compare the
  lifetimes of two major brands of water heaters,
  Eagle and National.
• Clickers
• Dependent Samples t-test
• Independent Samples t-test

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Example 6

• Dependent samples or independent samples?
• Ten married couples are selected at random to
  participate in a study about relative ages of
  married men and women. The data lists are the
  ages of husbands (list 1) and the ages of their
  wives (list 2). Do the data suggest married men
  are older than their wives?
• Clickers
• Dependent Samples t-test
• Independent Samples t-test

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Answers to Examples 2 - 6

• Dependent Samples (Pretest-Posttest)
• Independent Samples (Demographics Comparison)
• Independent Samples (Demographics Comparison)
• Independent Samples (No relationship between
  samples)
• Dependent Samples (Matched Pairs)

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2 Sample Tests 2 Types

• Independent Samples
• Data Lists Unrelated
• Demographic Comparisons
• Treatment vs. Control
• Samples MAY BE DIFFERENT SIZE

• Dependent Samples
• Data Lists Related
• Pretest-Posttest
• Twins, parent-child, husband-wife
• Called Matched-Pairs Data
• Data List MUST BE SAME SIZE

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Hypothesis Test Steps

• 1 Sample vs. 2 Samples
• 1 Sample Run Z or T? (Use T, except Chap. 14)
• 2 Samples Independent or Dependent?
• Hypothesis Symbolic Set-Up
• Sample (n lt 25?)
• Histogram (Normal?)
• Box-and-Whisker Plot (No outliers?)
• Set a (Analyze Type I II Error
• Run Test (get p-value)
• Is p lt a ? (reject null)
• State research conclusion in real-world context

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Example 7

• A researcher claims that college women have
  significantly more credit card debt than their
  male counterparts.
• Males (n 38)
• Average debt is 435
• s.d. 1,026
• Females (n 32)
• Average debt is 781
• s.d. 781
• Test this hypothesis at the .05 level of
  significance.

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Example 8

• A physical therapist wishes to determine whether
  an exercise program increases flexibility. He
  measures the flexibility (in inches) of 12
  randomly selected subjects both before and after
  an intensive 8-week training program. The data
  table is below. Test at the .05 level of
  significance.

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Example 8 Hypothesis

• Hypothesis Typical Pretest-Posttest Design
• H0 µ2 - µ1 0
  H0 µd 0
• Exercise has no effect on flexibility
• No difference between groups
• Note H0 µ2 µ1 gt µ2 - µ1 0
• Ha µ2 - µ1 gt 0
  Ha µd gt 0
• Exercise increases flexibility
• Positive difference between groups
• Note H0 µ2 gt µ1 gt µ2 - µ1 gt 0

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Data Set 8
Flexibility (inches)
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Example 9

• Researchers at the University of Mississippi
  wanted to determine whether the reaction time (in
  seconds) of males differed from that of females
  in a go/no go study.
• A go/no go stimulus requires participants to
  respond to particular stimuli and ignore others.
• The data table is given below.
• Test their hypothesis at the .05 level of
  significance.

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Data Set 9
Reaction Times (seconds)
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Example 10

• A test preparation company claims that its SAT
  prep course improves SAT math scores. The
  company randomly selects 12 seniors and
  determines their scores.
• The same students are placed in the prep course.
  Upon completion, they retake (a different version
  of) the SAT.
• Results are below.
• Test the companys claim at an appropriate level
  of significance.

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Data Set 10
SAT Scores Math Portion
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Solution Example 10

• Pretest-Posttest Design
• H0 µD 0Ha µD gt 0
• Make difference list verify normality (see
  graphics, next slide)
• Type I Error Falsely claim course improves SAT
  scoresType II Error Falsely claim course do
  not help (company would minimize Type II set a
  high, a 0.1)
• Run test (t 2.6955, p 0.0104)
• Since p 0.01 lt 0.1 a, reject null.
• Evidence suggests course helps improve SAT
  scores.

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Example 10 Graphics 1

• Making Difference List
• Box Plot (no outliers detected)

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Example 10 Graphics 2

• Histogram (approximately normal)
• Running Dependent Samples T-Test