Shuyu Chu

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Lisa Short Course Series R Statistical
Analysis
Laboratory for Interdisciplinary Statistical
Analysis
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Laboratory for Interdisciplinary Statistical
Analysis
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Outline
Laboratory for Interdisciplinary Statistical
Analysis

• Review of plots
• T-test
• 2.1 One sample t-test
• 2.2 Two sample t-test
• 2.3 Paired T-test
• 2.4 Normality Assumption Nonparametric
  test
• ANOVA
• 3.1 One-way ANOVA
• 3.2 Two-way ANOVA
• Logistic Regression

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Review of plots
Laboratory for Interdisciplinary Statistical
Analysis

• Using visual tools is a critical first step when
  analyzing data and it can often be sufficient in
  its own right!
• By observing visual summaries of the data, we
  can
• Determine the general pattern of data
• Identify outliers
• Check whether the data follow some theoretical
  distribution
• Make quick comparisons between groups of data

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Review of plots
Laboratory for Interdisciplinary Statistical
Analysis

• plot(x, y) (or equivalent plot(yx)) scatter plot
  of variables x and y
• pairs(cbind(x, y, z)) scatter plots matrix of
  variables x, y and z
• hist(y) histogram
• boxplot(y) boxplot
• lm(yx) fit a straight line
• between variable x and y

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Review of plots
Laboratory for Interdisciplinary Statistical
Analysis

• Low Birth Weight Data Description (lowbwt.csv)
• (189 observations, 11 variables)
• ID Identification Code
• LOW Low Birth Weight (0 Birth Weight gt
  2500g, 1 Birth Weight lt 2500g)
• AGE mothers age in years
• LWT mothers weight in lbs
• RACE mothers race (1 white, 2 black, 3
  other)
• SMOKE smoking status during pregnancy
• PTL no. of previous premature labors
• HT history of hypertension
• UI presence of uterine irritability
• FTVno. of physician visits during first
  trimester
• BWT Birth Weight in Grams

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T-Test
Laboratory for Interdisciplinary Statistical
Analysis

• 2.1 One sample t-test
• Research Question
• Is the mean of a population different from the
  null hypothesis (a nominal value, or some
  hypothesized value)?
• Example
• Testing whether a baby's average birth weight is
  different from 2500 g.
• Hypotheses
• Null hypothesis the baby's average birth weight
  is 2500 g
• Alternative hypothesis the baby's average birth
  weight is not equal to(or
  greater/less than) 2500 g
• In R t.test(x, y NULL, alternative
  c("two.sided", "less", "greater"), mu 0, paired
  FALSE, var.equal FALSE, conf.level 0.95)

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T-Test
Laboratory for Interdisciplinary Statistical
Analysis

• 2.2 Two sample t-test
• Research Question Are the means of two
  populations different?
• Example
• Consider whether the birth weight of these babies
  whose mothers smoke is different form those whose
  mothers dont smoke ?
• Hypotheses
• Null hypothesis the average birth weight of the
  babies whose mothers smoke equals to the babies
  average birth weight whose mothers dont smoke
• Alternative hypothesis the babies average birth
  weight of smoking mothers is not equal to (or
  greater/less than) that of non-smoking mothers
• In R t.test(BWTSMOKE)
• t.test(BWTSMOKE,var.equalT)

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T-Test
Laboratory for Interdisciplinary Statistical
Analysis

• 2.3 Sample size calculation
• Research Question
• How many observations are needed for a given
  power, or what is the power of the test given a
  sample size?
• Power probability rejecting null when null is
  false
• In R power.t.test(n NULL, delta NULL, sd
  1, sig.level 0.05, power NULL, type
  c("two.sample", "one.sample", "paired"),
  alternative c("two.sided", "one.sided"), strict
  FALSE)
• Calculate a sample size given a power
  power.t.test(delta2,sd2,power.8)
• Calculate a power given a sample size
  power.t.test(n20, delta2, sd2)

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T-Test
Laboratory for Interdisciplinary Statistical
Analysis

• 2.4 Paired T-test
• Research Question
• Given the paired structure of the data are the
  means of two sets of observations significantly
  different?
• Example In a warehouse, the employees have asked
  management to play music to relieve the boredom
  of the job. The manager wants to know whether
  efficiency is affected by the change. The table
  below gives efficiency ratings of 15 employees
  recorded before and after the music system was
  installed.
• (Link of the dataset
• http//www-ist.massey.ac.nz/dstirlin/CAST/CAST/Hte
  stPaired/testPaired_c1.html)
• In R t.test(efficiency_after,efficiency_before,pa
  iredT)
• or, t.test(diff), diff
  efficiency_after-efficiency_before

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T-Test
Laboratory for Interdisciplinary Statistical
Analysis

• 2.5 Checking assumptions Nonparametric test
• Using t-test, we assume the data follows a normal
  distribution, to check this normal assumption
  visualization and statistical test.
• Visualization
• Histogram shape of normal distribution
  symmetric, bell-shape with rapidly dying tails.
• QQ-plot plot the theoretical quintiles of the
  normal distribution and the quintiles of the
  data, straight line shows assumption hold.
• Statistical Test Shapiro-Wilk Normality Test
• In R shapiro.test(data)

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T-Test
Laboratory for Interdisciplinary Statistical
Analysis

• 2.5 Checking assumptions Nonparametric test
• When the normal assumption does not hold, we use
  the alternative nonparametric test.
• Wilcoxon Signed Rank Test
• Null hypothesis mean difference between the
  pairs is zero
• Alternative hypothesis mean difference is not
  zero
• In R wilcox.test(x, y NULL, alternative
  c("two.sided", "less", "greater"), mu 0, paired
  FALSE, exact NULL, correct TRUE, conf.int
  FALSE, conf.level 0.95, ...)

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T-Test
Laboratory for Interdisciplinary Statistical
Analysis

• 2.5 Checking assumptions Nonparametric test
• When the normal assumption does not hold, we use
  the alternative nonparametric test.
• Wilcoxon Signed Rank Test
• Null hypothesis mean difference between the
  pairs is zero
• Alternative hypothesis mean difference is not
  zero
• In R wilcox.test(x, y NULL, alternative
  c("two.sided", "less", "greater"), mu 0, paired
  FALSE, exact NULL, correct TRUE, conf.int
  FALSE, conf.level 0.95, ...)

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ANOVA- Analysis of Variance
Laboratory for Interdisciplinary Statistical
Analysis

• T-test Compare the mean of a population to a
  nominal value
• or compare the means of equivalence
  for two populations
• What if you want to compare the means of more
  than two populations?
• We use ANOVA!
• One-Way ANOVA Compare the means of populations
  where the variation are attributed to the
  different levels of one factor.
• Two-Way ANOVA Compare the means of populations
  where the variation are attributed to the
  different levels of two factors.

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ANOVA- Analysis of Variance
Laboratory for Interdisciplinary Statistical
Analysis

• 3.1 One-way ANOVA
• Example Compare the BWT(birth weight in grams)
  for 3 races
• bwt data BWT gams
• RACE mothers race (1 White,
  2 Black, 3 Other)
• SMOKE mothers smoking status
  during pregnancy (1 Yes, 0 No)
• Hypothesis
• Null hypothesis the three groups have equal
  average birth weight
• Alternative hypothesis at least two groups do
  not have equal bwt
• In R a.1aov(BWTfactor(RACE)) and summary(a.1)

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ANOVA- Analysis of Variance
Laboratory for Interdisciplinary Statistical
Analysis

• 3.2 Two-way ANOVA
• Example Compare the bwt for 3 races and 2 status
  of smoking
• Three effects to be considered RACE, SMOKE and
  the interactions
• In R a.2 aov(BWTfactor(SMOKE)factor(RACE))
  and summary(a.2)

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LOGISTIC Regression
Laboratory for Interdisciplinary Statistical
Analysis
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LOGISTIC Regression
Laboratory for Interdisciplinary Statistical
Analysis

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LOGISTIC Regression
Laboratory for Interdisciplinary Statistical
Analysis

• Example Low birth weight data
• We are interested in understanding the variables
  that predict the likelihood of a mother giving
  birth to a baby with low-birth weight (defined as
  a baby weighing less than 2500 grams).
• The response variable low 0, 1 (Indicator of
  birth weight less than 2.5 kg)
• The predict variables
• age mothers age in years
• lwt mothers weight in lbs
• race mothers race (1 white, 2 black, 3
  other)
• smoke smoking status during pregnancy
• ptl no. of previous premature labors
• ht history of hypertension
• ui presence of uterine irritability
• ftv no. of physician visits during first
  trimester

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LOGISTIC Regression
Laboratory for Interdisciplinary Statistical
Analysis

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Thank you!
Laboratory for Interdisciplinary Statistical
Analysis

• Please dont forget to fill the sign in sheet and
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  by email.