STAT 6020 Introduction to Biostatistics Fall 2005 Dr' G' H' Rowell

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STAT 6020Introduction to BiostatisticsFall
2005Dr. G. H. Rowell

• Class 2

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Review Questions

• Chapter 1
• Statistical Inference
• Chapter 2
• Data Types Numerical/Categorical
• Chapter 3
• What is the difference in a bar chart a
  histogram?
• Describe a useful transformation how it works.

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Ch4 Theoretical Distributions, An Overview

• Probability
• Samples/Population
• Distributions
• Continuous
• Normal, Lognormal, Uniform
• Discrete
• Binomial, Poisson

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Ch 4 Probability

• We teach an entire course on this STAT 6160
• Not a main focus of this course
• Understand
• Basic Axioms
• Randomness
• Independence
• Probability Distributions Functions

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Ch 4 Probability - Basics

• S Sample space
• E an event in the Sample Space
• P(E) Probability that event E occurs
• 0lt P(E) lt1
• P(S) 1
• If E1, E2, E3, are mutually exclusive events,
  then probability of the union of events sum of
  the individual events

P(E1 U E2 U E3 U ) P(E1) P(E2) P(E3)
for a finite or an infinitely countable number
of events
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Ch 4 Probability - Independence

• Independent Events
• Events A B are independent if and only if

P(A given that you know everything about B)
P(A) OR P(A and B) P(A) P(B) Over
simplifying A B are independent if knowing
the outcome of A tells us nothing about B
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Ch 4 Sample Populations

• Population
• Sample
• Goal of Statistics

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Ch 4 Probability Distributions

• Decision Continuous or Discrete ?
• If Continuous, what is the shape of the relative
  frequency of the outcomes?
• Flat Uniform
• Bellshaped Normal
• Positively Skewed Lognormal

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Ch 4 Probability Distributions

• Decision Continuous or Discrete ?
• If Continuous, what is the shape of the relative
  frequency of the outcomes?
• Flat Uniform
• Bellshaped Normal
• Positively Skewed Lognormal

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Ch 4 Probability Distributions

• If Discrete, what experiment is the variable
  modeling
• Counts number of successes might be binomial
• Counts number of trials to the first success
  might be geometric
• Counts independent, random, and RARE events
  might be Poisson

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Ch 4 Normal Distribution

• Mound-shaped and symmetrical
• Mean and standard deviation used to describe the
  distribution
• Empirical Rule

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Standard Normal

• Normal with mean zero and standard deviation 1
  Notation N(0, 1)
• Z-score
• Formula
• Meaning
• Tools for finding probabilities
• Tables, software, applets

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Statistical Software Online

• StatCrunch
• http//www.statcrunch.com/
• StatiCui
• http//stat-www.berkeley.edu/stark/Java/Html/Prob
  Calc.htm
• VassarStats
• http//faculty.vassar.edu/lowry/VassarStats.html

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Visualization

• What does normal look like?
• Histogram See Figure 4.7, page 60.
• Normal Density Function
• Normal Cumulative Distribution

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Ch 4 Example, Normal

• If the average daily energy intake of healthy
  women is normally distributed with a mean of 6754
  kJ and a standard deviation of 1142 kJ than what
  is the probability that a randomly selected women
  is below the recommended intake level of 7725 kJ
  per day? Above 7725 kJ? Between 6000 and 7000 kJ?

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Ch 4 Serum Albumin Example

• Data 216 patients with primary biliary
  cirrhosis
• mean serum albumin level 34.46 g/l,
• st dev 5.84 g/l
• See histogram, Fig 4.5 page 56, follows normal
  distribution
• Constructing Chart on Page

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Ch 4 A Continuous Skewed Right Distribution
Lognormal

• Example Serum Bilirubin, page 61

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Ch 4 Continuous Distribution Uniform

• Conditions for Uniform
• Visualization

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Ch 4 Discrete DistributionsBinomial
Distribution

• Binomial Experiment
• Binomial Random Variable
• Binomial Distribution Function

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Ch. 4 Binomial Example
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Ch. 4 Binomial Visualization

• Homework Complete the Binomial Visualization
  Activity found at
• http//www.mtsu.edu/smcdanie/BinomialWeb1/Pages1/
  Home.htm
• Be sure to submit the Pretest and the
  Lesson. You may want to print the results as a
  back-up.
• This is a Hand-in Homework worth 10 points.

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Ch 4 Discrete Distributions Poisson
Distribution

• Conditions for a Poisson Distribution
• Poisson Visualization
• http//kitchen.stat.vt.edu/sundar/java/applets/Po
  iDensityApplet.html

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Ch 4 Homework

• Exercises 1 8
• Check you answers in the Back of the book.
• Bring to class for next week the mean and
  standard deviation for heights of Americans of
  your gender.