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

STAT 6020 Introduction to Biostatistics Fall 2005 Dr. G. H. Rowell. Class 2. 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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STAT 6020 Introduction to Biostatistics Fall 2005 Dr. G. H. Rowell

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  1. STAT 6020Introduction to BiostatisticsFall 2005Dr. G. H. Rowell Class 2

  2. 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.

  3. Ch4: Theoretical Distributions, An Overview • Probability • Samples/Population • Distributions • Continuous • Normal, Lognormal, Uniform • Discrete • Binomial, Poisson

  4. 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

  5. Ch 4: Probability - Basics • S = Sample space • E = an event in the Sample Space • P(E) = Probability that event E occurs • 0<= P(E) <=1 • 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

  6. 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

  7. Ch 4: Sample & Populations • Population • Sample • Goal of Statistics

  8. 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

  9. 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

  10. 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

  11. Ch 4: Normal Distribution • Mound-shaped and symmetrical • Mean and standard deviation used to describe the distribution • “Empirical Rule”

  12. 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

  13. Statistical Software Online • StatCrunch • http://www.statcrunch.com/ • StatiCui • http://stat-www.berkeley.edu/~stark/Java/Html/ProbCalc.htm • VassarStats • http://faculty.vassar.edu/lowry/VassarStats.html

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

  15. 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?

  16. 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

  17. Ch 4: A Continuous Skewed Right Distribution: Lognormal • Example: Serum Bilirubin, page 61

  18. Ch 4: Continuous Distribution: Uniform • Conditions for Uniform • Visualization

  19. Ch 4: Discrete DistributionsBinomial Distribution • Binomial Experiment: • Binomial Random Variable: • Binomial Distribution Function:

  20. Ch. 4: Binomial Example

  21. 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.

  22. Ch 4: Discrete Distributions: Poisson Distribution • Conditions for a Poisson Distribution: • Poisson Visualization: http://kitchen.stat.vt.edu/~sundar/java/applets/PoiDensityApplet.html

  23. 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.

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