1. 1 STAT 6020 Introduction to Biostatistics Fall 2005 Dr. G. H. Rowell Class 1b

2. 2 Ch4: Theoretical Distributions, An Overview  Probability  Samples/Population  Distributions Continuous  Normal, Lognormal, Uniform Discrete  Binomial, Poisson

3. 3 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

4. 4 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

5. 5 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

6. 6 Ch 4: Sample & Populations  Population  Sample  Goal of Statistics

7. 7 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

8. 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. 9 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

10. 10 Ch 4: Normal Distribution  Mound-shaped and symmetrical  Mean and standard deviation used to describe the distribution  “Empirical Rule”

11. 11 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

12. 12 Statistical Software Online  StatCrunch http://www.statcrunch.com/  StatiCui http://stat- www.berkeley.edu/~stark/Java/Html/ProbCalc.htm http://stat- www.berkeley.edu/~stark/Java/Html/ProbCalc.htm  VassarStats http://faculty.vassar.edu/lowry/VassarStats.html

13. 13 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?