1 / 23

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.

sydnee
Télécharger la présentation

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

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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.

More Related