Biostatistics 621: Statistical Methods I Fall Semester 2007
Course Information Instructor: T. Mark Beasley, PhD Associate Professor of Biostatistics Office: Ryals Room 309E Phone: (205) 975-4957 Email: mbeasley@uab.edu When: Tuesday/Thursday 11:00 12:15 PM Where: Ryals Room 107 Office Hours: by appt Website: http://www.soph.uab.edu/statgenetics/people/mbeasley/courses/bst621.htm
Textbooks Available at HUC Bookstore Text: Biostatistics: A Foundation for Analysis in the Health Sciences by Wayne W. Daniel, published by John Wiley & Sons. ISBN 0-471-45654-3
Prerequisites This course is the first course in the basic applied statistical methods sequence for the first year graduate students in Biostatistics. It may be taken by other graduate students with a background in calculus and linear (matrix) algebra and those who will take more BST courses
Evaluation All material submitted for grading must be typed, no output will be accepted unless specifically requested Grading: Homework: 40% Midterm: 30% Final: 30% Five points will be deducted each day for late homework, unless there are extenuating circumstances.
Objectives BST 621 is an intermediate-level course in basic analysis methods, to introduce students to the elementary concepts, statistical models, and applications of: probability commonly used sampling distributions parametric and nonparametric one and two sample tests confidence intervals correlation and regression analysis of variance (ANOVA)
Introduction What are statistics? What is the practice of biostatistics? Statistics are just numbers The practice of statistics involves measuring variability of numbers to interpret results.
What can you do with statistics? Analyze data after an experiment has been carried out Make suggestions for how experiments can be designed Goals: Describe a population Estimate variation Prediction
Types of statistics Theoretical Statistics formulas and symbols; Derivation of Statistics; Mathematical Proof Applied Statistics Making sense out of data!
Useful Definitions Data: A collection of facts, not necessarily numeric, such as: Age Gender Hair color Weight Temperature
Measurement Scales Measurement is defined as the assignment of numbers to objects or events according to a defined set of rules. Measurement scales: various sets of rules by which numbers are assigned
Types of scales Nominal: Naming observations or classifying them into groups where one group is not better or higher than another. Ordinal: Groups or classes that can be ranked according to some criterion there is an order.
Scales (cont) Interval: Order measurements with a defined, measurable difference between groups. Ratio: A scale with a true zero, so that equal ratios and intervals can be defined.
Population: A well defined collection of objects, such as: students (at UAB, in engineering), paint colors (from 1 company, from multiple companies), etc.
Census vs. Sample If you collect information on all of the objects in a population, that is a census. If you collect information on some of the population, that is a sample.
Types of Sampling simple random sampling the most simple sampling procedure involves selecting a subset of n objects from the population, such that each object has an equal chance of being selected
Sampling (cont) stratified sampling sampling a subset of n from each gender, each age group, or each school class convenience sampling when it isn t possible to get a simple random sample, you sample what you have available to you
Variable: A measurement on an object that can change from one object to another. Usually denoted with lower case letters: x, y, z
Statistics Descriptive Statistics: summary statistics, such as N, µ, σ 2, σ. Often depicted using plots, such as: histograms, box and scatter plots. Inferential Statistics: using data to make generalizations to a population. Inference is a conclusion that patterns in the data are present in the population.
Parameters: unknown coefficients (variables) in the model, such as the mean or standard deviation. Unless you have a census (all subjects in a population), these are never truly known only estimated.
Statistical Significance: A precise statistical term that does not equate to practical significance. This usually means that the data provides evidence that the estimated parameter in not the null value (assumed value).
Model: an equation that predicts the response as a function of other variables.
What is a Hypothesis? The question you are trying to answer and the alternative (or opposite) of that question. In statistics, the null hypothesis is usually the current standard or what you are trying to disprove. The alternative is what you are trying to show by statistically rejecting the null. We will NEVER prove a hypothesis!
Case Study: CPR by Phone In an urban setting, ~ 6% of out-ofhospital cardiac arrests survive to hospital discharge. Survival can increase if a bystander witnesses the arrest and administers cardiopulmonary resuscitation but this happens < 50% of the time.
From the literature, when CPR is administered by a non-emt, survival probability can least 9%. In the Seattle area 1, emergency response personnel instructed bystanders in CPR over the phone. They found that 29 of 278 CPR patients survived to discharge from the hospital (> 10%)
Question? Does dispatcher-instructed bystander-administered CPR improve the chances of survival?
Answering the Question with Data 1. Begin by writing down what you understand 2. Outline the data and form clear and succinct questions pertaining to what the data may imply (or what you would like to show) 3. Form a scientific question to determine if the results are random 4. Compare the data from each side of the question and decide what to believe
Staticise the Steps Phase 1: State the Question Phase 2: Decide How to Answer the Question Phase 3: Answer the Question Phase 4: Communicate the Answer to the Question
Phase 1: State the Question 1. Evaluate and describe the data 2. Review the assumptions 3. State the question in the form of hypotheses
Phase 2: Decide How to Answer the Question 4. Decide on a summary number a statistic that reflects the question 5. How could random variation affect that statistic? 6. State a decision rule, using the statistic, to answer the question
Phase 3: Answer the Question 7. Calculate the statistic 8. Make a statistical decision 9. State the substantive conclusion
Phase 4: Communicate the Answer to the Question 10. Document your understanding with text, tables, or figures
How do we do this? We need to understand some basic principles about numbers, counting, and distributions We need to learn the best ways to display data and results in text, tables, and figures