Preparing for the First Hourly Summer Term

Summer Term Course Structure Probability and Design Issues  Descriptive Statistics, Confidence Intervals and Hypothesis Tests

Course Objectives: First Half, Summer Term Probability I.1. Conduct simple experiments in sampling and compute sample frequencies (counts and proportions). I.2. Understand the principles of frequentist probability theory. I.3. Understand the relationship between sample proportions and probabilities. I.4. Compute probabilities using the Additive, Multiplicative and Complementary rules. I.5. Understand the concept of the random variable, and how probabilities are computed for random variables. I.6. Understand the implications of observing events with small probabilities (rare events). I.7. Compute and interpret conditional probabilities. Design Issues I.8. Sketch clinical trials. I.9. Spot faults in sketches of clinical trials. I.10. Spot faults in sketches of random sample surveys.

Problem Tasks: I Bowls, Urns, Dice Estimate Probabilities Using Samples from Bowls, Urns, Dice Compute Probabilities from Probability Model for Bowls, Urns, Dice Compare Probabilities and Estimates from Bowls, Urns, Dice Random Variables Compute the Values of Random Variables Using the Definition Compute Probabilities of Outcomes Defined by Random Variables Probabilities Compute Probabilities from Scratch Using a Probability Model Compute Probabilities Using Computation Rules Interpret Probabilities Using Long Run Argument Compute Conditional Probabilities Using the Definition Random Samples and Probabilities Estimate Probabilities from Samples Compare Samples and Probability Models Evaluate the Rare Event Assumption Using Samples Six (6) cases will be presented on the First Hourly. They will be representative of cases worked in class and of cases from sample tests.

Problem Tasks: II Clinical Trial Methodology Sketch a clinical trial Spot faults in clinical trial sketches of designs Random Sample Survey Methodology Spot faults in clinical trial sketches of designs Six (6) cases will be presented on the First Hourly. They will be representative of cases worked in class and of cases from sample tests.

Will the problems count equally? Yes. There will be six (6) cases, at 25 points Maximum per case, for a total of 150 points maximum. The raw test score will be scaled to 100 percent Will there be partial credit? Yes, but be aware that full work and detail is required for full credit. Your work and details are the basis for scoring each case solution. What about the testing protocol and tool-sheet? The hourly is not a memory test. Hence, you are permitted the use of one (1) 8.5” by 11” sheet of paper. Put on this sheet whatever it is that you deem useful. You alone will use this sheet. Sign and abide by the test protocol that will accompany the hourly. What about the calculator? You must provide your own working calculator, and you must be able to use this calculator. Do not share calculators. Your calculator is your individual responsibility.

The Essential Randomized, Controlled, Blinded Clinical Trial The clinical trial as discussed in this course is a very simplified version of those designed and executed in the Real World. The method essentially requires the following: A Well Defined Disease or Condition of Interest An Appropriate Population at Risk A Set of Well Defined Treatments A Set of Well Defined End Points or Outcomes A Random Method for Assigning Subjects to Treatments A Method of Obtaining Informed Consent from Potential Subjects Implementation of a Double Blind We briefly sketched a variety of these simplified clinical trials. Examples of these are available online.

A few notes of clarification. The essential purpose of randomization is to assign subjects to treatments in such a way that the only systematic differences between treatment groups are random variations and the treatments themselves. Blinding of both subjects and clinic workers is employed to avoid differences in recorded responses due to either placebo effect or observer bias. Blinding also helps to avoid excessive subject loss when a placebo is employed. A placebo is a medically inert mock treatment, intended to resemble as closely as possible the active treatments in a study. Broad classes of study end points and outcomes include treatment effect in modifying disease or condition, survival/mortality, quality of life, side effects and adverse events.

The Essential Random Sample Survey The random sample survey was discussed in our class as a method for scientifically obtaining information in a representative manner from a population of interest. We presented some general principles on the design an execution of credible scientific polling. Our simplified design for a random sample survey included: A Well Defined Population of Interest A Sampling Frame Based on the Population of Interest A Random Sample Obtained from the Sampling Frame A Reasonable Set of Research Objectives A Well Defined Survey Instrument Based on the Research Objectives A Reasonable Protocol for Administering the Survey Instrument

Design Fault Spot In this case type, brief descriptions of clinical trials or sample surveys are presented. Briefly identify problems with these designs.

Notes for Study / Preparation Study for one case type at a time. Take notes as you go along. When you have finished study for all case types, compile your notes into a single tool sheet. Customize this tool sheet for your own personal use.

Some Advice Check your calculator’s health before the exam. Bring pens, and work the test in ink – or bring pre- sharpened pencils. Be sure to study your weakest areas. Study more recent material earlier, then work backwards. Tailor your tool-sheets to your individual needs. Recall that discussion and interpretation typically comprise about 40% of earned credit on individual cases. Be sure to use the methods and approaches specified in the cases.