Preparing for the First HourlySummer 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, DiceEstimate Probabilities Using Samples from Bowls, Urns, Dice

Compute Probabilities from Probability Model for Bowls, Urns, DiceCompare Probabilities and Estimates from Bowls, Urns, Dice

 Random Variables

Compute the Values of Random Variables Using the DefinitionCompute Probabilities of Outcomes Defined by Random Variables

 Probabilities

Compute Probabilities from Scratch Using a Probability ModelCompute Probabilities Using Computation Rules

Interpret Probabilities Using Long Run ArgumentCompute Conditional Probabilities Using the Definition

 Random Samples and ProbabilitiesEstimate Probabilities from Samples

Compare Samples and Probability ModelsEvaluate 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 MethodologySketch 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 InterestAn Appropriate Population at RiskA Set of Well Defined Treatments

A Set of Well Defined End Points or OutcomesA Random Method for Assigning Subjects to Treatments

A Method of Obtaining Informed Consent from Potential SubjectsImplementation 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.