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Presentation at a Course on Principles of Epidemiology Health Research Faculty of Medicine, King Fahad Medical City October 11-12, 2017 by Professor Omar Hasan Kasule Sr. MB ChB (MUK). MPH (Harvard), DrPH (Harvard) Chairman of the Institutional Review Board / Research Ethics Committee at King Fahad Medical City, Riyadh.
LECTURE 3: THE PROBABILITY THEORY AS A BASIS FOR
CONTINUOUS RANDOM VARIABLES
QUANTITATIVE (NUMERICAL) CONTINUOUS RANDOM VARIABLES:
- The continuous random variables can be natural such as the normal, the exponential, and the uniform, or artificial such as chi-square, t, and F variables.
- The normal represents the result of a measurement on the continuous numerical scale such as height and weight.
- The exponential is the time until the first occurrence of the event of interest.
- The uniform represents the results of a measurement and takes on the same value at repeated trials.
THE NORMAL DISTRIBUTION
THE EXPONENTIAL DISTRIBUTION
THE UNIFORM DISTRIBUTION
THE CHI-SQUARE DISTRIBUTION
THE STUDENT t DISTRIBUTION
THE F DISTRIBUTION
THE CONTINUOUS R.V: THE INTERVAL OR THE RATIO SCALES:
- Only 2 measurements are made on the interval scale, the calendar, and the thermometer. The rest of the measurements are on the ratio scale.
- The interval scale has the following properties: the difference between 2 readings has a meaning, the magnitude of the difference between 2 readings is the same at all parts of the scale, the ratio of 2 readings has no meaning, zero is arbitrary with no biological meaning, and both negative and positive values are allowed.
- The ratio scale zero has the following properties: zero has a biological significance, values can only be positive; the difference between 2 readings has a meaning, the ratio of 2 readings has a meaning and can be interpreted, and intervals between 2 readings have the same meaning at different parts of the scale.