221014P - COUNTING AND MEASURING IN SCIENTIFIC RESEARCH

Presentation prepared by Professor Omar Hasan Kasule Sr. MB ChB (MUK), MPH (Harvard), DrPH (Harvard) Consultant on Research at Almaarefa University

DISCRETE and CONTINUOUS VARIABLES:

The preponderant majority of scientific research is quantitative being based on counting and measuring both of which provide quantitative variables used in the statistical research. Discrete/categorical variables are obtained from counting for example the pulse rate and the number of children. Continuous variables are obtained from measuring for example blood pressure and weight. It is of utmost importance that researchers understand the difference between discrete and continuous variables to be able to use the correct statistical test. The most popular statistical tests are the test and the chi-square test. The t-test is supposed to be used for continuous data but is often misused for discrete data. The chi-square test is supposed to be used for discrete data but is often misused for continuous data with disastrous results.

 

COUNTING DISCRETE VARIABLES:

Different ways of COUNTING successes in trials (events) give rise to different discrete/categorical variables each suitable for a specific research design and therefore research statistical analysis. The Bernoulli variable is the number of successes in a single unrepeated trial with only 2 outcomes, success (S) or failure (F). The binomial variable is the number of successes in more than 2 consecutive trials each with a dichotomous outcome either S or F. The multinomial variable is the number of successes in several independent trials with each trial having more than 2 outcomes S, F, and U(unknown). The negative binomial variable is the total number of repeated trials until a given number of successes is achieved. The Poisson variable is the number of events for which no upper limit can be assigned a priori. The geometric is the number of trials until the first success is achieved. The hypergeometric variable is the number selected from a sub-sample of a larger sample for example selecting males from a sample of n persons from a population N.

MEASURING CONTINUOUS VARIABLES:

The commonest continuous random variables that are measured are normal and exponential. The normal variable represents the result of a measurement on a continuous numerical scale such as height and weight. Most measurements are around the center or mean and few at the extremes. The exponential variable is the time until the first occurrence of the event of interest for example the time it takes for a drug to disappear from the blood. The exponential decreases with time.