Biostatistics

84 CHAPTER 3 SOME BASIC PROBABILITY CONCEPTS
3.6 SUMMARY
In this chapter some of the basic ideas and concepts of probability were presented. The
objective has been to provide enough of a “feel” for the subject so that the probabilistic
aspects of statistical inference can be more readily understood and appreciated when this
topic is presented later.
We defined probability as a number between 0 and 1 that measures the likelihood of
the occurrence of some event. We distinguished between subjective probability and
objective probability. Objective probability can be categorized further as classical or
relative frequency probability. After stating the three properties of probability, we defined
and illustrated the calculation of the following kinds of probabilities: marginal, joint, and
conditional. We also learned how to apply the addition and multiplication rules to find
certain probabilities. We learned the meaning of independent, mutually exclusive, and
complementary events. We learned the meaning of specificity, sensitivity, predictive value
positive, and predictive value negative as applied to a screening test or disease symptom.
Finally, we learned how to use Bayes’s theorem to calculate the probability that a subject
has a disease, given that the subject has a positive screening test result (or has the symptom
of interest).
SUMMARY OF FORMULAS FOR CHAPTER 3
Formula number Name Formula
3.2.1 Classical probability PE ð Þ ¼ m N
3.2.2 Relative frequency
probability
PE ð Þ ¼ m n
3.3.1–3.3.3 Properties of probability PE ð i Þ 0
PE ð 1 ÞþPE ð 2 ÞþþPE ð n Þ ¼ 1
PE i þ E j ¼ PEi ð ÞþPE j
3.4.1 Multiplication rule PðA \ BÞ ¼PðBÞPðA j BÞ ¼PðAÞPðB j AÞ
3.4.2 Conditional probability
PðA \ BÞ
PðA j BÞ ¼
PðBÞ
3.4.3 Addition rule PðA [ BÞ ¼PðAÞþPðBÞ PðA \ BÞ
3.4.4 Independent events PðA \ BÞ ¼PðAÞPðBÞ
3.4.5 Complementary events PðAÞ ¼1 PðAÞ
3.4.6 Marginal probability PðA i Þ¼ P PðA i \ B j Þ
Sensitivity of a screening test PðT j DÞ ¼ a
ða þ cÞ
Specificity of a screening test
PðT j DÞ ¼
d
ðb þ dÞ