Independent events

Consider two events, event A followed by event B

if A and B are independent events (i.e. Likelihood of B is unaffected by the occurrence or non-occurrence of event A, and vice versa)

then Prob (A and B) = Prob (A) x Prob (B), if A and B are independent

Bayesian probability

A mathematical rule for relating conditional probabilities.
Bayes’ rule allows us to derive Prob (B given A has occurred) using the Probabilities of B, A and Prob (A given B has occurred).

Consider two events, event A followed by event B, where the probability of event B is conditional upon the occurrence of event A.

then Prob (A and B) = Prob (A) x Prob (B given that A has occurred)
Prob (A and B) = Prob (A) x Prob (B|A)
Prob (B and A) = Prob (B) x Prob (A|B)
But, Prob (A and B)= Prob (B and A),
Prob (A) x Prob (B|A) = Prob (B) x Prob (A|B)

Prob (B|A) = Prob (B) x Prob (A|B) / Prob (A)

For example,
5% of girls are anaemia, P(A)=0.05
10% of girls are malnourished, P(M)= 0.10
50% of anaemic girls are also malnourished, P (M|A)=0.50
What is the percentage of malnourished girls that are also anaemic, P (A|M)
P (A|M) = P(A) x P (M|A)/P(M) = 0.05 x 0.50/0.10 = 0.25
Thus, 25% of malnourished girls are also anaemic.

Comparison of parametric data

T-tests

Analysis of variance

Multiple regression

Comparison of non-parametric data

chi squared

Mann-Whitney U