Statistical Independence
Definition
Events A and B are independent if P(A|B) = P(A), equivalently P(A and B) = P(A) x P(B). Knowing B occurred gives no information about whether A occurred.
- Condition
- P(A given B) equals P(A)
- Equivalent form
- P(A and B) equals P(A) times P(B)
- Meaning
- Knowing B gives no information about A
Common questions
Why does assuming independence between two pieces of forensic evidence matter?+
If two findings are treated as independent when they actually share a common cause, multiplying their individual probabilities overstates the combined strength of the evidence, which is a documented source of erroneous likelihood-ratio calculations in forensic statistics.
How can independence between two events be tested rather than assumed?+
An analyst can compare the observed joint probability against the product of the individual probabilities using the available data; a substantial mismatch indicates the events are not independent and should not be combined by simple multiplication.
Related terms
- Conditional Probability
- The probability of event A given that event B has already occurred, written P(A|B). Conditional probability is the basis of the multiplication...
- Hardy-Weinberg Equilibrium
- A condition in a population where genotype frequencies at a single locus conform to expectations derived from allele frequencies alone, assuming random...
- Linkage Disequilibrium
- The non-random association of alleles at different loci within a population. Certain HLA allele combinations (e.g., HLA-A1 with HLA-B8 with HLA-DR3) occur...
- Multiplication Rule
- For any two events: P(A and B) = P(A) x P(B|A). When A and B are independent, this simplifies to P(A) x...
- Positive Dependence
- Events are positively dependent when the occurrence of one increases the probability of the other: P(A|B) > P(A). In this case P(A...