bfactor_interpret {pcal}

Interpretation of Bayes factors

Description

Quantify the strength of the evidence provided by the data to a model/hypothesis according to the Bayes factor interpretation scale suggested by Jeffreys (1961).

Usage

bfactor_interpret(bf)

Arguments

bf

A numeric vector of non-negative values.

Details

Bayes factors are a summary of the evidence provided by the data to a model/hypothesis. Jeffreys (1961) suggested the interpretation of Bayes factors in half-units on the base 10 logarithmic scale, as indicated in the following table:

log10(Bayes factor)	Bayes factor	Evidence
[-Inf, 0[	[0, 1[	Negative
[0, 0.5[	[1, 3.2[	Weak
[0.5, 1[	[3.2, 10[	Substantial
[1, 1.5[	[10, 32[	Strong
[1.5, 2[	[32, 100[	Very Strong
[2, +Inf[	[100, +Inf[	Decisive

bfactor_interpret takes Bayes factors as input and returns the strength of the evidence in favor of the model/hypothesis in the numerator of the Bayes factors (usually the null hypothesis) according to the aforementioned table.

When comparing results with those from standard likelihood ratio tests, it is convenient to put the null hypothesis in the denominator of the Bayes factor so that bfactor_interpret returns the strength of the evidence against the null hypothesis. If bf was obtained with the null hypothesis on the numerator, one can use bfactor_interpret(1/bf) to obtain the strength of the evidence against the null hypothesis.

Value

Returns a character vector with the same length as bf.

References

Jeffreys H (1961). Theory of probability, Oxford Classic Texts In The Physical Sciences, 3 edition. Oxford University Press.

See Also

• bfactor_interpret_kr for an alternative interpretation scale.

• bfactor_log_interpret and bfactor_log_interpret_kr for the interpretation of the logarithms of Bayes factors.

• bfactor_to_prob to turn Bayes factors into posterior probabilities.

• bcal for a p-value calibration that returns lower bounds on Bayes factors in favor of point null hypotheses.

Examples

# Interpretation of one Bayes factor
bfactor_interpret(1.5)

# Interpretation of many Bayes factors
bfactor_interpret(c(0.1, 1.2, 3.5, 13.9, 150))

# Application: chi-squared goodness-of-fit test.
# Strength of the evidence provided by the lower
# bound on the Bayes factor in favor of the null hypothesis:
x <- matrix(c(12, 15, 14, 15), ncol = 2)
bfactor_interpret(bcal(chisq.test(x)[["p.value"]]))