proportion (version 2.0.0)

hypotestBAF6x: Bayesain Hypothesis testing given x: Hypothesis 6: Theta < Theta1 Vs Theta > Theta2

Description

Bayesain Hypothesis testing given x: Hypothesis 6: Theta < Theta1 Vs Theta > Theta2

Usage

hypotestBAF6x(x, n, th1, a1, b1, th2, a2, b2)

Arguments

x

- Number of success

n

- Number of trials from data

th1

- Hypothetical parameter for H1

a1

- Priors for hypothesis H1

b1

- Priors for hypothesis H1

th2

- Hypothetical parameter for H2

a2

- Priors for hypothesis H2

b2

- Priors for hypothesis H2

Value

A dataframe with

x

Number of successes

BaFa01

Bayesian Factor

Details

Computes Bayes factor under Beta-Binomial model for the model: \(p < p1\) Vs \(p > p2\) from the given number of trials n and and for given number of successes \(x = 0, 1, 2......n \) We use the following guideline for reporting the results:

• 1/3 <= BaFa01 < 1: Evidence against H0 is not worth more than a bare mention.
• 1/20 <= BaFa01 < 1/3: Evidence against H0 is positive.
• 1/150 <= BaFa01 < 1/20: Evidence against H0 is strong.
• BaFa10 < 1/150: Evidence against H0 is very strong.
• 1 <= BaFa01 < 3: Evidence against H1 is not worth more than a bare mention.
• 3 <= BaFa01 < 20: Evidence against H1 is positive.
• 20 <= BaFa01 < 150: Evidence against H1 is strong.
• 150 <= BaFa01: Evidence against H1 is very strong.

References

[1] 2006 Ghosh M, Delampady M and Samanta T. An introduction to Bayesian analysis: Theory and Methods. Springer, New York

[2] 2014 Sakthivel S, Subbiah M and Ramakrishnan R Default prior approach for Bayesian testing of hypotheses involving single binomial proportion International Journal of Statistics and Analysis, 4 (2), 139 - 153

See Also

Other Hypothesis testing: hypotestBAF1x, hypotestBAF1, hypotestBAF2x, hypotestBAF2, hypotestBAF3x, hypotestBAF3, hypotestBAF4x, hypotestBAF4, hypotestBAF5x, hypotestBAF5, hypotestBAF6

Examples

x=682; n=925; th1=0.5; a1=1; b1=1; th2=0.9; a2=0.5; b2=0.5
hypotestBAF6x(x,n,th1,a1,b1,th2,a2,b2)