Bayes Factor for a Bayesian One-Proportion Test

Description

Calculate the Bayes factor (BF10) for a single-proportion test, either against a point null or an interval null hypothesis.

Usage

BF10.bin.test(
  x,
  n,
  alpha,
  beta,
  h0,
  scale,
  prior_analysis,
  alternative,
  ROPE = NULL
)

Arguments

Value

An object of class "BFvalue_bin" containing:

• bf10: Bayes factor in favor of the alternative hypothesis.

• type: Test type ("one-proportion").

• x: Number of successes.

• n: Sample size.

• h0: Null proportion value.

• analysis_h1: List describing the analysis prior, containing prior (prior distribution), alpha (alpha parameter), beta (beta parameter), and scale (scale parameter).

• alternative: the direction of the alternative hypothesis.

• ROPE: interval null bounds (if specified).

• p.value: p-value.

Examples

BF10.bin.test(
 x = 42,
 n = 52,
 h0 = 0.5,
 prior_analysis = "beta",
 alternative = "greater",
 alpha = 1,
 beta = 1)

Bayes factor for a Bayesian correlation test

Description

Calculate the Bayes factor (BF10) for a correlation coefficient, either against a point null or an interval null hypothesis. Supports default beta ("d_beta"), stretched beta ("beta"), and normal-moment ("Moment") priors for the alternative hypothesis.

Usage

BF10.cor(
  r,
  n,
  k,
  alpha,
  beta,
  h0,
  alternative,
  scale,
  prior_analysis,
  ROPE = NULL
)

Arguments

Value

A list with class "BFvalue_r" containing:

• type: "correlation"

• bf10: Calculated Bayes factor BF10

• h0: Null value of the correlation

• r: Observed correlation coefficient

• n: Sample size

• analysis_h1: List with the analysis prior parameters: prior_analysis, k, alpha, beta, and scale.

• alternative: the direction of the alternative hypothesis

• ROPE: Interval bounds if specified

• p.value: Numeric, p.value.

Examples

BF10.cor(
  r = 0.3930924,
  n = 46,
  prior_analysis = "d_beta",
  k = 1,
  h0 = 0,
  alternative = "two.sided")

Bayes Factor for a Bayesian F-Test

Description

Computes the Bayes factor (BF10) for an F-test, comparing a full model to a reduced model under either an effect-size prior or a Moment prior. Optionally, an interval null hypothesis can be specified.

Usage

BF10.f.test(fval, df1, df2, dff, rscale, f_m, prior_analysis, ROPE = NULL)

Arguments

Value

A list of class "BFvalue_f" containing:

fval

Input F-value.

df1, df2

Degrees of freedom.

ROPE

Interval bound (if specified).

analysis_h1

List containing the analysis prior specification, including the prior distribution, the scale rscale, f f_m, and degrees of freedom dff.

bf10

The computed Bayes factor.

p.value

p-value.

Examples

BF10.f.test(
  fval = 4.5,
  df1 = 2,
  df2 = 12,
  dff = 12,
  rscale = 0.707,
  f_m = 0.1,
  prior_analysis = "effectsize"
)

Bayes factor for comparing two proportions

Description

Compute the Bayes factor (BF10) for a Bayesian test of two proportions.

Usage

BF10.props(a0, b0, a1, b1, a2, b2, n1, n2, x1, x2)

Arguments

Value

A list of class BFvalue_2p containing:

• type: the string "Two-proportions".

• analysis_h0: list with a and b for the null prior.

• analysis_h1_theta_1: list with a and b for group 1 prior under H1.

• analysis_h1_theta_2: list with a and b for group 2 prior under H1.

• bf10: the computed Bayes factor (BF10).

• n1, x1, n2, x2: the input sample sizes and observed successes.

• OddRatio: observed odd ratio.

• p.value: p.value.

Examples

BF10.props(
a0 = 1,
b0 = 1,
a1 = 1,
b1 = 1,
a2 = 1,
b2 = 1,
n1 = 493,
n2 = 488,
x1 = 155,
x2 = 150)

Bayes Factor for a One-Sample Bayesian t-Test

Description

Computes the Bayes factor (BF10) for a one-sample t-test, comparing an observed t-value against either a point null hypothesis or an interval null hypothesis.

Usage

BF10.ttest.OneSample(
  tval,
  df,
  prior_analysis,
  location,
  scale,
  dff,
  alternative,
  ROPE = NULL
)

Arguments

Value

A list of class BFvalue_t containing:

type

Character, indicating "One-sample t-test".

bf10

Numeric, the Bayes factor (BF10).

tval

Observed t-value.

df

Degrees of freedom.

analysis_h1

List with the analysis prior parameters: prior_analysis, location, scale, and optionally dff.

alternative

Character, the direction of the alternative hypothesis.

ROPE

Optional numeric vector of interval null bounds.

d

Numeric, observed Cohen's d.

p.value

Numeric, p.value.

Examples

BF10.ttest.OneSample(
tval = 2,
df = 50,
prior_analysis = "t-distribution",
location = 0,
scale = 0.707,
dff = 1,
alternative = "two.sided")

Bayes Factor for Two-Sample Bayesian t-Test

Description

Compute the Bayes factor (BF10) for a two-sample independent-samples t-test. Supports both point-null and interval-null hypotheses.

Usage

BF10.ttest.TwoSample(
  tval,
  N1,
  N2,
  prior_analysis,
  location,
  scale,
  dff,
  alternative,
  ROPE = NULL
)

Arguments

Value

A list of class BFvalue_t containing:

type

Character string describing the test type.

bf10

Computed Bayes factor BF10.

tval

Observed t-value.

df

Degrees of freedom (currently NA / not computed).

analysis_h1

List with the analysis prior parameters: prior_analysis, location, scale, and optionally dff.

alternative

Hypothesis tested ("two.sided", "greater", or "less").

ROPE

Interval bounds used, if any.

N1

Sample size of group 1 .

N2

Sample size of group 2 .

d

Numeric, observed Cohen's d.

p.value

Numeric, p.value.

Examples

BF10.ttest.TwoSample(
 tval = -1.148,
 N1 = 53,
 N2 = 48,
 prior_analysis = "t-distribution",
 location = 0,
 scale = 0.707,
 dff = 1,
 alternative = "two.sided",
 ROPE = c(-0.36,0.36))

Sample Size Determination for the Bayesian one-proportion test

Description

Perform sample size determination or the calculation of compelling and misleading evidence for a Bayesian test of a single proportion.

Usage

BFpower.bin(
  alternative,
  threshold,
  h0,
  true_rate,
  false_rate,
  prior_analysis,
  alpha,
  beta,
  scale,
  prior_design = NULL,
  alpha_d,
  beta_d,
  location_d,
  scale_d,
  N = NULL,
  ROPE = NULL,
  type_rate = "positive",
  plot_power = FALSE,
  plot_rel = FALSE
)

Arguments

Details

1. Sample size determination mode (when N = NULL):

If no sample size is provided, the function calculates the minimum sample size needed to achieve the desired configuration below. The user must provide:

• type_rate - either "positive" to control true/false positive rates or "negative" to control true/false negative rates.

• true_rate - the targeted true positive or true negative rate (between 0.6 and 0.999).

• false_rate - the acceptable false positive or false negative rate (between 0.001 and 0.1).

• threshold - the Bayes factor threshold for compelling evidence (must be > 1).

The function iteratively finds the smallest sample size for which the probability of obtaining compelling evidence meets or exceeds true_rate, while the probability of misleading evidence does not exceed false_rate.

2. Fixed-sample analysis mode (when N is supplied):

If a positive numeric sample size N is provided, the function computes the probabilities of obtaining compelling or misleading evidence for that fixed sample size. In this mode, type_rate, true_rate, and false_rate are ignored; only the Bayes factor threshold threshold is used.

Model specification:

The user must specify the analysis prior under the alternative hypothesis using prior_analysis:

• prior_analysis = "beta": requires alpha and beta parameters (shape parameters of the beta distribution).

• prior_analysis = "Moment": requires scale parameter (scale of the moment prior).

The design prior under the alternative hypothesis can optionally be specified using prior_design:

• "beta": requires alpha_d and beta_d.

• "Moment": requires scale_d.

• "Point": requires location_d, representing the true proportion under the alternative hypothesis.

If prior_design is NULL, no design prior is used.

interval null Hypothesis:

If ROPE is provided, the function evaluates the Bayes factor for an interval null. Otherwise, a point-null hypothesis is assumed.

Hypothesis:

The function supports one-sided ("greater" or "less") and two-sided ("two.sided") tests. Design prior and interval null bounds must be consistent with the directionality of the hypothesis.

Plotting:

If plot_power = TRUE, the function plots the probability of compelling evidence as a function of sample size. If plot_rel = TRUE, the relationship between the Bayes factor and the number of successes (proportion) is plotted.

Value

A list of class "BFpower_bin" containing:

• type: Test type ("One proportion").

• alternative: alternative hypothesis.

• h0: The proportion under the null hypothesis.

• analysis_h1: List describing the analysis prior, containing prior (prior distribution), alpha (alpha parameter), beta (beta parameter), and scale (scale parameter).

• design_h1: List describing the design prior (if provided), containing prior (prior distribution), alpha (alpha parameter), beta (beta parameter), and scale (scale parameter).

• results: Data frame of probabilities of compelling/misleading evidence and the required or supplied sample size.

• threshold: Compelling-evidence threshold.

• plot_power: Logical, whether power curves are plotted.

• plot_rel: Logical, whether the relationship between the BF and data is plotted.

If sample size determination fails, the function returns NaN and prints a message.

Examples

BFpower.bin(
  alternative = "greater",
  threshold = 3,
  true_rate = 0.8,
  false_rate = 0.05,
  h0 = 0.5,
  prior_analysis = "beta",
  alpha = 1,
  beta = 1,
  plot_rel = TRUE,
  plot_power = TRUE)

Sample Size Determination for the Bayesian correlation test

Description

Perform sample size determination or the probability of obtaining compelling or misleading evidence for a Bayesian correlation test. Can handle both point-null and interval-null hypothesis, and allows specifying analysis and design priors.

Usage

BFpower.cor(
  alternative,
  h0,
  ROPE = NULL,
  threshold,
  true_rate,
  false_rate,
  prior_analysis,
  k,
  alpha,
  beta,
  scale,
  prior_design = NULL,
  alpha_d,
  beta_d,
  location_d,
  k_d,
  scale_d,
  N = NULL,
  type_rate = "positive",
  plot_power = FALSE,
  plot_rel = FALSE
)

Arguments

Details

1. Sample size determination mode (when N = NULL):

If no sample size is provided, the function determines the minimum sample size required to meet the desired requirements. In this mode, the user must supply the following arguments:

• type_rate - either "positive" to control true/false positive rates, or "negative" to control true/false negative rates.

• true_rate - the targeted true positive or true negative rate (between 0.6 and 0.999).

• false_rate - the acceptable false positive or false negative rate (between 0.001 and 0.1).

• threshold - the Bayes factor threshold for compelling evidence (must be > 1).

The function iteratively finds the smallest sample size for which the probability of obtaining compelling evidence meets or exceeds true_rate, while the probability of misleading evidence does not exceed false_rate.

2. Fixed-sample analysis mode (when N is supplied):

If a positive numeric sample size N is provided, the function computes the probabilities of obtaining compelling or misleading evidence for that fixed sample size. In this mode, the arguments type_rate, true_rate, and false_rate are ignored; only the Bayes factor threshold threshold is used.

Hypothesis specification:

The alternative argument defines the direction of the alternative hypothesis : "two.sided" for two-sided, "greater" for right-sided, or "less" for left-sided tests. The optional ROPE argument specifies bounds for an interval null hypothesis. If ROPE = NULL, a point-null test is assumed.

Analysis Priors:

The analysis prior specifies the prior distribution of the correlation under the alternative hypothesis. Depending on prior_analysis, the user must supply:

• d_beta (default beta): k > 0.

• beta (stretched beta): alpha and beta > 0.

• Moment (normal-moment prior): scale > 0.

Design Priors (optional):

A design prior can be supplied to reflect uncertainty about the correlation during study planning. If provided, prior_design must be one of "d_beta", "beta", "Moment", or "Point", and the corresponding parameters must be supplied:

• d_beta: k_d > 0.

• beta: alpha_d and beta_d > 0.

• Moment: scale_d > 0.

• Point: location_d numeric scalar.

interval null Hypothesis:

If ROPE is provided, the function evaluates the Bayes factor for an interval null. Otherwise, a point-null hypothesis is assumed.

Plotting:

If plot_power = TRUE, the function plots the probability of compelling evidence as a function of sample size. If plot_rel = TRUE, the relationship between the BF and correlation is plotted.

Value

A list of class BFpower_r containing:

• type: Test type (always "Correlation").

• alternative: the direction of the alternative hypothesis.

• h0: the value of correlation under the null hypothesis.

• ROPE: Bounds for interval null (if used).

• analysis_h1: List with the analysis prior parameters: prior_analysis, k, alpha, beta, and scale.

• design_h1: List with the design prior parameters: prior_design, k, alpha, beta, scale, and location.

• results: Data frame with the probabilities of compelling/misleading evidence, and with the required sample size.

• threshold: Threshold of compelling evidence.

• plot_power: Logical, whether power curves are plotted.

• plot_rel: Logical, whether the relationship between the BF and the correlation is plotted.

Examples

BFpower.cor(
 alternative = "greater",
   h0 = 0,
   threshold = 3,
   true_rate = 0.8,
   false_rate = 0.05,
   prior_analysis = "d_beta",
   k = 1,
   prior_design = "Point",
   location_d = 0.3,
   plot_power = TRUE,
   plot_rel = TRUE
 )

Sample Size Determination for the Bayesian F-test

Description

This function performs sample size determination (when N = NULL) or calculates the probability of compelling/misleading evidence for a fixed sample size.

Usage

BFpower.f.test(
  threshold,
  true_rate,
  false_rate,
  p,
  k,
  prior_analysis,
  dff,
  rscale,
  f_m,
  prior_design = NULL,
  dff_d,
  rscale_d,
  f_m_d,
  N = NULL,
  type_rate = "positive",
  ROPE = NULL,
  plot_power = FALSE,
  plot_rel = FALSE
)

Arguments

Details

Computes required sample size or probabilities of compelling or misleading evidence for a fixed sample size.

1. Sample size determination mode (when N = NULL):

If no sample size is provided, the function calculates the minimum sample size to achieve the desired configuration below. The user must provide:

• type_rate - either "positive" to control true/false positive rates, or "negative" to control true/false negative rates.

• true_rate - the targeted true positive or true negative rate (between 0.6 and 0.999).

• false_rate - the acceptable false positive or false negative rate (between 0.001 and 0.1).

• threshold - the Bayes factor threshold for compelling evidence (must be > 1).

The function iteratively finds the smallest sample size for which the probability of obtaining compelling evidence meets or exceeds true_rate, while the probability of misleading evidence does not exceed false_rate.

2. Fixed-sample analysis mode (when N is supplied):

If a positive numeric sample size N is provided, the function computes the probabilities of obtaining compelling or misleading evidence for that fixed sample size. In this mode, the arguments type_rate, true_rate, and false_rate are ignored; only the Bayes factor threshold threshold is used.

Model specification:

The function requires the user to specify the full model (k predictors) and the reduced model (p predictors, k > p), and the analysis prior under the alternative hypothesis. Depending on the chosen prior_analysis, different arguments are required:

• prior_analysis = "effectsize": requires rscale (scale parameter) and f_m (Cohen's f effect-size), and dff (degrees of freedom).

• prior_analysis = "Moment": requires f_m (Cohen's f effect-size) and dff (degrees of freedom, must be >= 3); rscale is not used.

The design prior under the alternative hypothesis can optionally be specified using prior_design, which can be:

• "effectsize": requires rscale_d, f_m_d, and dff_d.

• "Moment": requires f_m_d and dff_d (>=3); rscale_d is not used.

• "Point": requires f_m_d only; rscale_d and dff_d are not used.

interval null Hypothesis:

If ROPE is provided, the function evaluates the Bayes factor for an interval null. Otherwise, a point-null hypothesis is assumed.

Plotting:

If plot_power = TRUE, the function plots the probability of compelling evidence as a function of sample size. If plot_rel = TRUE, the relationship between the Bayes factor and Cohen's f is plotted.

Value

A list of class BFpower_f containing:

type

Test type (always "Regression/ANOVA").

k, p

Number of predictors in the full and reduced models.

ROPE

Bounds for interval null (if used).

analysis_h1

List containing the analysis prior specification, including the prior distribution, the scale rscale, f f_m, and degrees of freedom dff.

design_h1

List containing the design prior specification, including the prior distribution, the scale rscale, f f_m, and degrees of freedom dff (or NULL if not specified).

results

Data frame of probabilities of compelling/misleading evidence and the required or supplied sample size.

threshold

Threshold of compelling evidence.

plot_power

Logical; whether power curves are plotted.

plot_rel

Logical; whether the relationship between the Bayes factor and data is plotted.

If sample size determination fails, the function returns NaN and prints a message.

Examples

BFpower.f.test(
 threshold = 3,
 true_rate = 0.8,
 false_rate = 0.05,
 p = 3,
 k = 4,
 prior_analysis = "effectsize",
 dff = 3,
 rscale = 0.18,
 f_m = 0.1,
 prior_design = "Point",
 f_m_d = 0.1,
 plot_power = TRUE,
 plot_rel = TRUE)

Sample Size Determination for the Bayesian test of two proportions

Description

Perform sample size determination or calculate probabilities of compelling and misleading evidence for a Bayesian comparison of two proportions.

Usage

BFpower.props(
  threshold,
  true_rate,
  a0,
  b0,
  a1,
  b1,
  a2,
  b2,
  prior_design_1 = "same",
  a1d,
  b1d,
  dp1,
  prior_design_2 = "same",
  a2d,
  b2d,
  dp2,
  n1 = NULL,
  n2 = NULL,
  type_rate = "positive",
  plot_power = FALSE,
  plot_rel = FALSE
)

Arguments

Details

1. Sample size determination mode (when n1 = NULL and n2 = NULL):

If no sample sizes are provided for the two groups, the function calculates the minimum sample sizes needed to achieve the desired configuration. The user must provide:

• type_rate - either "positive" to control true/false positive rates or "negative" to control true/false negative rates.

• true_rate - the targeted true positive or true negative rate (between 0.6 and 0.999).

• threshold - the Bayes factor threshold for compelling evidence (must be > 1).

The function iteratively finds the smallest sample sizes for which the probability of obtaining compelling evidence meets or exceeds true_rate.

2. Fixed-sample analysis mode (when n1 and n2 are supplied):

If positive numeric sample sizes n1 and n2 are provided, the function computes the probabilities of obtaining compelling or misleading evidence for these fixed sample sizes. In this mode, type_rate and true_rate are ignored; only the Bayes factor threshold threshold is used.

Model specification:

The user must specify the analysis priors under the null and alternative hypotheses using Beta parameters:

• a0, b0 - Beta parameters for the null hypothesis prior.

• a1, b1 - Beta parameters for the analysis prior of group 1 under the alternative hypothesis.

• a2, b2 - Beta parameters for the analysis prior of group 2 under the alternative hypothesis.

Design priors for the alternative hypothesis can optionally be specified:

• prior_design_1, a1d, b1d, dp1 - design prior for group 1 ("same" uses the analysis prior, "beta" requires Beta parameters, "Point" uses a fixed proportion).

• prior_design_2, a2d, b2d, dp2 - design prior for group 2.

Plotting:

If plot_power = TRUE, a power curve is plotted showing the probability of compelling evidence as a function of sample sizes. If plot_rel = TRUE, a grid of Bayes factors across possible outcomes is plotted.

Value

An object of class BFpower_2p (a list) containing:

type

Character, always "Two-proportions".

analysis_h0

List of analysis prior parameters under the null, containing a and b.

analysis_h1_theta_1

List of analysis prior parameters for group 1 under the alternative, containing a and b.

analysis_h1_theta_2

List of analysis prior parameters for group 2 under the alternative, containing a and b.

design_h1_theta_1

List of design prior parameters for group 1 under the alternative, containing prior, a, b, and p.

design_h1_theta_2

List of design prior parameters for group 2 under the alternative, containing prior, a, b, and p.

results

Data frame of probabilities of compelling and misleading evidence.

grid

Grid used for computation.

threshold

Threshold of compelling evidence.

mode_bf

Character string specifying the mode (sample size determination or power calculation).

plot_power

Logical; whether the power curve is plotted.

plot_rel

Logical; whether the relationship between the Bayes factor and observed proportion differences is plotted.

Examples

BFpower.props(
threshold = 3,
true_rate = 0.8,
a0 = 1,
b0 = 1,
a1 = 156,
b1 = 339,
a2 = 151,
b2 = 339,
plot_power = TRUE,
plot_rel = TRUE)

Sample Size Determination for the One-Sample Bayesian t-Test

Description

Perform sample size determination or calculate the probability of obtaining compelling or misleading evidence for a one-sample Bayesian t-test. Can handle both point-null and interval-null hypothesis, and allows specifying analysis and design priors.

Usage

BFpower.ttest.OneSample(
  alternative,
  ROPE = NULL,
  prior_analysis,
  location,
  scale,
  dff,
  prior_design = NULL,
  location_d,
  scale_d,
  dff_d,
  N = NULL,
  type_rate = "positive",
  true_rate,
  false_rate,
  threshold,
  plot_power = FALSE,
  plot_rel = FALSE
)

Arguments

Details

1. Sample size determination mode (when N = NULL):

If no sample size is provided, the function determines the minimum sample size. In this mode, the user must supply the following arguments:

• type_rate - either "positive" to control true/false positive rates, or "negative" to control true/false negative rates.

• true_rate - the targeted true positive or true negative rate (between 0.6 and 0.999).

• false_rate - the acceptable false positive or false negative rate (between 0.001 and 0.1).

• threshold - the Bayes factor threshold for compelling evidence (must be > 1).

The function iteratively finds the smallest sample size for which the probability of obtaining compelling evidence meets or exceeds true_rate, while the probability of misleading evidence does not exceed false_rate.

2. Fixed-sample analysis mode (when N is supplied):

If a positive numeric sample size N is provided, the function computes the probabilities of obtaining compelling or misleading evidence for that fixed sample size. In this mode, the arguments type_rate, true_rate, and false_rate are ignored; only the Bayes factor threshold threshold is used.

Analysis Priors:

The analysis prior specifies the prior distribution of the effect under the alternative hypothesis. The user must provide:

• prior_analysis - the type of prior: "Normal", "Moment" (normal-moment prior), or "t-distribution".

• location - the mean or location of the prior.

• scale - the standard deviation or scale (must be positive).

• dff - degrees of freedom (required if prior_analysis = "t-distribution").

Design Priors (optional):

A design prior can be supplied to reflect uncertainty about the effect size during study planning. If provided, the following must be supplied:

• prior_design - the type of design prior: "Normal", "Moment", "t-distribution", or "Point".

• location_d - the location of the design prior.

• scale_d - the scale parameter (positive for all models except "Point").

• dff_d - degrees of freedom for "t-distribution" design priors.

interval null Hypothesis:

The argument ROPE specifies the bounds of an interval null hypothesis. If ROPE is provided, the function evaluates the Bayes factor for an interval null hypothesis. For a point-null hypothesis, ROPE should be left as NULL.

Plotting:

If plot_power = TRUE, the function plots the probability of compelling evidence as a function of sample size. If plot_rel = TRUE, the relationship betwwen the BF and data is plotted.

Value

An object of class BFpower_t (a list) containing:

type

Character, always "One-sample t-test".

alternative

Character, the direction of the alternative hypothesis.

ROPE

Optional numeric vector for interval null bounds.

analysis_h1

List with the analysis prior parameters: prior_analysis, location, scale, and optionally dff.

design_h1

List with the design prior parameters: prior_design, location, scale, and optionally dff (or NULL if not provided).

results

Data frame of probabilities: compelling/misleading evidence, or NaN if calculation fails.

threshold

Numeric, threshold of compelling evidence.

plot_power

Logical, whether to plot the power curve.

plot_rel

Logical, whether the relationship between the BF and t-value is plotted.

Examples

BFpower.ttest.OneSample(
 alternative = "two.sided",
 threshold = 3,
 true_rate = 0.8,
 false_rate = 0.05,
 prior_analysis = "t-distribution",
 location = 0,
 scale = 0.707,
 dff = 1
)

Sample Size Determination for the Two-Sample Bayesian t-Test

Description

Perform sample size determination or calculate the probabilities of obtaining compelling or misleading evidence for a two-sample Bayesian t-test. Supports point-null and interval-null hypotheses, and allows specifying analysis and design priors.

Usage

BFpower.ttest.TwoSample(
  alternative,
  ROPE = NULL,
  threshold,
  true_rate,
  false_rate,
  prior_analysis,
  location,
  scale,
  dff,
  prior_design = NULL,
  location_d,
  scale_d,
  dff_d,
  N1 = NULL,
  N2 = NULL,
  r = NULL,
  type_rate = "positive",
  plot_power = FALSE,
  plot_rel = FALSE
)

Arguments

Details

1. Sample size determination mode (when N1 = NULL and N2 = NULL, but r is provided):

If no sample sizes are provided, the function calculates the minimum required sample sizes for both groups. In this mode, the user must supply:

• type_rate - either "positive" to control true/false positive rates, or "negative" to control true/false negative rates.

• true_rate - the targeted true positive or true negative rate (between 0.6 and 0.999).

• false_rate - the acceptable false positive or false negative rate (between 0.001 and 0.1).

• threshold - the Bayes factor threshold for compelling evidence (must be > 1).

• r - the allocation ratio of group 2 to group 1 sample sizes (N2/N1).

The function iteratively finds the smallest sample sizes N1 and N2 = r * N1 for which the probability of obtaining compelling evidence meets or exceeds true_rate, while the probability of misleading evidence does not exceed false_rate.

2. Fixed-sample analysis mode (when N1 and N2 are supplied):

If positive numeric sample sizes N1 and N2 are provided, the function computes the probabilities of obtaining compelling or misleading evidence for those fixed sample sizes. In this mode, the arguments type_rate, true_rate, and false_rate are ignored; only the Bayes factor threshold threshold is used.

Analysis Priors:

The analysis prior specifies the prior distribution of the effect under the alternative hypothesis. The user must provide:

• prior_analysis - the type of prior: "Normal", "Moment" (normal-moment prior), or "t-distribution".

• location - the mean or location of the prior.

• scale - the standard deviation or scale (must be positive).

• dff - degrees of freedom (required if prior_analysis = "t-distribution").

Design Priors (optional):

A design prior can be supplied to reflect uncertainty about the effect size during study planning. If provided, the following must be supplied:

• prior_design - the type of design prior: "Normal", "Moment", "t-distribution", or "Point".

• location_d - the location of the design prior.

• scale_d - the scale parameter (positive for all models except "Point").

• dff_d - degrees of freedom for "t-distribution" design priors.

interval null Hypothesis:

The argument ROPE specifies the bounds of an interval null hypothesis. If ROPE is provided, the function evaluates the Bayes factor for an interval null hypothesis. For a point-null hypothesis, ROPE should be left as NULL.

Plotting:

If plot_power = TRUE, the function plots the probability of compelling evidence as a function of the sample sizes. If plot_rel = TRUE, the relationship between BF and data is plotted.

Value

An object of class BFpower_t containing:

type

Character string describing the test type.

alternative

alternative hypothesis ("two.sided", "greater", or "less").

ROPE

Interval bounds under the null used, if any.

analysis_h1

List with the analysis prior parameters: prior_analysis, location, scale, and optionally dff.

design_h1

List with the design prior parameters: prior_design, location, scale, and optionally dff (or NULL if not provided).

results

Data frame with probabilities of compelling/misleading evidence.

threshold

Threshold of compelling evidence.

plot_power

Logical flag for plotting power.

plot_rel

Logical flag for plotting the relationship between BF and t-value.

Examples

BFpower.ttest.TwoSample(
 alternative = "two.sided",
 ROPE = c(-0.36, 0.36),
 threshold = 3,
 true_rate = 0.8,
 false_rate = 0.05,
 prior_analysis = "Normal",
 location = -0.23,
 scale = 0.2,
 dff = 1,
 type_rate = "negative",
 r = 1)

Launch the BayesPower Shiny Application

Description

This function starts the interactive Shiny application for Bayesian power analysis using Bayes factors. The app provides a graphical user interface built with shiny.

Usage

BayesPower_BayesFactor()

Details

The application includes both the UI and server components, which are defined internally in the package. When run, a browser window or RStudio viewer pane will open to display the interface.

Value

No return value, called for its side effects.

Examples

if (interactive()) {
  # Launch the Shiny application
  BayesPower_BayesFactor()
}