safeguard.d: Safeguard power analysis for Cohen's d effect size and for...

In GiulioCostantini/safeguardpower: Safeguard Power Analysis

Description

Perform a safeguard power analysis starting from a Cohen's d effect size (assuming a two samples t-test) or from a Pearson correlation coefficient. It is also possible to perform the analysis by starting from the data, if these are available.

Usage

safeguard.d(d, n.1, n.2, sig.level = .05, power = .8, conf = .80)
safeguard.d2(m.1, m.2, sd.1, sd.2, n.1, n.2, sig.level = .05, power = .8, conf = .80)
safeguard.d.data(x, y, sig.level = .05, power = .8, conf = .80)
safeguard.r(r, n, sig.level = .05, power = .8, conf = .80)
safeguard.r.data(x, y, sig.level = .05, power = .8, conf = .80)

Arguments

x	A vector of data
y	A vector of data
d	Standardized mean difference (Cohen's d)
m.1	The mean value of the group 1
m.2	The mean value of the group 2
sd.1	The standard deviation of the group 1
sd.2	The standard deviation of the group 2
r	Pearson's correlation coefficient
n	Sample size of the original study
n.1	Sample size for group 1 of the original study
n.2	Sample size for group 2 of the original study
sig.level	Significance level (Type I error probability or alpha)
power	Power of the test (1 minus Type II error probability or 1 minus beta)
conf	Power of the test (1 minus Type II error probability or 1 minus beta)One-tailed confidence interval for computing the safeguard effect size, defaults to .80. It is required that .5 < conf < 1.

Details

Function safeguard.d computes the safeguard effect size (ds) as the lower limit of the specified confidence interval of d, subsequently a power analysis is performed using ds as input, as well as sig.level and power, to get the safeguard sample size. Function safeguard.d2 is a wrapper for safeguard.d that allows to specify the means and the standard deviations of the two groups instead of the Cohen's d. Function safeguard.r takes as input the Pearson's correlation coefficient instead of the Cohen's d. Functions safeguard.d.data and safeguard.r.data are wrappers for safeguard.d2 and safeguard.r respectively. They accept the data as input and are especially useful for post-hoc safeguard power analysis, when the original data are available.

Value

A vector of three elements is returned.

Lower_d	The safeguard effect size. (Lower_r in the output of safeguard.r and of safeguard.r.data)
N_required	The safeguard sample size (ns) required for the replication study (in safeguard.d this is the overall sample size for the two groups)

.

SSR	The safeguard sample ratio of the original study, namely the ratio of the safeguard sample size over the original sample size, N_required /(n.1+n.2).

Notes

If the safeguard effect size has the opposite sign of the original effect size the functions return a warning (this happens if the original effect size is significant at a certain p-level, one tailed, but conf is higher than one minus that p-level): should this happen, we suggest to lower the value of conf. Moreover in some situations it may happen that the value of the safeguard effect size is too high or too low to compute the exact value of the safeguard sample size. When the safeguard effect size is close to zero the N_required is set to Inf, while when it is much higher than zero the N_required is set to 2 (i.e., the minimum possible value for a sample size). In these situations, warning messages are returned.

Author(s)

Giulio Costantini ([e-mail])

References

Perugini, M., Gallucci, M., Costantini, G. (in preparation) Safeguard Power as a Protection Against Imprecise Power Estimates

Examples

# Most of the examples are taken from the main paper.
# Notice that all of the functions presented here require the one-tailed
# confidence interval as input (parameter conf). For the examples that consider
# the effect size of the differences of two means in two independent groups
# (safeguard.d and safeguard.d2), the total sample size is split in two equal
# groups, n.1 and n.2.

library(pwr)
library(MBESS)

# Safeguard power analysis for Cohen's d = .80 and n = 50.
# To mirror the example in the main text, that considers a CI 95% two-tailed,
# we specify as input the corresponding one-tailed CI, conf = .975.

safeguard.d(d = .8, n.1 = 25, n.2 = 25, sig.level = .05, power = .8,
  conf = 0.975)

# the same analysis using safeguard.d2, i.e., specifying a value for the means
# and for the pooled SD. We used means of 1.8 and 1, with a pooled SD of 1 to
# get an effect size of d = .8

safeguard.d2(m.1 = 1.8, m.2 = 1, sd.1 = 1, sd.2 = 1, n.1 = 25, n.2 = 25,
	conf = .975)

# The safeguard sample sizes the Table 1 of the paper can be reproduced with
# function safeguard.d by varying the values of d, n and conf. Here an example
# with a sample of 20 (two groups of 10), effect size .5 and one-tailed
# confidence inteval of .80

safeguard.d(d=.5, n.1=10, n.2=10, conf=.80)

#The examples discussed in the text, about evaluating empirical evidence.

safeguard.d(d = .5, n.1 = 30, n.2 = 30)
safeguard.d(d = .5, n.1 = 90, n.2 = 90)

# Some cases considered in the paper in which the SSR is one.

safeguard.d(d =  .5, n.1 = 91, n.2 = 91)
safeguard.d(d =  .8, n.1 = 37, n.2 = 37)
safeguard.d(d =   1, n.1 = 24, n.2 = 24)
safeguard.d(d = 1.5, n.1 = 12, n.2 = 12)

#The examples in Table 3

safeguard.d(d =  .7, n.1 =  25, n.2 = 25)
safeguard.d(d =  .7, n.1 = 100, n.2 = 100)
safeguard.d(d =   1, n.1 =  15, n.2 = 15)
safeguard.d(d = 1.5, n.1 =  10, n.2 = 10)
safeguard.d(d =  .4, n.1 =  40, n.2 = 40)

# an example of usage of the function safeguard.r

safeguard.r(r = .4, n = 100, sig.level = .05, power = .8, conf = .80)

# an example of the usage of safeguard.d.data

set.seed(100)
x <- rnorm(n = 50, mean = 1, sd = 1) 
y <- rnorm(n = 50, mean = 2, sd = 1)
safeguard.d.data(x,y)

# an example of the usage of safeguard.r.data

set.seed(100)
x <- rnorm(n = 100, mean = 1, sd = 1)
y <- x + rnorm(n = 100, mean = 1, sd = 1)
safeguard.r.data(x,y)

GiulioCostantini/safeguardpower documentation built on May 6, 2019, 6:29 p.m.