Description Usage Arguments Details Value References Examples
Given the hypothetical population effect size and the required power level,
the function prospective()
performs a prospective design analysis for
Pearson's correlation test between two variables or ttest comparing
group means (Cohen's d). According to the defined alternative
hypothesis and the significance level, the required sample size is computed
together with the associated Type M error, Type S error, and the critical
effect value (i.e., the minimum absolute effect size value that would
result significant).
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19  prospective(
effect_size,
power,
ratio_n = 1,
effect_type = c("correlation", "cohen_d"),
test_method = c("pearson", "two_sample", "welch", "paired", "one_sample"),
alternative = c("two_sided", "less", "greater"),
sig_level = 0.05,
ratio_sd = 1,
B = 10000,
tl = Inf,
tu = Inf,
B_effect = 1000,
sample_range = c(2, 1000),
eval_power = c("median", "mean"),
tol = 0.01,
display_message = TRUE,
seed = NULL
)

effect_size 
a numeric value or function (see details) indicating the hypothetical population effect size. 
power 
a numeric value indicating the required power level. 
ratio_n 
a numeric value indicating the ratio between 
effect_type 
a character string specifying the effect type, must be one
of 
test_method 
a character string specifying the test type, must be one of

alternative 
a character string specifying the alternative hypothesis, must be one of "two_sided" (default), "greater" or "less". You can specify just the initial letter. 
sig_level 
a numeric value indicating the significance level on which the alternative hypothesis is evaluated. 
ratio_sd 
a numeric value indicating the ratio between the standard deviation in the first group and in the second group. This argument is required only in the case of Welch's ttest. 
B 
a numeric value indicating the number of iterations. Increase the number of iterations to obtain more stable results. 
tl 
optional value indicating the lower truncation point if

tu 
optional value indicating the upper truncation point if

B_effect 
a numeric value indicating the number of sampled effects
if 
sample_range 
a length2 numeric vector indicating the minimum and
maximum sample size of the first group ( 
eval_power 
a character string specifying the function used to summarize the resulting distribution of power values. Must be one of "median" (default) or "mean". You can specify just the initial letters. See details. 
tol 
a numeric value indicating the tolerance of required power level. 
display_message 
a logical variable indicating whether to display or not the information about computational steps. 
seed 
a numeric value indicating the seed for random number generation. Set the seed to obtain reproducible results. 
Conduct a prospective design analysis to define the required sample
size and the associated inferential risks according to study design. A
general overview is provided in the vignette("prospective")
.
Population effect size
The hypothetical population effect size (effect_size
) can be set to
a single value or a function that allows sampling values from a given
distribution. The function has to be defined as function(x)
my_function(x, ...)
, with only one single argument x
representing
the number of sampled values (e.g., function(x) rnorm(x, mean = 0, sd
= 1)
; function(x) sample(c(.1,.3,.5), x, replace = TRUE)
). This
allows users to define hypothetical effect size distribution according to
their needs.
Argument B_effect
allows defining the number of sampled effects.
Users can access sampled effects in the effect_info
list included in
the output to evaluate if the sample is representative of their
specification. Increase the number to obtain more accurate results but it
will require more computational time (default is 1000). To avoid long
computational times, we suggest adjusting B
when using a function to
define the hypothetical population effect size.
Optional arguments tl
and tu
allow truncating the sampling
distribution specifying the lower truncation point and upper truncation
point respectively. Note that if effect_type = "correlation"
,
distribution is automatically truncated between 1 and 1.
When a distribution of effects is specified, a corresponding distribution
of power values is obtained as result. To evaluate whether the required
level of power is obtained, user can decide between the median or the mean
value as a summary of the distribution using the argument
eval_power
. They answer two different questions. Which is the
required sample size to obtain 50
than the required level (median)?; Which is the required sample size to
obtain on average a power equal or greater than the required level (mean)?
Effect type and test method options
The effect_type
argument can be set to "correlation"
(default) if a correlation is evaluated or "cohen_d"
for
standardized mean difference.
In the case of "correlation"
, only Pearson's correlation between two
variables is available. In this case "pearson"
has to be set as
test_method
and ratio_n
argument is ignored. The Kendall's
tau and Spearman's rho are not implemented.
In the case of "cohen_d"
, the available ttests can be
selected specifying the argument test_method
. For independent
twosample ttest, use "two_sample"
and indicate the ratio
between the sample size of the first group and the second group
(ratio_n
). For Welch's ttest, use "welch"
and
indicate the ratio between the sample size of the first group and the
second group (ratio_n
) and the ratio between the standard deviation
in the first group and in the second group (ratio_sd
). For dependent
ttest for paired samples, use "paired"
(ratio_n
has
to be 1). For onesample ttest, use "one_sample"
(ratio_n
has to be NULL
).
Study design
Study design can be further defined according to statistical test
directionality and required αlevel using the arguments
alternative
and sig_level
respectively.
A list with class "design_analysis" containing the following components:
design_analysis 
a character string indicating the type of design analysis: "prospective". 
call_arguments 
a list with all the arguments passed to the function. 
effect_info 
a list with all the information regarding the
considered hypothetical population effect size. The list includes:

test_info 
a list with all the information regarding the test
performed. The list includes: 
prospective_res 
a data frame with the results of the design
analysis. Columns names are 
Altoè, G., Bertoldo, G., Zandonella Callegher, C., Toffalini, E., Calcagnì, A., Finos, L., & Pastore, M. (2020). Enhancing Statistical Inference in Psychological Research via Prospective and Retrospective Design Analysis. Frontiers in Psychology, 10. https://doi.org/10.3389/fpsyg.2019.02893
Bertoldo, G., Altoè, G., & Zandonella Callegher, C. (2020). Designing Studies and Evaluating Research Results: Type M and Type S Errors for Pearson Correlation Coefficient. Retrieved from https://psyarxiv.com/q9f86/
Gelman, A., & Carlin, J. (2014). Beyond Power Calculations: Assessing Type S (Sign) and Type M (Magnitude) Errors. Perspectives on Psychological Science, 9(6), 641–651. https://doi.org/10.1177/1745691614551642
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33  # Pearson's correlation
prospective(effect_size = .3, power = .8, effect_type = "correlation",
test_method = "pearson", B = 1e3, seed = 2020)
# Twosample ttest
prospective(effect_size = .3, power = .8, ratio_n = 1.5,
effect_type = "cohen_d", test_method = "two_sample",
B = 1e3, seed = 2020)
# Welch ttest
prospective(effect_size = .3, power = .8, ratio_n = 2,
effect_type ="cohen_d", test_method = "welch",
ratio_sd = 1.5, B = 1e3, seed = 2020)
# Paired ttest
prospective(effect_size = .3, power = .8, ratio_n = 1,
effect_type = "cohen_d", test_method = "paired",
B = 1e3, seed = 2020)
# Onesample ttest
prospective(effect_size = .3, power = .8, ratio_n = NULL,
effect_type = "cohen_d", test_method = "one_sample",
B = 1e3, seed = 2020)
## Not run:
# Define effect_size using functions (long computational time)
prospective(effect_size = function(x) rnorm(x, .3, .1), power = .8,
effect_type = "correlation", test_method = "pearson",
B_effect = 500, B = 500, tl = .15, seed = 2020)
prospective(effect_size = function(x) rnorm(x, .3, .1), power = .8,
effect_type = "cohen_d", test_method = "two_sample", ratio_n = 1,
B_effect = 500, B = 500, tl = .2, tu = .4, seed = 2020)
## End(Not run)

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