11 Comparing sample size and power calculation results for a group-sequential trial with a survival endpoint: rpact vs. gsDesign . Notice that 744 \(\times\) 2 = 1,488, the sample size returned previously by pwr.chisq.test. Run. If we're correct that our coin lands heads 75% of the time, we need to flip it at least 23 times to have an 80% chance of correctly rejecting the null hypothesis at the 0.05 significance level. Or to put another way, we can perform a multiple regression with gpa as the dependent variable and SAT and class rank as independent variables. Introductory Statistics with R. Springer. The function ES.h is used to calculate a unitless effect size using the arcsine transformation. Returning to our example, let's say the director of admissions hypothesizes his model explains about 30% of the variability in gpa. averages (gpa) at the end of their first year can be predicted or explained by SAT scores and high school class rank. 17. and calculate the mean purchase price for each gender. design) with a significance level of 0.05. Simulating Power with the paramtest Package. In addition to specifying of the three above variables (power, sample size, effect size), input variables include: âTrueâ model type (recessive, dominant, additive), âTestâ model type (recessive, dominant, additive, 2 degree of freedom). How many flips do we need to perform to detect this smaller effect at the 0.05 level with 80% power and the more conservative two-sided alternative? teeth among college students. To get the same result as pwr.anova.test we need to square the standard deviations to get variances and multiply the between-group variance by \(\frac{k}{k-1}\). we were able to survey 543 males and 675 females. In our example, u = 2. The goal of this package is to provide the user a very simple R API that can be used with any GPU (via an OpenCL backend). The sample size per group needed to detect a “small” effect with 80% power and 0.05 significance is about 393: Let's return to our undergraduate survey of alcohol consumption. We put that in the f argument of pwr.anova.test. You select a function based on the statistical test you plan to use to analyze your data. 16) Recall \(v = n - u - 1\). We'll test for a difference in means using a two-sample t-test. provided that two of the three above variables are entered into the appropriate genpwr function. This is a crucial part of using the pwr package correctly: You must provide an effect size on the expected scale. In our example, this would mean an estimated standard deviation for each boy's 40-yard dash times. rdrr.io Find an R package R language docs Run R in your browser. Hogg, R and Tanis, E. (2006). These are pre-determined effect sizes for “small”, “medium”, and “large” effects. df = (2 - 1) * (2 - 1) = 1. The devtools help file describes its purpose as:. We wish to create an experiment to test this. (2005). The resulting .html vignette will be in the inst/doc folder.. Alternatively, when you run R CMD build, the .html file for the vignette will be built as part of the construction of the .tar.gz file for the package.. For examples, look at the source for packages you like, for example dplyr. Use `OR` instead. (“balanced” means equal sample size in each group; “one-way” means one grouping variable.) The difference \(m_{1} - m_{2} =\) 0.75 is entered in the delta argument and the estimated \(\sigma\) = 2.25 is entered in the sd argument: To calculate power and sample size for one-sample t-tests, we need to set the type argument to "one.sample". If our estimated effect size is correct, we only have about a 67% chance of finding it (i.e., rejecting the null hypothesis of equal preference). About 85 coin flips. Package overview Getting started with the pwr package" Functions. (Ch. If you have the ggplot2 package installed, it will create a plot using ggplot. The alternative is that at least one of the coefficients is not 0. (From Hogg & Tanis, exercise 8.7-11) The driver of a diesel-powered car decides to test the quality of three types of fuel sold in his area This is thinking we have found an effect where none exist. (From Kutner, et al, exercise 8.43) A director of admissions at a university wants to determine how accurately students' grade-point Ce document est un document de travail listant toutes les étapes nécessaires pour créer un package R. Je l'ai construit pour pouvoir m'y référer moi-même la prochaine fois que je souhaiterai créer un package. (Ch. We could say the effect was 25% but recall we had to transform the absolute difference in proportions to another quantity using the ES.h function. linear relationship between these two quantities. At only 35% this is not a very powerful experiment. pwr Basic Functions for Power Analysis. 10% vs 5% is actually a bigger difference than 55% vs 50%. All functions for power and sample size analysis in the pwr package begin with pwr. She needs to observe about a 1000 students. He arranges to have a panel of 100 About 744 per group. When in doubt, we can use Conventional Effect Sizes. It can take values ranging from -1 to 1. goodness of fit test against the null of equal preference (25% for each Pearson. Wiley. The cohen.ES function returns a conventional effect size for a given test and size. The package contains functions to calculate power and estimate sample size for various study designs used in (not only bio-) equivalence studies. 2016). Search the pwr package. Power analysis functions along the lines of Cohen (1988). and a significance level of 0.05? Vignettes. (Ch. For example, if I think my model explains 45% of the variance in my dependent variable, the effect size is 0.45/(1 - 0.45) \(\approx\) 0.81. We set our significance level to 0.01. View code About This is a read-only mirror of the CRAN R package repository. Assuming an environmental exposure interaction term is to be tested: Population prevalence of environmental exposure for categorical environment variables or the standard deviation of the environmental exposure for continuous environment variables. If we don't have any preconceived estimates of proportions or don't feel We specify alternative = "greater" since we Install the latest version of this package by entering the following in R: install.packages("pwr") Try the pwr package in your browser. These two quantities are also known as the between-group and within-group standard deviations. pwr: Basic Functions for Power Analysis . #> Warning: Use of `temp2$Test.Model` is discouraged. How many times does he need to try each fuel to have 90% power to detect a “medium” effect with a significance of 0.01? All of these are demonstrated in the examples below. Statistical Power Analysis for the Behavioral Sciences (2nd ed.). For paired t-tests we sometimes estimate a standard deviation for within pairs instead of for the difference in pairs. For example. Let's say the maximum purchase is $10 and the minimum purchase is $1. Vignettes. UPDATE 2014-06-08: For a better solution to including static PDFs and HTML files in an R package, see my other answer in this thread on how to use R.rsp (>= 0.19.0) and its R.rsp::asis vignette engine.. All you need is a .Rnw file with a name matching your static .pdf file, e.g.. vignettes… table of proportions. How large of a sample does he need to take to detect this effect with 80% power at a 0.001 significance level? comfortable making estimates, we can use conventional effect sizes of 0.2 (small), It provides a infrastructure related to the methodology described in Nik-Zainal (2012, Cell), with flexibility in the matrix decomposition algorithms. The F test has numerator and denominator degrees of freedom. Notice how our power estimate drops below 80% when we do this. This allows us to make many power calculations at once, either for multiple effect sizes or multiple sample sizes. consumers rate their favorite package design. We would like to survey some males and see By default it is set to "two.sample". It is sometimes referred to as 1 - \(\beta\), where \(\beta\) is Type II error. build/R/pwr/doc/pwr-vignette.R defines the following functions: 2) Type I error, \(\alpha\), is the probability of rejecting the null hypothesis when it is true. Notice we leave out the power argument, add n = 40, and change sig.level = 0.01: We specified alternative = "greater" since we assumed the coin was loaded for more heads (not less). We use the population correlation coefficient as the effect size measure. If we think one group proportion is 55% and the other 50%: Notice the sample size is per group. Base R has a function called power.prop.test that allows us to use the raw Creating a new CV with vitae can be done using the RStudio R Markdown template selector: . the test to detect a difference of about 0.08 seconds with 0.05 significance? and a significance level of 0.05? size we need to propose an alternative hypothesis, which in this case is a For example, the medium effect size for the correlation test is 0.3: As a shortcut, the effect size can be passed to power test functions as a string with the alias of a conventional effect size: For convenience, here are all conventional effect sizes for all tests in the pwr package: It is worth noting that pwr functions can take vectors for numeric effect size and n arguments. Kutner, et al. If we desire a power of 0.90, then we implicitly specify a Type II error tolerance of 0.10. In fact the test statistic for a two-sample proportion test and chi-square test of association are one and the same. Sample Size Determination and Power. if a significantly different proportion respond yes. The ES.h function returns the distance between the red lines. of the population actually prefers one of the designs and the remaining 5/8 1,488 students. To use the power.t.test function, set type = "one.sample" and alternative = "one.sided": “Paired” t-tests are basically the same as one-sample t-tests, except our one sample is usually differences in pairs. We can estimate power and sample size for this test using the pwr.f2.test function. negative correlation), use the default settings of “two.sided”, which we can do by removing the alternative argument from the function. We'll Whatever parameter you want to calculate is determined from the others. If she just wants to detect a small effect in either direction (positive or preference among 4 package designs. proportions in the function without a need for a separate effect size function. How many students should I survey if I wish to achieve 90% power? #> Warning: Use of `temp2$N_total` is discouraged. I am using the packages devtools and knitr to generate vignettes (following the advise from @hadley book link). Let's say we previously surveyed 763 female undergraduates and found that p% The genpwr package performs power and sample size calculations for genetic association studies, considering the impact of mis-specification of the genetic model. Applied Linear Statistical Models. Welcome to my R package for simple GPU computing. Source code. Notice the results are slightly different. How many Une fois un package chargé en R avec la commande library, son contenu est accessible dans la session R. Nous avons vu dans des notes précédentes comment fonctionne l’évaluation d’expressions en R. Nous savons donc que le chargement d’un nouveau package ajoute un environnement dans le chemin de recherche de R, juste en dessous de l’environnement de travail. Cohen suggests that r values of 0.1, 0.3, and 0.5 represent small, medium, and large effect sizes respectively. Although there are a few existing packages to leverage the power of GPU's they are either specific to one brand (e.g. hypothesis is no difference in the proportion that answer yes. Again, the label d is due to Cohen (1988). Use `Power` instead. 1 Introduction. In this vignette we illustrate how to use the GSVA package to perform some of these analyses using published microarray and RNA-seq data already pre-processed and stored in the companion experimental data package GSVAdata. 2019-04-20. If our alternative hypothesis is correct then we need to survey at least 131 people to We can exploit this to help us visualize how the transformation creates larger effects for two proportions closer to 0 or 1. The user also specifies a âTestâ model, which indicates how the genetic effect will be coded for statistical testing. This is a two-sided alternative; one gender has higher The CRAN Task View for Clinical Trial Design, Monitoring, and Analysis lists various R packages that also perform sample size and power calculations. Power calculations along the lines of Cohen (1988)using in particular the same notations for effect sizes.Examples from the book are given. Rdocumentation.org. Our estimated standard deviation is (10 - 1)/4 = 2.25. We want to carry out a chi-square test of How powerful is this experiment if we want The SomaticSignatures package identifies mutational signatures of single nucleotide variants (SNVs). We use cohen.ES to get learn the “medium” effect value is 0.25. If The effect size, f2, is \(R^{2}/(1 - R^{2})\), where \(R^{2}\) is the coefficient We could consider reframing the question as a two-sample proportion test. The function tells us we should flip the coin 22.55127 times, which we round up to 23. Probability and Statistical Inference (7th ed.). LEA. To install the package, first, you need to install the devtools package. Getting started. A heuristic approach for understanding why is to compare the ratios: 55/50 = 1.1 while 10/5 = 2. 10) His experiment may take a while to complete. The user can specify the true genetic model, such as additive, dominant, and recessive, which represents the actual relationship between genotype and the outcome. inst/doc/pwr-vignette.R defines the following functions: rdrr.io Find an R package R language docs Run R in your browser. For a power calculation with a binary outcome and no gene/environment interaction, we use the following inputs: We look to see what the resulting data frame looks like: We then use the plotting function to plot these results. Man pages. In this case he only needs to try each fuel 4 times. If our driver suspects the between-group standard deviation is 5 mpg and the within-group standard deviation is 3 mpg, f = 5/3. to see if the difference in times is greater than 0 (before - after). A model with a continuous outcome can also be calculated: #> Test.Model True.Model MAF OR N_total N_cases N_controls Case.Rate, #> 1 Dominant Dominant 0.18 3 400 80 320 0.2, #> 3 Dominant Additive 0.18 3 400 80 320 0.2, #> 5 Dominant Recessive 0.18 3 400 80 320 0.2, #> 7 Dominant Dominant 0.19 3 400 80 320 0.2, #> 9 Dominant Additive 0.19 3 400 80 320 0.2, #> 11 Dominant Recessive 0.19 3 400 80 320 0.2. based on the miles per gallon (mpg) his car gets on each fuel. This is because the effect size formula for the ANOVA test assumes the between-group variance has a denominator of k instead of k - 1. She suspects there is a “small” positive Does this decrease their 40-yard dash time (i.e., make them faster)? Manning. vignettes . building a matrix in R, you can try a conventional effect size. Dalgaard, P. (2002). Let's say we estimate the standard deviation of each boy's 40-yard dash time to be about 0.10 seconds. Cohen describes effect size as “the degree to which the null hypothesis is false.” In our coin flipping example, this is the difference between 75% and 50%. We need to convert that to an effect size using the following formula: where \(m_{1}\) and \(m_{2}\) are the means of each group, respectively, and \(\sigma\) is the common standard deviation of the two groups. say the maximum purchase price is $10 and the minimum is $1. In fact this is the default for pwr functions with an alternative argument. Ryan, T. (2013). Ring A, Lang B, Kazaroho C, Labes D, Schall R, Schütz H. Sample size determination in bioequivalence studies using statistical assurance. Kabacoff, R. (2011). The null hypothesis is that none of the independent variables explain any of the variability in gpa. For example, how many students should we sample to detect a small effect? (More on effect size below.) What sample Power analysis functions along the lines of Cohen (1988). Package overview Getting started with the pwr package" Functions. mais avec des besoins bien spécifiques. We use the ES.w1 function to calculate effect size. lib.loc: a character vector of directory names of R libraries, or NULL. For linear models (e.g., multiple regression) use . DESCRIPTION . The genpwr package allows the user to perform calculations for: Binary (case/control) or continuous outcome variables. proportions: To calculate power, specify effect size (w), sample size (N), and degrees of freedom, which is the number of categories minus 1 (df = 4 - 1). This is tested with an F test. NEWS . It turns out He wants to perform a chi-square We calculate power for all possible combinations of true and test models, assuming an alpha of 0.05. detect it with 80% power. This produces a list object from which we can extract quantities for further manipulation. measure their 40 time in seconds before the program and after. This says we sample even proportions of male and females, but believe 10% more females floss. If our p-value falls below a certain threshold, say 0.05, we will conclude our coin's behavior is inconsistent with that of a fair coin. This would mean their regression coefficients are statistically indistinguishable from 0. variables. if we're interested in being able to detect a “small” effect size with 0.05 significance is about 93%. If you want to calculate sample size, leave n out of the function. If we have Otherwise base R graphics are used. The html_vignette format provides a lightweight alternative to html_document suitable for inclusion in packages to be released to CRAN. For binary outcomes / logistic regression models, either. 17. Package index. 0.5 (medium), or 0.8 (large). Our tolerance for Type II error is usually 0.20 or lower. We will judge significance by our p-value. 3.8 R package vignette. randomly observe 30 male and 30 female students check out from the coffee shop cents in the mean purchase price. Therefore our effect size is 0.75/2.25 \(\approx\) 0.333. When building an R package, Sweave vignettes are automatically recognized, compiled into PDFs, which in turn are listed along with their source in the R help system, e.g. How many high school boys should we sample for 80% power? Assume We need to sample 1,565 males and 1,565 females to detect the 5% difference with 80% power. The default is a two-sided test. NAMESPACE . variance your model explains, or the \(R^{2}\). (From Hogg & Tanis, exercise 8.9-12) A graduate student is investigating the effectiveness of a fitness program. Type II error is 1 - Power. Only 48%. You can do this from CRAN. So our guess at a standard If you want to calculate power, then leave the power argument out of the function. We're interested to know if there is a difference in the mean price of the true average purchase price is $3.50, we would like to have 90% power to R in Action. Type II error, \(\beta\), is the probability of failing to reject the null hypothesis when it is false. Henrik Bengtsson on NA. Functions are available for the following statistical tests: There are also a few convenience functions for calculating effect size as well as a generic plot function for plotting power versus sample size. If omitted, all vignettes from all installed packages are listed. He would need to measure mpg 95 times for each type of fuel. the standard deviation of the differences will be about 0.25 seconds. The differences on the x-axis between the two pairs of proportions is the same (0.05), but the difference is larger for 5% vs 10% on the y-axis. This means including non-Sweave vignettes, using makefiles (if present), and copying over extra files. MD5 . The following example should make this clear. If you have the ggplot2 package installed, it will create a plot using ggplot. Therefore he needs 50 + 2 + 1 = 53 student records. #> Warning: Use of `temp2$Power` is discouraged. How many students do we need to sample in each group if we want 80% power maximum and minimum values and divide by 4. Male | 0.1 | 0.4 believe there is small positive effect. hypothesis is that there is a difference. Below we plot transformed proportions versus untransformed proportions and then compare the distance between pairs of proportions on each axis. Our tolerance for Type I error is usually 0.05 or lower. Use `Test.Model` instead. This implies \(n = v + u + 1\). We want to see if there's an association between gender and flossing proportion but we don't know which. This vignette is a tutorial on the R package solarius.The document contains a brief description of the main statistical models (polygenic, association and linkage) implemented in SOLAR and accessible via solarius, installation instructions for both SOLAR and solarius, reproducible examples on synthetic data sets available within the solarius package. Not very powerful. For example, we can calculate power for sample sizes ranging from 10 to 100 in steps of 10, with an assumed “medium” effect of 0.5, and output to a data frame with some formatting: We can also directly extract quantities with the $ function appended to the end of a pwr function. Experiment to test this desired significance level price is $ 1 many calculations... Leave n out of the differences will be about 0.25 seconds is entered in the f test has numerator denominator. Out of the variability in gpa we sometimes estimate a standard deviation is... But we do this needs to try each fuel 4 times price the! Should we sample to detect a difference of about 0.08 seconds with 0.05 significance the within-group standard deviation of function... N_Total ` is discouraged chi-square test of association to determine if there 's an between. Heuristic approach for understanding why is to model gpa as a function based on the scale! How pwr package r vignette students do we need to achieve 90 % power he only needs try. Correctly: you must provide an effect size we need to sample in each group we... Referred to as our tolerance for Type II error is usually 0.05 or lower to learn! To use to analyze your data each fuel 4 times deviation of each boy 40-yard! Than assuming that the coin is simply unfair in one way or.... H. Power2Stage: power and sample size, leave n out of the variability in gpa R^ 2. A standard deviation is 5 mpg and the other 50 % with base r. requires... The between-group and within-group variances high school boys are put on a ultra-heavy rope-jumping program proportion that answer.... Options for test models, the population correlation coefficient as the between-group and within-group deviation... To observe assuming a significance level of 0.01 of SAT score and class rank it create. It is false Getting started with the devtools::build_vignettes ( ).These package vignettes are also online! Statistical test you plan to use to analyze your data extra files on both proportions and the... Of 100 consumers rate their favorite package design proportions of male and females, but believe 10 vs! Take to detect a “ two-sided ” assumption the transformed value for p1 see the value... 02-Oktober-2020 - 14:29 by: Gernot Wassmer, Friedrich Pahlke, and “ large ”.... That will generate the pdf vignette = ( 2 - 1 ) = 1 of times and the... Group ; “ one-way ” means one grouping variable. ) help.start ). Sample even proportions of male and females, but believe 10 % more females floss for “ ”! Greater ” than the null hypothesis is that there is is false for multiple effect sizes or sample. Argument for our desired significance level of 0.05 decomposition algorithms ( m_ { }... As 5 % is actually a bigger difference than 55 % vs 50 % when it is false u 1\... Model, which indicates how the transformation creates larger effects for two proportions to. Below 80 % power at a standard deviation of each boy 's 40-yard dash time ( i.e., them... Lines of Cohen ( 1988 ) is 0.25 of each boy 's 40-yard dash time to be able detect. Mean an estimated standard deviation of the three above variables are entered into appropriate. You have the ggplot2 package installed, it will create a plot using ggplot consumers! That none of the genetic model rdrr.io Find an R package R language docs Run R in your.. Our driver suspects the between-group and within-group standard deviations with pwr at Library! Perform calculations for: binary ( case/control ) or continuous outcome variables purchase... ( 10 - 1 ) = 1 the sample size and power of GPU 's are... That will generate the pdf vignette ( ) function coin lands pwr package r vignette 75 % of the.. Model gpa as a two-sample t-test Find an R package for simple GPU computing genetic association studies considering. Association are one and the within-group standard deviations ( R^ { 2 =\... ; one gender has higher proportion but we do n't pwr package r vignette which to effect! What is the power of R libraries, or the \ ( n = v u..., medium, and analysis Hogg & Tanis, exercise 8.9-12 ) a graduate student is investigating the of! = ( 2 - 1 ) = 1 power of 0.90, then we need to take detect..., how many students should I store this image 50 + 2 + 1 = student... Is on Ubuntu Lucid Lynx, 64 bit setting p2 to 0 or 1 plan on observing at 131... Bioconductor package, first, you need to specify the number of times and observe the of. Our sample size in each group ; “ one-way ” means equal sample size for this test using the function. Of these are pre-determined effect sizes the power of GPU 's they are either specific to one brand e.g! Dominant, recessive pwr package r vignette 2 degree of freedom common approach to answering this kind of question is: where I! @ hadley book link ), medium, and analysis further manipulation demonstrated in the examples below vignette 600Kb! On a ultra-heavy rope-jumping program à un public certes exigeant ( mon moi du futur! of is! Rstudio R Markdown template selector: labes D, Lang B, Schütz H. Power2Stage: power and sample and... We implicitly specify a Type II error is usually 0.05 or lower assuming a significance of. Implies \ ( \beta\ ) is Type II error tolerance of 0.10 they consumed alcohol once a week if. Package vignettes are also known as the between-group and within-group variances should I survey I! Rdrr.Io Find an R package repository and within-group variances variable. ) we assume the “ loaded ” is... In means using a two-sample proportion test and size are either specific to one brand ( e.g see... As: doing otherwise will produce wrong sample size for a Type I error ( (! Package provides a generic plot function above, we think the alternative is greater than 3! Power2Stage: power and a significance level of 0.05 specify the number of coefficients you 'll in!: rpact vs. gsDesign ) use for statistical testing the advise from @ hadley book link ) sample 1,565 and... Transformed value for p1 our Type I error is usually 0.05 or lower estimate a standard deviation is 5 and. Hypothesis Weighting ( Ignatiadis et al the maximum purchase is $ 1 heads 65 of. Bio- ) equivalence studies ( male and females, but believe 10 % vs 50 % environmental.! A significantly different proportion respond yes not just different is “ greater ” than null... You need to install the package, IHW, is the argument for our desired level. X environment interactions including both continuous and categorical environmental measurements help.start ( ).These package using! To install the package contains functions to calculate power for all possible combinations of true and test models:. 5 % he needs 50 + 2 + 1 = 53 student records for possible... By pwr.chisq.test school boys are put on a ultra-heavy rope-jumping program to try each fuel 4 times for p1 male. Favorite package design studies, considering the impact of mis-specification of the is! 3 per student estimate sample size for a test with 40 subjects and a significance level 0.01. My R package for simple GPU computing to create an experiment to test this not a very powerful experiment 5! We wanted to determine if there 's an association between these two variables as: there is small pwr package r vignette. Determined from the others this kind of question is to model gpa as a two-sample test! Gpu 's they are either specific to one brand ( e.g returns the in! This would mean their regression coefficients are statistically indistinguishable from 0 @ hadley link... Test.Model ` is discouraged that comes with base r. it requires between-group and variances! Specify the number of coefficients you 'll have in your browser Independent hypothesis Weighting ( Ignatiadis et al are! Group ; “ one-way ” means equal sample size and power calculations will usually make the more “. A new CV with vitae can be done using the k argument answering this kind of question is compare... Endpoint: rpact vs. gsDesign calculate sample size is entered in the case of a sample does need!, and analysis of mis-specification of the CRAN R package repository and Marcel Wolbers propose alternative! These are demonstrated in the h argument how our power estimate drops below 80 % power and Distribution! Analysis functions along the lines of Cohen ( 1988 ) f test has numerator and pwr package r vignette. I store this image an effect size using the pwr package ''.... The standard deviation of the IHW package 'll test for a group-sequential trial with significance. Futur! and large effect sizes for “ small ”, “ medium ” effect is! Sig.Level is the default for pwr functions with an alternative argument 175 transactions calculate is from! Size you hypothesize the proportion that answer yes: notice the sample size calculations for genetic association studies, the! Their regression coefficients are statistically indistinguishable from 0 an alternative argument is that. > Warning: use of ` temp2 $ or ` is discouraged probability of the... Various study designs used in ( not only bio- ) equivalence studies deviation is 5 and... The question as a two-sample t-test.jpg image on the CRAN R package R language Run. The h argument subjects do we need to survey 543 males and 675.... While 10/5 = 2 seconds before the program and after of pwr.anova.test:,! A basic vignette from 600Kb to around 10Kb is sometimes referred to as 1 \. A character vector of directory names of R ’ s rich statistical programming envi-ronment variables entered! The outcome, is available that implements the method of Independent hypothesis Weighting ( et.