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Parametric, non-parametric, robust, and Bayesian one-way ANOVA.

Usage

oneway_anova(
  data,
  x,
  y,
  subject.id = NULL,
  type = "parametric",
  paired = FALSE,
  k = 2L,
  conf.level = 0.95,
  effsize.type = "omega",
  var.equal = FALSE,
  bf.prior = 0.707,
  tr = 0.2,
  nboot = 100L,
  ...
)

Arguments

data

A data frame (or a tibble) from which variables specified are to be taken. Other data types (e.g., matrix,table, array, etc.) will not be accepted. Additionally, grouped data frames from {dplyr} should be ungrouped before they are entered as data.

x

The grouping (or independent) variable from data. In case of a repeated measures or within-subjects design, if subject.id argument is not available or not explicitly specified, the function assumes that the data has already been sorted by such an id by the user and creates an internal identifier. So if your data is not sorted, the results can be inaccurate when there are more than two levels in x and there are NAs present. The data is expected to be sorted by user in subject-1,subject-2, ..., pattern.

y

The response (or outcome or dependent) variable from data.

subject.id

Relevant in case of a repeated measures or within-subjects design (paired = TRUE, i.e.), it specifies the subject or repeated measures identifier. Important: Note that if this argument is NULL (which is the default), the function assumes that the data has already been sorted by such an id by the user and creates an internal identifier. So if your data is not sorted and you leave this argument unspecified, the results can be inaccurate when there are more than two levels in x and there are NAs present.

type

A character specifying the type of statistical approach:

  • "parametric"

  • "nonparametric"

  • "robust"

  • "bayes"

You can specify just the initial letter.

paired

Logical that decides whether the experimental design is repeated measures/within-subjects or between-subjects. The default is FALSE.

k

Number of digits after decimal point (should be an integer) (Default: k = 2L).

conf.level

Scalar between 0 and 1 (default: 95% confidence/credible intervals, 0.95). If NULL, no confidence intervals will be computed.

effsize.type

Type of effect size needed for parametric tests. The argument can be "eta" (partial eta-squared) or "omega" (partial omega-squared).

var.equal

a logical variable indicating whether to treat the two variances as being equal. If TRUE then the pooled variance is used to estimate the variance otherwise the Welch (or Satterthwaite) approximation to the degrees of freedom is used.

bf.prior

A number between 0.5 and 2 (default 0.707), the prior width to use in calculating Bayes factors and posterior estimates. In addition to numeric arguments, several named values are also recognized: "medium", "wide", and "ultrawide", corresponding to r scale values of 1/2, sqrt(2)/2, and 1, respectively. In case of an ANOVA, this value corresponds to scale for fixed effects.

tr

Trim level for the mean when carrying out robust tests. In case of an error, try reducing the value of tr, which is by default set to 0.2. Lowering the value might help.

nboot

Number of bootstrap samples for computing confidence interval for the effect size (Default: 100L).

...

Additional arguments (currently ignored).

Value

The returned tibble data frame can contain some or all of the following columns (the exact columns will depend on the statistical test):

  • statistic: the numeric value of a statistic

  • df: the numeric value of a parameter being modeled (often degrees of freedom for the test)

  • df.error and df: relevant only if the statistic in question has two degrees of freedom (e.g. anova)

  • p.value: the two-sided p-value associated with the observed statistic

  • method: the name of the inferential statistical test

  • estimate: estimated value of the effect size

  • conf.low: lower bound for the effect size estimate

  • conf.high: upper bound for the effect size estimate

  • conf.level: width of the confidence interval

  • conf.method: method used to compute confidence interval

  • conf.distribution: statistical distribution for the effect

  • effectsize: the name of the effect size

  • n.obs: number of observations

  • expression: pre-formatted expression containing statistical details

For examples, see data frame output vignette.

One-way ANOVA

The table below provides summary about:

  • statistical test carried out for inferential statistics

  • type of effect size estimate and a measure of uncertainty for this estimate

  • functions used internally to compute these details

between-subjects

Hypothesis testing

TypeNo. of groupsTestFunction used
Parametric> 2Fisher's or Welch's one-way ANOVAstats::oneway.test()
Non-parametric> 2Kruskal-Wallis one-way ANOVAstats::kruskal.test()
Robust> 2Heteroscedastic one-way ANOVA for trimmed meansWRS2::t1way()
Bayes Factor> 2Fisher's ANOVABayesFactor::anovaBF()

Effect size estimation

TypeNo. of groupsEffect sizeCI available?Function used
Parametric> 2partial eta-squared, partial omega-squaredYeseffectsize::omega_squared(), effectsize::eta_squared()
Non-parametric> 2rank epsilon squaredYeseffectsize::rank_epsilon_squared()
Robust> 2Explanatory measure of effect sizeYesWRS2::t1way()
Bayes Factor> 2Bayesian R-squaredYesperformance::r2_bayes()

within-subjects

Hypothesis testing

TypeNo. of groupsTestFunction used
Parametric> 2One-way repeated measures ANOVAafex::aov_ez()
Non-parametric> 2Friedman rank sum teststats::friedman.test()
Robust> 2Heteroscedastic one-way repeated measures ANOVA for trimmed meansWRS2::rmanova()
Bayes Factor> 2One-way repeated measures ANOVABayesFactor::anovaBF()

Effect size estimation

TypeNo. of groupsEffect sizeCI available?Function used
Parametric> 2partial eta-squared, partial omega-squaredYeseffectsize::omega_squared(), effectsize::eta_squared()
Non-parametric> 2Kendall's coefficient of concordanceYeseffectsize::kendalls_w()
Robust> 2Algina-Keselman-Penfield robust standardized difference averageYesWRS2::wmcpAKP()
Bayes Factor> 2Bayesian R-squaredYesperformance::r2_bayes()

Examples

# for reproducibility
set.seed(123)
library(statsExpressions)

# ----------------------- parametric -------------------------------------

# between-subjects
oneway_anova(
  data = mtcars,
  x    = cyl,
  y    = wt
)
#> # A tibble: 1 × 14
#>   statistic    df df.error   p.value
#>       <dbl> <dbl>    <dbl>     <dbl>
#> 1      20.2     2     19.0 0.0000196
#>   method                                                   effectsize estimate
#>   <chr>                                                    <chr>         <dbl>
#> 1 One-way analysis of means (not assuming equal variances) Omega2        0.637
#>   conf.level conf.low conf.high conf.method conf.distribution n.obs expression
#>        <dbl>    <dbl>     <dbl> <chr>       <chr>             <int> <list>    
#> 1       0.95    0.370         1 ncp         F                    32 <language>

# within-subjects design
oneway_anova(
  data       = iris_long,
  x          = condition,
  y          = value,
  subject.id = id,
  paired     = TRUE
)
#> # A tibble: 1 × 18
#>   term      sumsq sum.squares.error    df df.error meansq statistic  p.value
#>   <chr>     <dbl>             <dbl> <dbl>    <dbl>  <dbl>     <dbl>    <dbl>
#> 1 condition 1656.              318.  1.15     171.   1.86      776. 1.32e-69
#>   method                                              effectsize       estimate
#>   <chr>                                               <chr>               <dbl>
#> 1 ANOVA estimation for factorial designs using 'afex' Omega2 (partial)    0.707
#>   conf.level conf.low conf.high conf.method conf.distribution n.obs expression
#>        <dbl>    <dbl>     <dbl> <chr>       <chr>             <int> <list>    
#> 1       0.95    0.673         1 ncp         F                   150 <language>

# ----------------------- non-parametric ----------------------------------

# between-subjects
oneway_anova(
  data = mtcars,
  x    = cyl,
  y    = wt,
  type = "np"
)
#> # A tibble: 1 × 15
#>   parameter1 parameter2 statistic df.error   p.value
#>   <chr>      <chr>          <dbl>    <int>     <dbl>
#> 1 wt         cyl             22.8        2 0.0000112
#>   method                       effectsize      estimate conf.level conf.low
#>   <chr>                        <chr>              <dbl>      <dbl>    <dbl>
#> 1 Kruskal-Wallis rank sum test Epsilon2 (rank)    0.736       0.95    0.624
#>   conf.high conf.method          conf.iterations n.obs expression
#>       <dbl> <chr>                          <int> <int> <list>    
#> 1         1 percentile bootstrap             100    32 <language>

# within-subjects design
oneway_anova(
  data       = iris_long,
  x          = condition,
  y          = value,
  subject.id = id,
  paired     = TRUE,
  type       = "np"
)
#> # A tibble: 1 × 15
#>   parameter1 parameter2 statistic df.error  p.value method                
#>   <chr>      <chr>          <dbl>    <dbl>    <dbl> <chr>                 
#> 1 value      condition        410        3 1.51e-88 Friedman rank sum test
#>   effectsize  estimate conf.level conf.low conf.high conf.method         
#>   <chr>          <dbl>      <dbl>    <dbl>     <dbl> <chr>               
#> 1 Kendall's W    0.911       0.95    0.904         1 percentile bootstrap
#>   conf.iterations n.obs expression
#>             <int> <int> <list>    
#> 1             100   150 <language>

# ----------------------- robust -------------------------------------

# between-subjects
oneway_anova(
  data = mtcars,
  x    = cyl,
  y    = wt,
  type = "r"
)
#> # A tibble: 1 × 12
#>   statistic    df df.error p.value
#>       <dbl> <dbl>    <dbl>   <dbl>
#> 1      12.7     2     12.2 0.00102
#>   method                                           
#>   <chr>                                            
#> 1 A heteroscedastic one-way ANOVA for trimmed means
#>   effectsize                         estimate conf.level conf.low conf.high
#>   <chr>                                 <dbl>      <dbl>    <dbl>     <dbl>
#> 1 Explanatory measure of effect size     1.02       0.95    0.828      1.35
#>   n.obs expression
#>   <int> <list>    
#> 1    32 <language>

# within-subjects design
oneway_anova(
  data       = iris_long,
  x          = condition,
  y          = value,
  subject.id = id,
  paired     = TRUE,
  type       = "r"
)
#> # A tibble: 1 × 12
#>   statistic    df df.error p.value
#>       <dbl> <dbl>    <dbl>   <dbl>
#> 1      368.  1.09     97.1       0
#>   method                                                             
#>   <chr>                                                              
#> 1 A heteroscedastic one-way repeated measures ANOVA for trimmed means
#>   effectsize                                                      estimate
#>   <chr>                                                              <dbl>
#> 1 Algina-Keselman-Penfield robust standardized difference average   -0.349
#>   conf.level conf.low conf.high n.obs expression
#>        <dbl>    <dbl>     <dbl> <int> <list>    
#> 1       0.95   -0.755     0.123   150 <language>

# ----------------------- Bayesian -------------------------------------

# between-subjects
oneway_anova(
  data = mtcars,
  x    = cyl,
  y    = wt,
  type = "bayes"
)
#> # A tibble: 6 × 17
#>   term     pd prior.distribution prior.location prior.scale   bf10
#>   <chr> <dbl> <chr>                       <dbl>       <dbl>  <dbl>
#> 1 mu    1     cauchy                          0       0.707 20968.
#> 2 cyl-4 1     cauchy                          0       0.707 20968.
#> 3 cyl-6 0.552 cauchy                          0       0.707 20968.
#> 4 cyl-8 1     cauchy                          0       0.707 20968.
#> 5 sig2  1     cauchy                          0       0.707 20968.
#> 6 g_cyl 1     cauchy                          0       0.707 20968.
#>   method                          log_e_bf10 effectsize         estimate std.dev
#>   <chr>                                <dbl> <chr>                 <dbl>   <dbl>
#> 1 Bayes factors for linear models       9.95 Bayesian R-squared    0.577  0.0869
#> 2 Bayes factors for linear models       9.95 Bayesian R-squared    0.577  0.0869
#> 3 Bayes factors for linear models       9.95 Bayesian R-squared    0.577  0.0869
#> 4 Bayes factors for linear models       9.95 Bayesian R-squared    0.577  0.0869
#> 5 Bayes factors for linear models       9.95 Bayesian R-squared    0.577  0.0869
#> 6 Bayes factors for linear models       9.95 Bayesian R-squared    0.577  0.0869
#>   conf.level conf.low conf.high conf.method n.obs expression
#>        <dbl>    <dbl>     <dbl> <chr>       <int> <list>    
#> 1       0.95    0.379     0.707 HDI            32 <language>
#> 2       0.95    0.379     0.707 HDI            32 <language>
#> 3       0.95    0.379     0.707 HDI            32 <language>
#> 4       0.95    0.379     0.707 HDI            32 <language>
#> 5       0.95    0.379     0.707 HDI            32 <language>
#> 6       0.95    0.379     0.707 HDI            32 <language>

# within-subjects design
oneway_anova(
  data       = iris_long,
  x          = condition,
  y          = value,
  subject.id = id,
  paired     = TRUE,
  type       = "bayes"
)
#> Multiple `BFBayesFactor` models detected - posteriors are extracted from
#>   the first numerator model.
#>   See help("get_parameters", package = "insight").
#> # A tibble: 8 × 19
#>   term                      pd prior.distribution prior.location prior.scale
#>   <chr>                  <dbl> <chr>                       <dbl>       <dbl>
#> 1 mu                         1 cauchy                          0       0.707
#> 2 condition-Petal.Length     1 cauchy                          0       0.707
#> 3 condition-Petal.Width      1 cauchy                          0       0.707
#> 4 condition-Sepal.Length     1 cauchy                          0       0.707
#> 5 condition-Sepal.Width      1 cauchy                          0       0.707
#> 6 sig2                       1 cauchy                          0       1    
#> 7 g_condition                1 cauchy                          0       1    
#> 8 g_.rowid                   1 cauchy                          0       1    
#>   effect     bf10 method                          log_e_bf10 effectsize        
#>   <chr>     <dbl> <chr>                                <dbl> <chr>             
#> 1 fixed  1.55e182 Bayes factors for linear models       420. Bayesian R-squared
#> 2 fixed  1.55e182 Bayes factors for linear models       420. Bayesian R-squared
#> 3 fixed  1.55e182 Bayes factors for linear models       420. Bayesian R-squared
#> 4 fixed  1.55e182 Bayes factors for linear models       420. Bayesian R-squared
#> 5 fixed  1.55e182 Bayes factors for linear models       420. Bayesian R-squared
#> 6 fixed  1.55e182 Bayes factors for linear models       420. Bayesian R-squared
#> 7 fixed  1.55e182 Bayes factors for linear models       420. Bayesian R-squared
#> 8 fixed  1.55e182 Bayes factors for linear models       420. Bayesian R-squared
#>   estimate std.dev conf.level conf.low conf.high conf.method component   n.obs
#>      <dbl>   <dbl>      <dbl>    <dbl>     <dbl> <chr>       <chr>       <int>
#> 1    0.818 0.00846       0.95    0.801     0.834 HDI         conditional   150
#> 2    0.818 0.00846       0.95    0.801     0.834 HDI         conditional   150
#> 3    0.818 0.00846       0.95    0.801     0.834 HDI         conditional   150
#> 4    0.818 0.00846       0.95    0.801     0.834 HDI         conditional   150
#> 5    0.818 0.00846       0.95    0.801     0.834 HDI         conditional   150
#> 6    0.818 0.00846       0.95    0.801     0.834 HDI         conditional   150
#> 7    0.818 0.00846       0.95    0.801     0.834 HDI         conditional   150
#> 8    0.818 0.00846       0.95    0.801     0.834 HDI         conditional   150
#>   expression
#>   <list>    
#> 1 <language>
#> 2 <language>
#> 3 <language>
#> 4 <language>
#> 5 <language>
#> 6 <language>
#> 7 <language>
#> 8 <language>