Parametric, non-parametric, robust, and Bayesian one-way ANOVA.
Usage
oneway_anova(
data,
x,
y,
subject.id = NULL,
type = "parametric",
paired = FALSE,
digits = 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 asdata.- x
The grouping (or independent) variable from
data. In case of a repeated measures or within-subjects design, ifsubject.idargument 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 inxand there areNAs 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 isNULL(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 inxand there areNAs 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.- digits
Number of digits for rounding or significant figures. May also be
"signif"to return significant figures or"scientific"to return scientific notation. Control the number of digits by adding the value as suffix, e.g.digits = "scientific4"to have scientific notation with 4 decimal places, ordigits = "signif5"for 5 significant figures (see alsosignif()).- conf.level
Scalar between
0and1(default:95%confidence/credible intervals,0.95). IfNULL, 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
TRUEthen 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
0.5and2(default0.707), 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
robusttests. In case of an error, try reducing the value oftr, which is by default set to0.2. 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 statisticdf: the numeric value of a parameter being modeled (often degrees of freedom for the test)df.erroranddf: 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 statisticmethod: the name of the inferential statistical testestimate: estimated value of the effect sizeconf.low: lower bound for the effect size estimateconf.high: upper bound for the effect size estimateconf.level: width of the confidence intervalconf.method: method used to compute confidence intervalconf.distribution: statistical distribution for the effecteffectsize: the name of the effect sizen.obs: number of observationsexpression: 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
| Type | No. of groups | Test | Function used |
| Parametric | > 2 | Fisher's or Welch's one-way ANOVA | stats::oneway.test() |
| Non-parametric | > 2 | Kruskal-Wallis one-way ANOVA | stats::kruskal.test() |
| Robust | > 2 | Heteroscedastic one-way ANOVA for trimmed means | WRS2::t1way() |
| Bayes Factor | > 2 | Fisher's ANOVA | BayesFactor::anovaBF() |
Effect size estimation
| Type | No. of groups | Effect size | CI available? | Function used |
| Parametric | > 2 | partial eta-squared, partial omega-squared | Yes | effectsize::omega_squared(), effectsize::eta_squared() |
| Non-parametric | > 2 | rank epsilon squared | Yes | effectsize::rank_epsilon_squared() |
| Robust | > 2 | Explanatory measure of effect size | Yes | WRS2::t1way() |
| Bayes Factor | > 2 | Bayesian R-squared | Yes | performance::r2_bayes() |
within-subjects
Hypothesis testing
| Type | No. of groups | Test | Function used |
| Parametric | > 2 | One-way repeated measures ANOVA | afex::aov_ez() |
| Non-parametric | > 2 | Friedman rank sum test | stats::friedman.test() |
| Robust | > 2 | Heteroscedastic one-way repeated measures ANOVA for trimmed means | WRS2::rmanova() |
| Bayes Factor | > 2 | One-way repeated measures ANOVA | BayesFactor::anovaBF() |
Effect size estimation
| Type | No. of groups | Effect size | CI available? | Function used |
| Parametric | > 2 | partial eta-squared, partial omega-squared | Yes | effectsize::omega_squared(), effectsize::eta_squared() |
| Non-parametric | > 2 | Kendall's coefficient of concordance | Yes | effectsize::kendalls_w() |
| Robust | > 2 | Algina-Keselman-Penfield robust standardized difference average | Yes | WRS2::wmcpAKP() |
| Bayes Factor | > 2 | Bayesian R-squared | Yes | performance::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>