One-Way ANOVA
The Analysis of Variance (ANOVA) is used to explore the relationship between a continuous dependent variable, and one or more categorical explanatory variables. This ‘One-Way ANOVA’ is a simplified version of the ‘normal’ ANOVA, allowing only a single explanatory factor, however also providing a Welch’s ANOVA. The Welch’s ANOVA has the advantage that it need not assume that the variances of all groups are equal.
For convenience, this method allows specifying multiple dependent variables, resulting in multiple independent tests.
Note that the Welch’s ANOVA is the same procedure as the Welch’s independent samples t-test.
Example usage
data('ToothGrowth')
dat <- ToothGrowth
dat$dose <- factor(dat$dose)
anovaOneW(formula = len ~ dose, data = dat)
#
# ONE-WAY ANOVA
#
# One-Way ANOVA (Welch's)
# ────────────────────────────────────────
# F df1 df2 p
# ────────────────────────────────────────
# len 68.4 2 37.7 < .001
# ────────────────────────────────────────
#
Arguments
| data | the data as a data frame |
| deps | a string naming the dependent variables in data |
| group | a string naming the grouping or independent variable in data |
| welchs | TRUE (default) or FALSE, perform Welch's one-way ANOVA which does not assume equal variances |
| fishers | TRUE or FALSE (default), perform Fisher's one-way ANOVA which assumes equal variances |
| miss | 'perAnalysis' or 'listwise', how to handle missing values; 'perAnalysis' excludes missing values for individual dependent variables, 'listwise' excludes a row from all analyses if one of its entries is missing. |
| desc | TRUE or FALSE (default), provide descriptive statistics |
| descPlot | TRUE or FALSE (default), provide descriptive plots |
| norm | TRUE or FALSE (default), perform Shapiro-Wilk test of normality |
| TRUE or FALSE (default), provide a Q-Q plot of residuals | |
| eqv | TRUE or FALSE (default), perform Levene's test for homogeneity of variances |
| phMethod | 'none', 'gamesHowell' or 'tukey', which post-hoc tests to provide; 'none' shows no post-hoc tests, 'gamesHowell' shows Games-Howell post-hoc tests where no equivalence of variances is assumed, and 'tukey' shows Tukey post-hoc tests where equivalence of variances is assumed |
| phMeanDif | TRUE (default) or FALSE, provide mean differences for post-hoc tests |
| phSig | TRUE (default) or FALSE, provide significance levels for post-hoc tests |
| phTest | TRUE or FALSE (default), provide test results (t-value and degrees of freedom) for post-hoc tests |
| phFlag | TRUE or FALSE (default), flag significant post-hoc comparisons |
Returns
A results object containing:
| results$anova | a table |
| results$desc | a table |
| results$assump$norm | a table |
| results$assump$eqv | a table |
| results$plots | an array of groups |
| results$postHoc | an array of tables |
Tables can be converted to data frames with asDF or as.data.frame(). For example:
results$anova$asDF
as.data.frame(results$anova)
Elements in arrays can be accessed with [[n]]. For example:
results$plots[[1]] # accesses the first element