Performs omnibus tests to evaluate overall differences between three or more groups. Automatically selects the appropriate statistical test based on data characteristics and assumption testing. Supports both independent groups and repeated measures designs. Tests include one-way ANOVA, repeated measures ANOVA, Kruskal-Wallis test, and Friedman test. Performs comprehensive assumption checking (normality, homogeneity of variance, sphericity) and post-hoc testing when significant results are detected.
Usage
omnibus(
data,
y,
x,
paired_by = NULL,
alpha = 0.05,
p_method = "holm",
na.action = "na.omit"
)
# S3 method for class 'omnibus'
print(x, ...)Arguments
- data
Dataframe containing the variables to be analyzed. Data must be in long format with one row per observation.
- y
Character string indicating the dependent variable (outcome).
- x
An object of class "omnibus".
- paired_by
Character string indicating the source of repeated measurements. If provided, a repeated measures design is assumed. If NULL, independent groups design is assumed. Default: NULL.
- alpha
Numeric value indicating the significance level for hypothesis tests. Default: 0.05.
- p_method
Character string indicating the method for p-value adjustment in post-hoc multiple comparisons to control for Type I error inflation. Options: "holm" (Holm), "hochberg" (Hochberg), "hommel" (Hommel), "bonferroni" (Bonferroni), "BH" (Benjamini-Hochberg), "BY" (Benjamini-Yekutieli), "none" (no adjustment). Default: "holm".
- na.action
Character string indicating the action to take if NAs are present ("na.omit" or "na.exclude"). Default: "na.omit"
- ...
Further arguments passed to or from other methods.
Value
An object of class "omnibus" containing the formula, statistic summary, name of the test performed, value of the test statistic, p value, alpha, the results of the post-hoc test and assumptions, the sample size's coefficient of variance, and corresponding degrees of freedom.
References
Blanca, M., Alarcón, R., Arnau, J. et al. Effect of variance ratio on ANOVA robustness: Might 1.5 be the limit?. Behav Res. 2017 Jun 22; 50:937–962. https://doi.org/10.3758/s13428-017-0918-2 Field, A., Miles, J., & Field, Z. (2012). Discovering Statistics Using R. London: SAGE Publications.
Examples
# Simulated clinical data with multiple treatment arms and visits
clinical_df <- clinical_data(n = 300, visits = 6, arms = c("A", "B", "C"))
# Compare numerical variable across treatments
omnibus(data = clinical_df, y = "biomarker", x = "treatment")
#>
#> Omnibus Test: One-way ANOVA
#>
#> Assumption Testing Results:
#>
#> Normality (Shapiro-Wilk Test):
#> A: W = 0.9976, p = 0.571
#> B: W = 0.9974, p = 0.633
#> C: W = 0.9980, p = 0.556
#> Overall result: Normal distribution assumed.
#>
#> Homogeneity of Variance (Bartlett Test):
#> Chi-squared(2) = 0.7143, p = 0.700
#> Effect size (Cramer's V) = 0.0141
#> Result: Homogeneous variances.
#>
#> Test Results:
#> Formula: biomarker ~ treatment
#> alpha: 0.05
#> Result: significant (p = <0.001)
#>
#> Post-hoc Multiple Comparisons
#>
#> Tukey Honest Significant Differences (alpha: 0.050):
#> Comparison Diff Lower Upper p-adj
#> ---------------------------------------------------------
#> B - A -1.982 -3.368 -0.596 0.002*
#> C - A -5.698 -6.966 -4.430 <0.001*
#> C - B -3.716 -5.045 -2.387 <0.001*
#>
#> The study groups show a moderately imbalanced distribution of sample sizes (Δn = 0.206).
#>
# Filter simulated data to just one treatment
clinical_df_A <- clinical_df[clinical_df$treatment == "A", ]
# Compare numerical variable changes across visits
omnibus(y = "biomarker", x = "visit", data = clinical_df_A, paired_by = "participant_id")
#>
#> Omnibus Test: Repeated measures ANOVA
#>
#> Assumption Testing Results:
#>
#> Sphericity (Mauchly Test):
#> W = 0.8528, p = 0.368
#> Result: Sphericity assumed.
#>
#> Normality (Shapiro-Wilk Test):
#> 1: W = 0.9815, p = 0.183
#> 2: W = 0.9803, p = 0.150
#> 3: W = 0.9787, p = 0.113
#> 4: W = 0.9943, p = 0.956
#> 5: W = 0.9890, p = 0.602
#> 6: W = 0.9880, p = 0.519
#> Overall result: Normal distribution assumed.
#>
#> Homogeneity of Variance (Bartlett Test):
#> Chi-squared(5) = 2.7023, p = 0.746
#> Effect size (Cramer's V) = 0.0303
#> Result: Homogeneous variances.
#>
#> Test Results:
#> Formula: biomarker ~ visit + Error(participant_id/visit)
#> alpha: 0.05
#> Result: not significant (p = 0.344)
#> Post-hoc tests not performed (results not significant).
#>
#> The study groups show a moderately imbalanced distribution of sample sizes (Δn = 0.199).
#>