mariposa (version 0.7.3)

oneway_anova: Compare Multiple Groups: Are Their Averages Different?

Description

oneway_anova() helps you determine if average values differ across three or more groups. For example, does average income vary by education level? Or is customer satisfaction different across regions?

Think of it as:

• An extension of t-test for more than two groups

• A way to test if group membership affects outcomes

• A tool to identify meaningful group differences

The test tells you:

• Whether at least one group is different from the others

• How much variation is explained by group membership

• Which variance assumption fits your data best

Usage

oneway_anova(
  data,
  ...,
  group,
  weights = NULL,
  var.equal = TRUE,
  conf.level = 0.95
)

Value

ANOVA results showing whether groups differ, including:

• F-statistic (F_statistic) and p-value (are groups different?)

• Effect sizes (how much do groups matter?)

• Group statistics (means and standard deviations)

• Both standard and Welch ANOVA results Use summary() for the full SPSS-style output with toggleable sections.

Arguments

data

Your survey data (a data frame or tibble)

...

The numeric variables you want to analyze. You can list multiple variables or use helpers like starts_with("income")

group

The categorical variable that defines your groups (e.g., education, region, age_group). Must have at least 3 groups for ANOVA.

weights

Optional survey weights for population-representative results

var.equal

Deprecated and ignored (a warning is issued when set to FALSE). Like SPSS ONEWAY, the classical ANOVA table and Welch's robust test are always both computed and displayed.

conf.level

Confidence level for intervals (Default: 0.95 = 95%)

Details

Understanding the Results

P-value: If p < 0.05, at least one group average is different

• p < 0.001: Very strong evidence of group differences

• p < 0.01: Strong evidence of group differences

• p < 0.05: Moderate evidence of group differences

• p >= 0.05: No significant group differences found

Effect Sizes (How much do groups matter?):

• Eta-squared: Proportion of variance explained by groups

  • < 0.01: Negligible effect

  • 0.01-0.06: Small effect

  • 0.06-0.14: Medium effect

  • 0.14 or higher: Large effect

• Omega-squared: More conservative estimate (usually preferred)

• Omega-squared and epsilon-squared are truncated at 0; a negative raw estimate (which occurs when F < 1) is reported as 0.

When to Use This

Use ANOVA when:

• You have one numeric outcome (income, satisfaction score, etc.)

• You have one categorical grouping variable with 3+ groups

• You want to know if group averages differ

• Your data is roughly normally distributed within groups

Variance Assumptions

Like SPSS ONEWAY, both results are always shown for comparison:

• Standard ANOVA: valid when group variances are similar

• Welch's ANOVA: robust when group variances differ

• Use levene_test to check which situation applies

What Comes Next?

If ANOVA is significant:

1. Look at group means to see the pattern

2. Use tukey_test() to find which specific groups differ

3. Consider effect sizes to judge practical importance

Tips for Success

• Check that each group has sufficient observations (ideally 20+)

• Look at both p-values and effect sizes

• Use Welch's ANOVA if group sizes are very unequal

• Follow up with post-hoc tests to identify specific differences

• Welch's robust test for equality of means

References

Cohen, J. (1988). Statistical Power Analysis for the Behavioral Sciences (2nd ed.). Lawrence Erlbaum Associates.

Welch, B. L. (1951). On the comparison of several mean values: an alternative approach. Biometrika, 38(3/4), 330-336.

Olejnik, S., & Algina, J. (2003). Generalized eta and omega squared statistics: measures of effect size for some common research designs. Psychological Methods, 8(4), 434-447.

See Also

aov for the base R ANOVA function.

oneway.test for Welch's ANOVA.

tukey_test for post-hoc pairwise comparisons.

levene_test for testing homogeneity of variances.

summary.oneway_anova for detailed output with toggleable sections.

Other hypothesis_tests: ancova(), binomial_test(), chi_square(), chisq_gof(), factorial_anova(), fisher_test(), friedman_test(), kruskal_wallis(), mann_whitney(), mcnemar_test(), t_test(), wilcoxon_test()

Examples

# Load required packages and data
library(dplyr)
data(survey_data)

# Basic one-way ANOVA (comparing across education levels)
survey_data %>%
  oneway_anova(life_satisfaction, group = education)

# Multiple dependent variables
survey_data %>%
  oneway_anova(life_satisfaction, trust_government, group = education)

# Using tidyselect helpers
survey_data %>%
  oneway_anova(starts_with("trust_"), group = education)

# Weighted analysis
survey_data %>%
  oneway_anova(income, group = education, weights = sampling_weight)

# Grouped analysis (separate ANOVA for each region)
survey_data %>%
  group_by(region) %>%
  oneway_anova(life_satisfaction, group = education)

# Store results for post-hoc analysis
result <- survey_data %>%
  oneway_anova(life_satisfaction, group = education)

# Follow up with post-hoc tests
result %>% tukey_test()
result %>% levene_test()  # Check homogeneity of variances

# --- Three-layer output ---
result              # compact one-line overview
summary(result)     # full detailed output with all sections
summary(result, descriptives = FALSE)  # hide group statistics