ancova() tests whether group means differ after controlling for one or
more continuous covariates. It performs a factorial ANCOVA using Type III Sum of
Squares, matching SPSS UNIANOVA output with the WITH keyword.
Think of it as:
An ANOVA that removes the effect of confounding variables first
Testing group differences on "adjusted" means
Combining regression (covariates) and ANOVA (factors) in one model
The test tells you:
Whether each factor has a significant effect AFTER controlling for covariates
The relationship between each covariate and the outcome
Effect sizes for factors and covariates (partial eta squared)
Estimated marginal means (group means adjusted for covariates)
Arguments
- data
Your survey data (a data frame or tibble)
- dv
The numeric dependent variable to analyze (unquoted)
- between
Character vector or unquoted variable names specifying the between-subjects factors (1-3 factors). These must be categorical variables (factor, character, or labelled numeric).
- covariate
Unquoted variable names of the continuous covariates to control for. Use
c(age, income)for multiple covariates.- weights
Optional survey weights for population-representative results (unquoted variable name)
- ss_type
Type of Sum of Squares: 3 (default, SPSS standard) or 2. Type III is recommended for unbalanced designs.
Value
An object of class "ancova" containing:
- anova_table
Tibble with Source, SS, df, MS, F, p, Partial Eta Squared
- parameter_estimates
Tibble with regression coefficients (B, SE, t, p)
- descriptives
Tibble with unadjusted cell means, SDs, and Ns
- estimated_marginal_means
Tibble with adjusted means (covariates at grand mean)
- levene_test
Tibble with Levene's test results
- r_squared
R-squared and Adjusted R-squared
- model
The underlying lm model object
- call_info
List with metadata (dv, factors, covariates, weighted, etc.)
Use summary() for the full SPSS-style output with toggleable sections.
Details
Understanding the Results
Adjusted Means (Estimated Marginal Means): These are the group means after statistically removing the effect of the covariate(s). They answer: "What would the group means be if all groups had the same covariate values?"
Covariate Effects: The covariate row in the ANOVA table shows whether the covariate significantly predicts the DV after adjusting for the factors.
Factor Effects: These show whether the factor affects the DV after controlling for the covariate. This is the primary test of interest.
Partial Eta Squared (Effect Size):
Less than 0.01: Negligible
0.01 to 0.06: Small
0.06 to 0.14: Medium
0.14 or greater: Large
When to Use This
Use ANCOVA when:
You have group comparisons (ANOVA) but want to control for a confound
Your covariate is continuous and linearly related to the DV
You want to increase statistical power by removing known variance sources
The covariate's relationship with the DV is the same across groups (homogeneity of regression slopes assumption)
References
Huitema, B. E. (2011). The Analysis of Covariance and Alternatives (2nd ed.). Wiley.
IBM Corp. (2023). IBM SPSS Statistics 29 Algorithms. IBM Corporation.
See also
factorial_anova for ANOVA without covariates.
linear_regression for regression analysis.
oneway_anova for single-factor ANOVA.
summary.ancova for detailed output with toggleable sections.
Other hypothesis_tests:
binomial_test(),
chi_square(),
chisq_gof(),
factorial_anova(),
fisher_test(),
friedman_test(),
kruskal_wallis(),
mann_whitney(),
mcnemar_test(),
oneway_anova(),
t_test(),
wilcoxon_test()
Examples
# Load required packages and data
library(dplyr)
#>
#> Attaching package: ‘dplyr’
#> The following objects are masked from ‘package:stats’:
#>
#> filter, lag
#> The following objects are masked from ‘package:base’:
#>
#> intersect, setdiff, setequal, union
data(survey_data)
# One-way ANCOVA: income by education, controlling for age
survey_data %>%
ancova(dv = income, between = c(education), covariate = c(age))
#> ANCOVA: income by education, covariate: age
#> age (covariate): F(1, 2181) = 0.030, p = 0.862 , eta2p = 0.000
#> education: F(3, 2181) = 466.246, p < 0.001 ***, eta2p = 0.391, N = 2186
# Two-way ANCOVA with weights
survey_data %>%
ancova(dv = income, between = c(gender, education),
covariate = c(age), weights = sampling_weight)
#> ANCOVA: income by gender, education, covariate: age [Weighted]
#> age (covariate): F(1, 2177) = 0.013, p = 0.911 , eta2p = 0.000
#> gender: F(1, 2177) = 0.115, p = 0.735 , eta2p = 0.000
#> education: F(3, 2177) = 455.614, p < 0.001 ***, eta2p = 0.386
#> gender:education: F(3, 2177) = 0.298, p = 0.827 , eta2p = 0.000, N = 2186
# Multiple covariates
survey_data %>%
ancova(dv = income, between = c(education),
covariate = c(age, political_orientation))
#> ANCOVA: income by education, covariate: age, political_orientation
#> age (covariate): F(1, 2002) = 0.018, p = 0.895 , eta2p = 0.000
#> political_orientation (covariate): F(1, 2002) = 1.366, p = 0.243 , eta2p = 0.001
#> education: F(3, 2002) = 419.350, p < 0.001 ***, eta2p = 0.386, N = 2008
# --- Three-layer output ---
result <- ancova(survey_data, dv = income, between = c(education),
covariate = c(age))
result # compact overview
#> ANCOVA: income by education, covariate: age
#> age (covariate): F(1, 2181) = 0.030, p = 0.862 , eta2p = 0.000
#> education: F(3, 2181) = 466.246, p < 0.001 ***, eta2p = 0.391, N = 2186
summary(result) # full detailed output with all sections
#> ANCOVA (One-Way ANCOVA) Results
#> -------------------------------
#>
#> - Dependent variable: income
#> - Factor(s): education
#> - Covariate(s): age
#> - Type III Sum of Squares: Type 3
#> - N (complete cases): 2186
#> - Missing: 314
#>
#> Tests of Between-Subjects Effects
#> -----------------------------------------------------------------------------
#> Source Type III SS df Mean Square F Sig. Partial Eta Sq
#> Corrected Model 1.752821e+09 4 4.382053e+08 349.723 <.001 0.391
#> Intercept 3.472401e+09 1 3.472401e+09 2771.252 <.001 0.560
#> age 3.772141e+04 1 3.772141e+04 0.030 0.862 0.000
#> education 1.752631e+09 3 5.842102e+08 466.246 <.001 0.391
#> Error 2.732810e+09 2181 1.253008e+06
#> Total 3.529079e+10 2186
#> Corrected Total 4.485631e+09 2185
#>
#> ***
#> ***
#>
#> ***
#>
#>
#>
#> -----------------------------------------------------------------------------
#> R Squared = 0.391 (Adjusted R Squared = 0.390)
#>
#> Parameter Estimates
#> ---------------------------------------------------------------------
#> Parameter B Std. Error t Sig. Lower Bound Upper Bound
#> (Intercept) 3990.641 75.806 52.643 <.001 3841.981 4139.301
#> age -0.245 1.412 -0.174 0.862 -3.014 2.524
#> education.L 1870.578 50.838 36.795 <.001 1770.881 1970.274
#> education.Q 139.427 49.566 2.813 0.005 42.226 236.629
#> education.C 152.695 48.167 3.170 0.002 58.236 247.154
#> Partial Eta Sq
#> 0.560
#> 0.000
#> 0.383
#> 0.004
#> 0.005
#> ---------------------------------------------------------------------
#>
#> Estimated Marginal Means
#> (Evaluated at covariate means)
#> -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
#> education Mean Std. Error Lower Bound Upper Bound
#> Basic Secondary 2758.939 41.294 2677.960 2839.918
#> Intermediate Secondary 3592.634 47.822 3498.852 3686.416
#> Academic Secondary 4224.320 47.836 4130.511 4318.130
#> University 5336.870 59.438 5220.309 5453.431
#> -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
#>
#> Levene's Test of Equality of Error Variances
#> F(3, 2182) = 103.901, p = <.001
#>
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05
summary(result, marginal_means = FALSE) # hide estimated marginal means
#> ANCOVA (One-Way ANCOVA) Results
#> -------------------------------
#>
#> - Dependent variable: income
#> - Factor(s): education
#> - Covariate(s): age
#> - Type III Sum of Squares: Type 3
#> - N (complete cases): 2186
#> - Missing: 314
#>
#> Tests of Between-Subjects Effects
#> -----------------------------------------------------------------------------
#> Source Type III SS df Mean Square F Sig. Partial Eta Sq
#> Corrected Model 1.752821e+09 4 4.382053e+08 349.723 <.001 0.391
#> Intercept 3.472401e+09 1 3.472401e+09 2771.252 <.001 0.560
#> age 3.772141e+04 1 3.772141e+04 0.030 0.862 0.000
#> education 1.752631e+09 3 5.842102e+08 466.246 <.001 0.391
#> Error 2.732810e+09 2181 1.253008e+06
#> Total 3.529079e+10 2186
#> Corrected Total 4.485631e+09 2185
#>
#> ***
#> ***
#>
#> ***
#>
#>
#>
#> -----------------------------------------------------------------------------
#> R Squared = 0.391 (Adjusted R Squared = 0.390)
#>
#> Parameter Estimates
#> ---------------------------------------------------------------------
#> Parameter B Std. Error t Sig. Lower Bound Upper Bound
#> (Intercept) 3990.641 75.806 52.643 <.001 3841.981 4139.301
#> age -0.245 1.412 -0.174 0.862 -3.014 2.524
#> education.L 1870.578 50.838 36.795 <.001 1770.881 1970.274
#> education.Q 139.427 49.566 2.813 0.005 42.226 236.629
#> education.C 152.695 48.167 3.170 0.002 58.236 247.154
#> Partial Eta Sq
#> 0.560
#> 0.000
#> 0.383
#> 0.004
#> 0.005
#> ---------------------------------------------------------------------
#>
#> Levene's Test of Equality of Error Variances
#> F(3, 2182) = 103.901, p = <.001
#>
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05