reliability() calculates Cronbach's Alpha, McDonald's Omega, and
detailed item statistics to evaluate whether your survey items form a
reliable scale. This is the R
equivalent of SPSS's RELIABILITY /MODEL=ALPHA /STATISTICS=DESCRIPTIVE CORR
/SUMMARY=TOTAL.
For example, if you have 3 items measuring "trust", reliability analysis tells you whether these items consistently measure the same concept.
Arguments
- data
Your survey data (a data frame or tibble)
- ...
The items to analyze. Use bare column names separated by commas, or tidyselect helpers like
starts_with("trust").- weights
Optional survey weights for population-representative results
- na.rm
Remove missing values before calculating? (Default: TRUE). Uses listwise deletion (only complete cases across all items).
Value
A reliability result object containing:
- alpha
Cronbach's Alpha (unstandardized)
- alpha_standardized
Cronbach's Alpha based on standardized items
- omega
McDonald's Omega (raw/total, one-factor ML model; NA for fewer than 3 items)
- omega_std
Standardized Omega (correlation metric)
- n_items
Number of items in the scale
- item_statistics
Mean, SD, and N for each item
- item_total
Corrected Item-Total Correlation, Alpha if Item Deleted, and Omega if Item Deleted
- inter_item_cor
Inter-item correlation matrix
- n
Sample size (listwise)
Use summary() for the full SPSS-style output with toggleable sections.
Details
Understanding the Results
Cronbach's Alpha tells you how internally consistent your scale is:
Alpha > 0.90: Excellent reliability
Alpha 0.80 - 0.90: Good reliability
Alpha 0.70 - 0.80: Acceptable reliability
Alpha 0.60 - 0.70: Questionable reliability
Alpha < 0.60: Poor reliability - reconsider items
Item-Total Correlation shows how well each item fits the scale:
Values > 0.40: Item fits well
Values 0.20 - 0.40: Item may need review
Values < 0.20: Consider removing the item
Alpha if Item Deleted shows what happens if you remove an item:
If alpha increases when removing an item, that item hurts reliability
If alpha decreases, the item contributes to the scale
McDonald's Omega
McDonald's Omega (omega total) is a factor-model-based reliability coefficient. Where alpha assumes every item measures the construct equally well (tau-equivalence), omega fits a one-factor model and lets each item carry its own loading. The two agree when items are roughly tau-equivalent; omega is typically slightly higher (and the more accurate estimate) when loadings differ across items, which is the common case in survey scales (Hayes & Coutts, 2020).
reliability() reports two variants, mirroring the two alpha
variants: omega from the covariance metric (analogous to raw
alpha) and omega_std from the correlation metric (analogous to
standardized alpha). Omega if Item Deleted refits the one-factor
model without each item, mirroring Alpha if Item Deleted.
A one-factor model needs at least 3 items to be identified: with fewer
than 3 items the omega fields are NA (alpha is still computed),
and Omega if Item Deleted is NA whenever the reduced scale would
fall below 3 items.
Weighted variants and validation status
Cronbach's alpha and the item statistics are validated against SPSS v29
RELIABILITY output (weighted and unweighted). McDonald's omega is
currently an R-only statistic (Tier 4 per the Validation Charter): SPSS
offers omega from v27 onward, but IBM's algorithm documentation for it is
not publicly retrievable and no SPSS v29 reference run exists yet.
mariposa computes omega from a one-factor maximum-likelihood solution
(the same estimator family as efa with fm = "ml").
The weighted omega uses the same weighted correlation and covariance
matrices as the weighted alpha and reduces exactly to the unweighted
omega when all weights equal 1 (enforced by an internal invariance
suite); see vignette("spss-compatibility") for validation status.
When to Use This
Run reliability() before creating scale scores with
row_means:
Select your items
Check reliability
If acceptable (alpha > .70), create the index
If not, review items and consider removing problematic ones
References
McDonald, R. P. (1999). Test Theory: A Unified Treatment. Mahwah, NJ: Lawrence Erlbaum.
Hayes, A. F., & Coutts, J. J. (2020). Use omega rather than Cronbach's alpha for estimating reliability. But... Communication Methods and Measures, 14(1), 1-24.
See also
row_means for creating mean indices after checking reliability.
pearson_cor for bivariate correlations.
summary.reliability for detailed output with toggleable sections.
Other scale:
efa(),
pomps(),
row_count(),
row_means(),
row_sums()
Examples
library(dplyr)
data(survey_data)
# Check reliability of trust items
reliability(survey_data, trust_government, trust_media, trust_science)
#> Reliability Analysis: 3 items
#> Cronbach's Alpha = 0.047 (Poor), McDonald's Omega = 0.047, N = 2135
# With survey weights
reliability(survey_data, trust_government, trust_media, trust_science,
weights = sampling_weight)
#> Reliability Analysis: 3 items [Weighted]
#> Cronbach's Alpha = 0.052 (Poor), McDonald's Omega = 0.053, N = 2150
# Using tidyselect helpers
reliability(survey_data, starts_with("trust"))
#> Reliability Analysis: 3 items
#> Cronbach's Alpha = 0.047 (Poor), McDonald's Omega = 0.047, N = 2135
# Grouped by region
survey_data %>%
group_by(region) %>%
reliability(trust_government, trust_media, trust_science)
#> [region = 1]
#> Reliability Analysis: 3 items
#> Cronbach's Alpha = 0.037 (Poor), McDonald's Omega = 0.349, N = 422
#> [region = 2]
#> Reliability Analysis: 3 items
#> Cronbach's Alpha = 0.050 (Poor), McDonald's Omega = 0.071, N = 1713
# --- Three-layer output ---
result <- reliability(survey_data, trust_government, trust_media, trust_science)
result # compact one-line overview
#> Reliability Analysis: 3 items
#> Cronbach's Alpha = 0.047 (Poor), McDonald's Omega = 0.047, N = 2135
summary(result) # full detailed output with all sections
#>
#> Reliability Analysis Results
#> ----------------------------
#> - Items: trust_government, trust_media, trust_science
#> - N of Items: 3
#>
#> Reliability Statistics
#> ----------------------------------------
#> Cronbach's Alpha: 0.047
#> Alpha (standardized): 0.048
#> McDonald's Omega: 0.047
#> Omega (standardized): 0.048
#> N of Items: 3
#> N (listwise): 2135
#>
#> Item Statistics
#> ----------------------------------------
#> item mean sd n
#> trust_government 2.621 1.162 2135
#> trust_media 2.430 1.156 2135
#> trust_science 3.624 1.034 2135
#>
#> Inter-Item Correlation Matrix:
#> ------------------------------
#> trust_government trust_media trust_science
#> trust_government 1.000 0.014 0.020
#> trust_media 0.014 1.000 0.015
#> trust_science 0.020 0.015 1.000
#> ------------------------------
#>
#> Item-Total Statistics
#> ----------------------------------------
#> item scale_mean_deleted scale_var_deleted corrected_r
#> trust_government 6.05 2.440 0.024
#> trust_media 6.25 2.467 0.020
#> trust_science 5.05 2.723 0.025
#> alpha_deleted omega_deleted
#> 0.029 NA
#> 0.040 NA
#> 0.027 NA
#> Note: Omega if item deleted requires at least 4 items
#> (a one-factor model on the remaining 2 items is not identified).
summary(result, inter_item_correlations = FALSE) # hide correlations
#>
#> Reliability Analysis Results
#> ----------------------------
#> - Items: trust_government, trust_media, trust_science
#> - N of Items: 3
#>
#> Reliability Statistics
#> ----------------------------------------
#> Cronbach's Alpha: 0.047
#> Alpha (standardized): 0.048
#> McDonald's Omega: 0.047
#> Omega (standardized): 0.048
#> N of Items: 3
#> N (listwise): 2135
#>
#> Item Statistics
#> ----------------------------------------
#> item mean sd n
#> trust_government 2.621 1.162 2135
#> trust_media 2.430 1.156 2135
#> trust_science 3.624 1.034 2135
#>
#> Item-Total Statistics
#> ----------------------------------------
#> item scale_mean_deleted scale_var_deleted corrected_r
#> trust_government 6.05 2.440 0.024
#> trust_media 6.25 2.467 0.020
#> trust_science 5.05 2.723 0.025
#> alpha_deleted omega_deleted
#> 0.029 NA
#> 0.040 NA
#> 0.027 NA
#> Note: Omega if item deleted requires at least 4 items
#> (a one-factor model on the remaining 2 items is not identified).