mariposa (version 0.7.3)

reliability: Check How Reliably Your Scale Measures a Concept

Description

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.

Usage

reliability(data, ..., weights = NULL, na.rm = TRUE)

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.

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).

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:

1. Select your items

2. Check reliability

3. If acceptable (alpha > .70), create the index

4. 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)

# With survey weights
reliability(survey_data, trust_government, trust_media, trust_science,
            weights = sampling_weight)

# Using tidyselect helpers
reliability(survey_data, starts_with("trust"))

# Grouped by region
survey_data %>%
  group_by(region) %>%
  reliability(trust_government, trust_media, trust_science)

# --- Three-layer output ---
result <- reliability(survey_data, trust_government, trust_media, trust_science)
result              # compact one-line overview
summary(result)     # full detailed output with all sections
summary(result, inter_item_correlations = FALSE)  # hide correlations