Cronbach’s Alpha Calculator

Cronbach's Alpha

Item 1 (Question 1)

Item 2 (Question 2)

Item 3 (Question 3)

Item 4 (Question 4)

Psychometric Reliability Analysis

What Is Cronbach's Alpha?

Cronbach's Alpha ($\alpha$) is a measure of internal consistency reliability. It assesses how closely related a set of survey questions, questionnaire scale items, or test sub-components are as a unified construct.

Alpha values range from 0 to 1 (values above 0.70 are generally deemed acceptable in social science research, while $\ge 0.80$ is good for diagnostic scales). Negative values typically indicate unreversed reverse-coded items.

When to Use It

Survey & Likert Scales: Validating whether multi-item scales measure a single underlying latent variable.
Dissertation & Thesis Research: Confirming questionnaire construct reliability before running SEM or regression.
Scale Refinement: Identifying low-performing questions using Alpha if Item Deleted diagnostics.
Psychometric Testing: Evaluating the test-retest and internal consistency of educational and clinical instruments.

The Mathematical Formulas

$$\alpha = \frac{k}{k - 1} \left( 1 - \frac{\sum_{i=1}^k s_i^2}{s_X^2} \right)$$ $$\alpha_{\text{standardized}} = \frac{k \bar{r}}{1 + (k - 1)\bar{r}}$$ $$s_i^2 = \frac{1}{n-1}\sum_{j=1}^n (y_{ij} - \bar{y}_i)^2, \quad s_X^2 = \frac{1}{n-1}\sum_{j=1}^n (X_j - \bar{X})^2$$

Where $k$ is the number of items, $n$ is the number of respondents, $s_i^2$ is the sample variance of item $i$, $s_X^2$ is the sample variance of the total composite score $X_j = \sum y_{ij}$, and $\bar{r}$ is the average inter-item correlation.

Worked Example

Scenario: 5 respondents complete a 4-item questionnaire ($k = 4, n = 5$).

Step 1: Compute Item Variances ($s_i^2$):
$s_1^2 = 0.7000, \quad s_2^2 = 0.8000, \quad s_3^2 = 0.3000, \quad s_4^2 = 0.5000$
$\sum s_i^2 = 0.70 + 0.80 + 0.30 + 0.50 = 2.3000$.

Step 2: Total Scores ($X_j$) & Composite Variance ($s_X^2$):
Totals: $[16, 18, 12, 17, 18], \quad \bar{X} = 16.20, \quad s_X^2 = 6.2000$.

Step 3: Calculate Cronbach's Alpha:
$\alpha = \frac{4}{4 - 1}\left(1 - \frac{2.3000}{6.2000}\right) = \frac{4}{3}(1 - 0.3710) = 1.3333 \times 0.6290 = 0.8387$.

Conclusion: $\alpha = 0.8387$ demonstrates Good internal reliability for the 4-item scale.

Computation Complete

Reliability Results

Computed Cronbach's Alpha (Raw)

α = 0.8387

Good Internal Consistency Reliability

Standardized Alpha 0.8409

Number of Items (k) 4

Sample Size (n) 5

Sum of Item Var (Σsᵢ²) 2.3000

Total Variance (sₓ²) 6.2000

Mean Inter-Item r 0.5684

Step-by-Step Calculation

Item-Total Statistics & Diagnostics

Item	Scale Mean if Deleted	Scale Var if Deleted	Corrected Item-Total r	Cronbach's α if Deleted

Cronbach’s Alpha Calculator

Cronbach's Alpha

Reliability Results

Step-by-Step Calculation

Item-Total Statistics & Diagnostics

Interpretation

Internal Consistency Benchmark Gauge

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