What is a good Cronbach's alpha value?

Generally, alpha >= .70 is acceptable for research, >= .80 is good, and >= .90 is excellent. However, values above .95 may indicate item redundancy rather than superior reliability. Always inspect the inter-item correlation matrix alongside the alpha value.

When should I use Cronbach's alpha?

Use Cronbach's alpha when you need to assess the internal consistency of a multi-item scale, such as a Likert-type questionnaire. It is essential for scale development, construct validation, and reporting measurement reliability in research papers. All items must measure the same underlying construct.

How do I report Cronbach's alpha in APA format?

APA 7th edition requires reporting the scale name, number of items, and the alpha value. For example: 'Internal consistency of the 5-item Customer Satisfaction Scale was good (α = .85).' StatMate automatically generates APA-formatted reliability results you can use directly in your manuscript.

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What is Cronbach's Alpha?

Cronbach's alpha is the most widely used statistical measure of internal consistency reliability. It evaluates how consistently a set of items designed to measure a single construct relate to one another. Alpha ranges from 0 to 1, with higher values indicating greater internal consistency among the items. The measure was introduced by Lee J. Cronbach in 1951 as a generalization of the Kuder-Richardson formula 20 (KR-20), extending reliability estimation from dichotomous items to polytomous items such as Likert scales.

The formula is: α = (k / (k − 1)) × (1 − Σσ²_i / σ²_t), where k is the number of items, σ²_i is the variance of each item, and σ²_t is the variance of total scores. When item variances are small relative to the total variance, alpha approaches 1.

Interpreting Cronbach's Alpha

George and Mallery (2003) provide the most commonly cited benchmarks:

Alpha Value	Level	Interpretation
≥ .90	Excellent	Very high internal consistency; check for redundancy if > .95
≥ .80	Good	Suitable for most research purposes
≥ .70	Acceptable	Minimum threshold for exploratory research
≥ .60	Questionable	Item revision recommended
≥ .50	Poor	Scale revision strongly recommended
< .50	Unacceptable	Scale should not be used; full reconstruction needed

Related Reliability Measures

Measure	Type	Best For
Cronbach's α	Internal consistency	Polytomous items on a single scale
Split-half	Internal consistency	Single-administration reliability with Spearman-Brown correction
Test-retest	Stability	Temporal stability over a defined interval
Inter-rater	Equivalence	Observer agreement in coding or scoring tasks

Assumptions and Cautions

1. Unidimensionality

All items should measure a single latent construct. Run exploratory or confirmatory factor analysis before computing alpha. For multidimensional scales, compute alpha per subscale.

2. Tau-equivalence

Alpha assumes equal factor loadings across items. When this assumption is violated, alpha serves as a lower bound of reliability. Consider McDonald's ω as an alternative.

3. Consistent Item Coding

All items must be coded in the same direction. Reverse-coded items must be recoded before analysis, or alpha will be artificially deflated.

4. Minimum Items (≥ 3)

Alpha is unstable with fewer than 3 items. With very many items, alpha can be inflated regardless of actual consistency. Report mean inter-item correlation (.15–.50) alongside alpha for short scales.

5. Adequate Sample Size

Aim for at least 5–10 respondents per item, with a minimum of 30 total. Small samples produce wide confidence intervals around alpha.

Reporting in APA Format

Internal consistency reliability of the Customer Satisfaction Scale was assessed using Cronbach's alpha. The 5-item scale demonstrated good reliability, α = .85. Alpha-if-item-deleted analysis indicated that all items contributed positively to scale reliability (range: .82–.84).

Common Mistakes to Avoid

Alpha too high (> .95): May indicate item redundancy rather than superior reliability. Inspect the inter-item correlation matrix for highly overlapping items.
Forgetting reverse-coded items: Failing to recode negatively worded items before analysis will drastically deflate alpha or produce a negative value.
Applying alpha to multidimensional scales: Computing a single alpha across subscales that tap different constructs distorts the reliability estimate. Report alpha per subscale instead.
Ignoring item count effects: A small number of items can depress alpha even with strong inter-item correlations. Supplement with mean inter-item correlation for short scales.
Equating reliability with validity: High alpha confirms internal consistency, not that the scale measures the intended construct. Validity requires separate evidence (e.g., convergent, discriminant, criterion validity).

Calculation Accuracy

StatMate's Cronbach's alpha calculations have been validated against R's psych::alpha() function and SPSS Reliability Analysis. Item variances use the N − 1 denominator (sample variance). Item-total correlations are corrected (item removed from total). All supplementary statistics—alpha-if-deleted, split-half reliability, and Spearman-Brown prophecy—match R and SPSS output to four decimal places.

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t検定

2群の平均値を比較

分散分析

3群以上の平均値を比較

カイ二乗検定

カテゴリ変数の関連を検定

相関分析

関係の強さを測定

記述統計

データを要約

サンプルサイズ

検出力分析・標本計画

1標本t検定

既知の値との比較

マン・ホイットニーU

ノンパラメトリック群間比較

ウィルコクソン検定

ノンパラメトリック対応検定

回帰分析

X-Yの関係をモデル化

重回帰分析

複数の予測変数

ロジスティック回帰

二値アウトカムの予測

因子分析

潜在因子構造の探索

クラスカル・ウォリス

ノンパラメトリック3群以上比較

反復測定

被験者内分散分析

二元配置分散分析

要因計画の分析

フリードマン検定

ノンパラメトリック反復測定

フィッシャーの正確検定

2×2表の正確検定

マクネマー検定

対応のある名義データの検定

What is Cronbach's Alpha?

Interpreting Cronbach's Alpha

George and Mallery (2003) provide the most commonly cited benchmarks:

Alpha Value	Level	Interpretation
≥ .90	Excellent	Very high internal consistency; check for redundancy if > .95
≥ .80	Good	Suitable for most research purposes
≥ .70	Acceptable	Minimum threshold for exploratory research
≥ .60	Questionable	Item revision recommended
≥ .50	Poor	Scale revision strongly recommended
< .50	Unacceptable	Scale should not be used; full reconstruction needed

Related Reliability Measures

Measure	Type	Best For
Cronbach's α	Internal consistency	Polytomous items on a single scale
Split-half	Internal consistency	Single-administration reliability with Spearman-Brown correction
Test-retest	Stability	Temporal stability over a defined interval
Inter-rater	Equivalence	Observer agreement in coding or scoring tasks

Assumptions and Cautions

1. Unidimensionality

All items should measure a single latent construct. Run exploratory or confirmatory factor analysis before computing alpha. For multidimensional scales, compute alpha per subscale.

2. Tau-equivalence

Alpha assumes equal factor loadings across items. When this assumption is violated, alpha serves as a lower bound of reliability. Consider McDonald's ω as an alternative.

3. Consistent Item Coding

All items must be coded in the same direction. Reverse-coded items must be recoded before analysis, or alpha will be artificially deflated.

4. Minimum Items (≥ 3)

5. Adequate Sample Size

Aim for at least 5–10 respondents per item, with a minimum of 30 total. Small samples produce wide confidence intervals around alpha.

Reporting in APA Format

Common Mistakes to Avoid

Alpha too high (> .95): May indicate item redundancy rather than superior reliability. Inspect the inter-item correlation matrix for highly overlapping items.

Forgetting reverse-coded items: Failing to recode negatively worded items before analysis will drastically deflate alpha or produce a negative value.

Applying alpha to multidimensional scales: Computing a single alpha across subscales that tap different constructs distorts the reliability estimate. Report alpha per subscale instead.

Ignoring item count effects: A small number of items can depress alpha even with strong inter-item correlations. Supplement with mean inter-item correlation for short scales.

Equating reliability with validity: High alpha confirms internal consistency, not that the scale measures the intended construct. Validity requires separate evidence (e.g., convergent, discriminant, criterion validity).