Shapiro-Francia Test
A simplified version of the Shapiro-Wilk test that uses simpler weights and is computationally more efficient while maintaining good statistical power.
Shapiro-Francia Test Overview & Methodology
Similar to Shapiro-Wilk, it examines the correlation between the sample data and normal scores, but uses simplified weights that make computation faster and more straightforward. The test statistic W' measures how well the data fits a normal distribution pattern.
Strengths:
- • Simpler computation than Shapiro-Wilk
- • Good statistical power
- • Faster processing
- • Reliable for moderate sample sizes
- • Less complex implementation
Limitations:
- • Slightly less powerful than Shapiro-Wilk
- • Still limited to smaller samples
- • Less commonly available in software
- • Fewer critical value tables
Shapiro-Francia test statistic
= simplified expected normal order statistics
x(i)
= i-th order statistic (sorted sample value)
= sample mean
W' close to 1 indicates good agreement with normality; smaller values suggest departure.
W' Statistic & Correlation Focus
Shapiro-Francia is derived from the squared correlation between the ordered sample values and the expected normal order statistics, using simplified (uncorrelated) weights rather than the full covariance-based weights of Shapiro-Wilk.
Approximate normalized test statistic
= sample size
= Shapiro-Francia statistic
The normalized statistic is compared to the standard normal distribution to obtain a p-value.
Reading the Shapiro-Francia Probability Plot
Example Result & Signal Interpretation
For a sample of 22 measurements, suppose W'=0.974 withp=0.63.
Consistent with Normality
- • p > 0.05: fail to reject normality
- • W' close to 1
- • Proceed with parametric methods
Departure from Normality
- • p ≤ 0.05: reject normality
- • W' notably below 1
- • Consider transformation or non-parametric tests
sixsigmacenter.com Implementation Guide
This platform provides Shapiro-Francia test analysis with automated calculations and interpretation guidance, serving as an efficient alternative to Shapiro-Wilk for computational efficiency.
Sample Size Guidelines:
- • n = 5-50: Excellent performance
- • n = 50-500: Good results
- • n > 500: Consider alternatives
- • Minimum n = 5
Decision Rules:
- • p > 0.05: Fail to reject normality
- • p ≤ 0.05: Reject normality
- • W' close to 1: More normal
- • W' significantly < 1: Non-normal
Platform Implementation:
The sixsigmacenter.com platform automatically performs Shapiro-Francia test calculations with proper coefficient handling, eliminating manual computation complexity and ensuring accurate results.
Example Data Layout for Shapiro-Francia Test
Single column of continuous data for efficient normality testing with simplified computation. Sample Size Recommendation: Minimum 5-50 observations for optimal performance - Shapiro-Francia is designed as a computationally efficient alternative to Shapiro-Wilk for small to medium samples.
This is how your spreadsheet or CSV file should be structured before you upload it. Match the column names, keep one row per observation, and leave the analysis to the platform.