# Table 2 Overview of the statistical approach, criteria, and results of the Rasch analysis of the LFS short form scale when used with people with stroke and osteoarthritis (n = 525)

Aspect of validity evidence measuredStatistical approach and criteriaInitial LFS short form scale (5 items)Final LFS short form scale (3 items)
Step 1:
Evidence based on internal structure
Rating scale functioning
The average measures for each response category should advance monotonically, with outfit MnSq values < 2.0 for each of the step calibrations
Criteria were metCriteria were met
Step 2:
Evidence based on internal structure (item misfit)
Item goodness-of-fit statistics
A sample-size adjusted criterion for item goodness-of-fit requiring infit MnSq values between 0.7 and 1.3
#17 close eyes: MnSq = 1.78
#16 conversation: MnSq = 1.42
#5 worn out: MnSq = 0.75
#1 tired: MnSq = 0.67
#4 fatigued: MnSq = 0.66
#5 worn out: MnSq = 1.02
#1 tired: MnSq = 1.10
#4 fatigued: MnSq = 0.80
Step 3:
Evidence based on internal structure (unidimensionality)
Principal component analysis of the residuals
The criterion was set for at least 50% of the total variance to be explained by the first latent variable
63.2%81.6%
Step 4:
Evidence based on response processes
Person goodness-of-fit statistics
A criterion of < 5% of the sample has unacceptable person goodness-of-fit, as indicated by infit MnSq values < 1.4 and standardized z values < 2.0.
24 (4.6%)29 (5.6%)
Floor and ceiling effects
A criterion of up to 10% of the sample could demonstrate minimum or maximum scores.
Maximum score = None
Minimum score = 77 (14.0%)
Maximum score = 3 (0.6%)
Minimum score = 88 (16.9%)
Step 5:
Item stability
Differential item functioning (DIF)
No Mantel-Haenzel statistics have a p < .01.
Items 4 and 5 demonstrated DIF by diagnosisNo item demonstrated DIF by diagnosis
Step 6:
Person-separation reliability
Person-separation index
An index of > 2.0 was required to ensure that the scale could differentiate the sample into at least three different levels of fatigue severity
Separation index = 1.82Separation index = 2.49
Step 7:
Internal consistency
Person reliability (Rasch)
Cronbach’s alpha coefficient (Cr-α) (raw scores)
Relationship between individual sum scores and Rasch-based measures
The criterion was that all values should be > 0.80
Person reliability (Rasch) = .77
Cr-α (raw score) = .87
Correlation between sum scores and Rasch measures = .91
Person reliability (Rasch) = .89
Cr-α (raw score) = .91
Correlations between sum scores and Rasch measures = .98
1. MnSq Mean sq