Project 2. Assessing Reliability of a Short Service Quality Scale

Background

A customer-service team piloted a three-item service-quality scale with 36 respondents across three branches. The aim is to assess whether the items are coherent enough for a pilot composite and to identify any wording or distribution problems before the study is scaled up.

Item Distributions

Table P2.1

Item descriptive statistics for the service-quality pilot

Item Mean SD Median Floor % Ceiling %
Clarity 5.08 1.38 5.0 2.8 16.7
Professionalism 4.69 1.43 5.0 8.3 11.1
Responsiveness 4.61 1.34 4.0 5.6 11.1

Note. Floor percentage is the proportion of respondents scoring at the lowest possible scale value; ceiling percentage is the proportion scoring at the highest possible scale value.

Figure P2.1: Item score distributions for the three-item service-quality scale.

The item distributions do not show severe floor or ceiling compression. With only three items, the most important checks are conceptual coherence, item-total correlations, and the width of the reliability interval.

Reliability Summary

Table P2.2

Internal-consistency summary for the short scale

Quantity Value
Cronbach's alpha 0.793
Bootstrap 95% CI 0.633 to 0.884
Mean inter-item correlation 0.564
Number of items 3
Sample size 36

Note. The confidence interval uses the asymptotic standard error reported by psych::alpha(); with n = 36 it should be treated as approximate.

The alpha estimate is acceptable for a short pilot scale, and the mean inter-item correlation is within a plausible range for a narrow construct. This does not prove unidimensionality, but it supports using a provisional composite while documenting uncertainty.

Item Diagnostics

Table P2.3

Corrected item-total diagnostics

Item Corrected item-total r Alpha if deleted Decision
Responsiveness 0.719 0.631 Retain
Professionalism 0.593 0.766 Retain
Clarity 0.601 0.755 Retain

Note. Values below about 0.30 would usually trigger a wording and content review rather than automatic deletion.

All three corrected item-total correlations exceed 0.30. The deletion diagnostics do not suggest that a single item is undermining the scale, so the next revision step should focus on respondent feedback and content coverage rather than statistical item removal.

Branch-Level Check

Table P2.4

Reliability and composite means by branch

Branch n Alpha Mean composite
East 8 0.769 4.54
North 15 0.578 5.07
South 13 0.886 4.64

Note. Branch-level alpha estimates are descriptive because each subgroup is very small.

The branch summaries are useful for screening but not for formal comparison. If one branch showed a markedly different alpha or composite mean, the appropriate response would be to inspect administration conditions and item interpretation, not to claim a branch-level psychometric difference.

Reporting Summary

The three-item pilot scale showed acceptable internal consistency, alpha = 0.793, bootstrap 95% CI [0.633, 0.884]. Corrected item-total correlations were all above 0.30. The scale can be used as a provisional pilot composite, but a larger sample and qualitative item review are still needed before treating it as an established measure.

Extension Task

Create a revised two-item version by removing one item of your choice, then recompute alpha, the mean inter-item correlation and the composite score. Write a short justification for whether the shorter version improves interpretability or merely reduces content coverage.