A To determine whether the satisfaction rating of an airline...

a To determine whether the satisfaction rating of an airline differs between business class and economy class, a survey was performed. Random samples of both groups were asked to rate their satisfaction with the quality of service using the following responses: $\bullet$ Very satisfied $\bullet$ Quite satisfied $\bullet$ Somewhat satisfied $\bullet$ Neither satisfied nor dissatisfied $\bullet$ Somewhat dissatisfied $\bullet$ Quite dissatisfied $\bullet$ Very dissatisfied The results were recorded using a 7-6-5-4-3-2-1 coding system. Can we infer that business and economy class travellers differ in their degree of satisfaction with the service? b XR20-06b The responses were recoded using the values 88-67-39-36-25-21-18. Can we now infer that business and economy class travellers differ in their degree of satisfaction with the service? c What is the effect of changing the codes? Explain why this could be expected. Sample statistics: (a and b): $T_1=4004, n_1=40$, $T_2=8086, n_2=115$.

a To determine whether the satisfaction rating of an airline differs between business class and economy class, a survey was performed.
Random samples of both groups were asked to rate their satisfaction with the quality of service using the following responses:
$\bullet$ Very satisfied
$\bullet$ Quite satisfied
$\bullet$ Somewhat satisfied
$\bullet$ Neither satisfied nor dissatisfied
$\bullet$ Somewhat dissatisfied
$\bullet$ Quite dissatisfied
$\bullet$ Very dissatisfied
The results were recorded using a 7-6-5-4-3-2-1 coding system. Can we infer that business and economy class travellers differ in their degree of satisfaction with the service?
b XR20-06b The responses were recoded using the values 88-67-39-36-25-21-18. Can we now infer that business and economy class travellers differ in their degree of satisfaction with the service?
c What is the effect of changing the codes? Explain why this could be expected.
Sample statistics: (a and b): $T_1=4004, n_1=40$, $T_2=8086, n_2=115$.

Key Concepts

Ordinal Data

Ordinal data refers to variables that indicate order or ranking among categories without assuming equal intervals between the ranks. In the context of satisfaction ratings, while the responses have a natural order from 'Very satisfied' to 'Very dissatisfied', the distances between these categories may not be equal, which must be considered when choosing appropriate statistical methods.

Rank?Based Statistical Methods

Rank?based statistical methods are techniques used to analyze ordinal data by ranking individual observations rather than relying on their numerical values. These methods, such as the Mann–Whitney U test, are particularly useful in comparing groups because they focus on the order of data rather than the actual codes assigned, thereby mitigating issues arising from unequal intervals between categories.

Monotonic Transformation

A monotonic transformation involves converting a set of numbers using a function that preserves the order of values while potentially altering the scale. When satisfaction ratings are recoded using a different set of numbers—as in the question—the relative order of responses remains unchanged. Consequently, statistical tests that depend solely on this order, like rank?based methods, yield consistent results regardless of the specific numeric codes used, underscoring the invariance property of such tests.

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