The researchers used a natural experimental method. One characteristic is that the independent variable is naturally occurring and not manipulated by the researcher.  In this, the IV was the imposition of the smoking ban.  One group (Scotland) had the IV and the other group (UK) served as the control.  A second characteristic of natural experiments is that the participants cannot be randomly allocated to conditions. In this experiment, participants were allocated to conditions based on whether they were in the part of the UK with the smoking ban in place or not. 

The sample is a geographically stratified sample.  Each geographic district in Scotland and the rest of the UK was represented.  From each district telephone numbers were randomly selected to be in the study. This may have been done by a random number generator or by pulling phone numbers out of a hat. As the numbers were randomly selected, this increases the probability that the sample is representative and thus the results may be generalized to the population from which the sample was drawn.

Representational generalizability: As the sample was randomly selected from each geographic division of the two areas of the UK - and the sample size was relatively large - it can be assumed that the sample is representative of the population.  This means that we can generalize to the larger population of both Scotland and the rest of the UK

Transferability: However, it would be difficult to generalize the findings to other populations. Cultural dimensions such as power distance, socioeconomic status, and accessibility of cigarettes could all be variables that may affect the effectiveness of a smoking ban in a different country.  Higher power distance may make individuals more likely to obey a smoking ban; more highly individualistic cultures may be more likely to oppose any such top-down approach to limiting unhealthy behavior. You would also have to look at, for example, the availability of cigarettes.  If tobacco is cheap and easily accessible, then smoking rates may not change; but if in addition to the ban there is an increase in the cost of cigarettes, then there is more than one variable that must be considered and the findings could only be applied to similar situations.

Theoretical generalizability: Although you could generalize cautiously to other countries, it would be best to look at studies of other countries.  If there are several studies from different countries with the same results (which there are), then we can generalize the findings more confidently about smoking bans in general. In addition, the study could be generalized to support theories of social cognition as a way to change behaviour - e.g. conformity or obedience.