Originally posted by DoctorScribblesYou know what would really kick ass now? If kingdanwa withdrew his hypothesis that smokers are more likely to litter.
Ok, I withdraw my hypothesis that the inter-littering times are exponential.
RC, both of your observations about my experimental design are important to consider when interpreting the results of the experiment, as both may yield a bias in the observed proportion of litterers who are smokers. However, I don't expect that either will cripple the ex ...[text shortened]... the non-memoryless distribution times coupled with the non-instantaneous observe-sniff cycle.
As I understand it, the goal is to determine whether the proportion, at any given time, of smokers who litter in non-cigarette-butt-related ways is the same as the proportion of non-smokers who litter in non-cigarette-butt-related ways.
In view of that, I agree that my first objection was completely specious. I also don't see the relevance of your exchange to this specific question, however. We reliably know what proportion of the population smokes (or we can assume we do; detailed figures on this are available), so provided we know which population we're sampling from on our street corner, I have no objections to Dr. S's experiment besides the second practical one I raised.
We simply need to determine whether the proportion of observed litterers who smoke is significantly different from the proportion of smokers the general population. If the hypothesis that smokers tend to litter more is true, we should observe more smokers among the litterers than in the general population (this follows from Bayes' theorem:
P(Litterbug | Nic fitter)/P(Litterbug) = P(Nic fitter | Litterbug)/P(Nic fitter)
We claim to observe P(Nic fitter | Litterbug) in Dr. S's experiment and know P(Nic fitter). If RHS > 1, ie we observe more smoking among litterers than in the general population, then it follows that people are more prone to littering if they smoke, since RHS = LHS.)
There is no reason why any change in these proportions with time would affect the truth of the hypothesis that smokers litter more, since the above equation has to hold regardless of any changes in P(Nic fitter) and P(Litterbug) -- we just have to have accurate knowledge of P(Nic fitter) at any given time to be able to compare something to our observations of P(Nic fitter | Litterbug). Specifically, we don't need to observe P(Litterbug) at all, so my objection about missing litterers was stupid.
In view of your previous post, Dr. S, explain how my first objection could possibly be relevant. We're observing the proportion of known litterers who smoke, compared to the proportion of people who smoke. If we knew, for example, that 1/3 of the population smokes and observed 50 smokers in 100 litterers, why would it matter if 500 litterers had walked by unbeknownst to us (assuming we didn't ignore litterers who didn't have a fag on the go, or something)?
EDIT Sorry if this makes no sense, I'm an hour into a phone conversation with my lunatic of a father 🙂.
Originally posted by royalchickenMaybe most non-smokers only litter immediately after seeing somebody else do it, similar to the phenomenon of looting, the crowd mentality, follow the leader. This isn't too far removed from kingdanwa's idea of debris begets debris. If true, we'd expect to miss a significant number of non-smoking litterers while we chase the first one down the block to smell him. After the chase, the probability that a non-smoker will be observed littering is significantly lower than during the chase. Meanwhile, smokers who don't need a leader to litter are equally likely to observed after the chase as during it.
If we knew, for example, that 1/3 of the population smokes and observed 50 smokers in 100 litterers, why would it matter if 500 litterers had walked by unbeknownst to us (assuming we didn't ignore litterers who didn't have a fag on the go, or something)?
This is of course based on an assumption of ignorance, giving equal credence to this distribution and the exponential distribution, and of course for fairness, the Weibull distribution.
Your model adds great clarity to the discussion.
I'm not one for posting links, but I have no expertise in this field of study, so I must rely on the research done by others.
"Where and when littering occurs:
Lack of bins is not a major factor in littering. Most littering occurs within five metres of a bin. This is particularly the case for cigarettes.
Bin use is most common between 11:00am and 2:00pm. Littering is most common about 4:00pm.
Site factors are powerful determinants of behaviour — the more litter present, the more people are inclined to litter. Also, the more convenient the bin placement and the more obtrusive its appearance, the less people are likely to litter. People do respond to signage, and the more polite the signage, the better the response. However, over time the impact of signage diminishes. "
http://www.environment.nsw.gov.au/litter/research.htm
This points out that in some sense, "litter begets litter," as was claimed above.