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Consider the following scientific hypothesis, "One is more likely to observe a kangaroo at night than during the day". In other words, "the conditional probability of observing a kangaroo given it is night is greater than the conditional probability of observing a kangaroo given it is daytime".

Do you think there are any problems with this hypothesis?

One problem that I see is that we need to specify the means of observation, like "with the naked eye standing in the bush". But more generally, is a hypothesis that involves not only a testable statement of fact, but also involves the observability or perceptibility of the fact a good hypothesis?

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    It would seem to me that, at least in this case, "good" is a function of the suitability of the object being evaluated for a particular use; are you asking whether measurable predictions make a hypothesis "good"? Is there any chance I might be able to persuade you to tell us a little more about the context and motivations behind the concern here? – Joseph Weissman Oct 18 '12 at 6:45
  • I am asking because I an developing a hypothesis for a study in social science. Explaining the context would take a fair bit of time. I specifically wanted to be vague about the criteria for "goodness" because I wanted to hear what criteria people would use. – Nikita Samoylov Oct 23 '12 at 5:17
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What I can see is that this hypothesis is way too general for practical purposes and leaves several open questions. But you have already mentioned this in the answer.

Furthermore, I think that including the notion of observation might make sense in a case in which it this notion itself is of particular interest. However, it is usually necessary to specify the hypothesis.

We could look at different examples:

"One is more likely to observe a kangaroo at night than during the day".

If your goal is to take a photograph of a kangaroo, and want to decide when your chances are best this hypothesis is still better as:

"There are more kangaroos in the area of interest at night than during the day" It might be the case, that you have a limited view at night, which leads to a situation in which there are many kangaroos, but they are hard to observe.

However, in this example it might be better to include the additional information in the hypothesis.

Next example, "Children are more likely to observe explicit content in TV at night than during the day".

Here, you might be interested in finding a good time in which children could be advised to watch TV. (Trying to minimize the likelihood of them observing explicit content)

This hypothesis is still better as: "There is more explicit content in TV at night than during the day". Just think of a case in which there is such content in TV, but children cannot access it.

To conclude, I would not say that it is generally a bad idea to use the notion of observation. Maybe think of cases in astronomy in which you are not only interested in specific things to happen, but also if we can with our limited capabilities will be able to actually observe phenomena.

However, in many cases the notion of observation may be something like a bad smell that might indicate that the hypothesis does not formulate exactly what you are interested in.

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It's a perfectly fine hypothesis, but since you need to estimate the rate of observation of kangaroos over all people where kangaroos are ever observed, it's not very practical to confirm it, nor is it likely to stay true if conditions change appreciably between the time of measurement and the time when you're wondering if it is still true.

You probably want to ask things about the activity of kangaroos during the day vs. night, how willing they are to approach human dwellings during the day vs. night (as compared to their visibility during the day vs. night) and stuff like that. Armed with evidence regarding these hypotheses, you can then have a better hope of predicting whether you should go outside today or tonight if you want to see a kangaroo.

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