## complementary hypothesis

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wildfunguy
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### complementary hypothesis

A simple and intrigueing realization I've had: each hypothesis has a complementary hypothesis that is its logical negation. Whenever you falsify a hypothesis, you have proven its complementary hypothesis. Also interesting, a given hypothesis may be more or less testable than its complement.

For example, the complement of "Somebody is sneaking into my room" (A) would be "Nobody is sneaking into my room" (AC). A is unfalsifiable because a really good sneaker will not leave any evidence of their sneaking; no set of hypothetical observations would be inconsistent with A. However, there are some observations that would be inconsistent with AC, such as written messages appearing on the room's walls before you return to it. Thus AC is falsifiable. By falsifying AC, you prove A. By repeatedly failing to find evidence that falsifies AC, you gather support for AC.

Come on, I want a debate.

ughaibu
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### Re: complementary hypothesis

wildfunguy wrote:Come on, I want a debate.
You'll need to be more specific about the respective positions.

wildfunguy
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Upon further thought, the name "complementary hypothesis" may be misleading. It is an hypothesis in the mathematical sense, but not in the scientific method sense (i.e. an explanation for some observation). That is, proving or supporting the complementary "hypothesis" doesn't serve to explain a given phenomena, it only rules out a particular explanation.

ughaibu wrote:You'll need to be more specific about the respective positions.

Well, I have contradicted the idea that an unfalsifiable hypothesis is necessarily outside the boundaries of scientific inquiry. As I said, a given hypothesis may be more or less testable than its complement.

Most people would say that the absence of evidence is only evidence of absense if we know how much evidence should be expected. This approach never brings in the complementary hypothesis idea. But the consideration of how much evidence we should expect may be irrelevant may be independent of the testability of the complementary hypothesis.
Suppose we don't know how much evidence should be left behind by a person sneaking into the room, only knowing that the leaving of evidence is a possibility. However, that doesn't matter if the absence of evidence is actually a prediction of the complementary hypothesis.

animartco
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### Re: complementary hypothesis

There may be lots of clues that someone was sneaking into your room, but if it is a regular occurrence and you want to be certain, try leaving a hair stuck through the door. Or install a camera. For no-one sneaking in, the same tests apply making both hypotheses equally provable. Try another example?

ughaibu
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### Re:

wildfunguy wrote:I have contradicted the idea that an unfalsifiable hypothesis is necessarily outside the boundaries of scientific inquiry.
I don't see how, but I suspect that your usage of "hypothesis" is other than what I take it to generally mean. Generally, as I understand the usage in science, a hypothesis is the statement of a prediction, that given a set of circumstances we will observe a specified phenomenon. That prediction can be correct or incorrect, being incorrect doesn't necessarily falsify the theory, however, it never supports the theory, and the prediction must be non-trivial.
It's not clear to me what hypothesis you're proposing to scientifically enquire into the conjecture that someone is sneaking into your room, and it's not clear how this phenomenon, if it were established, would support a theory or what that theory would be. That we form our conclusion from evidence based on observation is not sufficient for the claim that we're involved in scientific enquiry. Your scenario sounds more like police work than science.

wildfunguy
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### Re: Re:

animartco wrote:There may be lots of clues that someone was sneaking into your room, but if it is a regular occurrence and you want to be certain, try leaving a hair stuck through the door. Or install a camera. For no-one sneaking in, the same tests apply making both hypotheses equally provable. Try another example?

If I change it to "Somebody was sneaking into my room", then the hair-in-door idea and camera idea are no longer applicable.

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ughaibu wrote:I don't see how, but I suspect that your usage of "hypothesis" is other than what I take it to generally mean. Generally, as I understand the usage in science, a hypothesis is the statement of a prediction, that given a set of circumstances we will observe a specified phenomenon.
My understanding was that, in the mathematical sense, an hypothesis is an if/then statement. There may be some confusion because I was referring to the "if" portion as the hypothesis, whereas the hypothesis may refer to both "if" and "then" (the claim bein tested, and the prediction being made). I will start using the word "claim" instead.

ughaibu wrote:That prediction can be correct or incorrect, being incorrect doesn't necessarily falsify the theory, however, it never supports the theory

I am arguing that any failed prediction, whether it falsifies the claim or not, must support the idea that the claim is false to some degree. Whether one has been falsified or not, their relative probabilities (P(A) + P(AC) = 1.0) have shifted.
An accumulation of such failed predictions can be taken as evidence against.

ughaibu wrote:and the prediction must be non-trivial.

What does non-trivial mean? That it must be a prediction that depends on the claim?

ughaibu wrote:It's not clear to me what hypothesis you're proposing to scientifically enquire into the conjecture that someone is sneaking into your room, and it's not clear how this phenomenon, if it were established, would support a theory or what that theory would be. That we form our conclusion from evidence based on observation is not sufficient for the claim that we're involved in scientific enquiry. Your scenario sounds more like police work than science.

It could be part of many theories. I could be on my way toward supporting the theory that my little brother misbehaves when I'm not around. However, this empirical investigation is not scientific because it is not independently verifiable. Should I come up with an example hypothesis that is more scientific?

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I briefly returned to another forum, and I started a thread there. I didn't get much direct input, but I did propose the idea in a more evolved form. http://www.sciencechatforum.com/viewtop ... 10&t=25546
In my third post, I make a good case for the complementary hypotheses being taken together. I'll reiterate it here.

I wrote:[...] I initially thought that each mathematical hypothesis (if/then statement) is [considered] on its own. I began to wonder why people never state the complementary hypothesis and test that instead. For example, if I want to know whether somebody is sneaking into my room (A), I could test the complementary hypothesis (AC) instead.
After some thought, I decided that they should be taken together. After all, everything could be consistent with AC even if A really is true. [Everything could be very consistent with AC, making AC look appealing, but AC is never really proven until A is falsified.]

It is necessary that both complements are taken together because the probability of an event (E) can be high in both conditions or low in both conditions. The degree to which the fulfillment of a prediction supports my claim doesn't merely depend on the probability of that event in the true condition P(E|T), but also the probability of the event in the false condition P(E|F). The only requirement for it to support my claim is that P(E|T) > P(E|F).

Without taking this into consideration, a person could make irrelevant predictions that have the same high probability whether the claim is true or not
Given that we already know the sky is blue, 1 and 2 are both true.
(1) "If carbon monoxide is dangerous, the sky should be blue."
(2) "If carbon monoxide is not dangerous, the sky should be blue."

What if I presented this to someone?
*If carbon monoxide is not dangerous, the sky should be blue.
*The sky is blue.

JackBean
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does the term null hypothesis tell you something?
http://www.biolib.cz/en/main/

Cis or trans? That's what matters.

wildfunguy
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### Re:

JackBean wrote:does the term null hypothesis tell you something?

Yes, I learned about that recently.

wildfunguy
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Its meaning is nearly identical to that of my invented term.

Now I know.

JackBean
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I'd say it's completely the same, but whatever.
http://www.biolib.cz/en/main/

Cis or trans? That's what matters.

wildfunguy
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The normal hypothesis and null hypothesis would each be the complementary hypothesis to the other.

It's from the term absolute complement, used in set theory. https://en.wikipedia.org/wiki/Complemen ... complement\
The universe would be the set of all possibilities.

wildfunguy
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Actually, are they that similar? I describe a scenario where two hypothesis are phrased such that they are exhaustive.

https://en.wikipedia.org/wiki/Null_hypothesis
"In statistical inference of observed data of a scientific experiment, the null hypothesis refers to a general statement or default position that there is no relationship between two measured phenomena.[1]"

Showing a relationship disproves the null hypothesis, but it may support many different alternative hypotheses without proving any of them. If J were the absolute complement of the null hypothesis, disproving the null hypothesis would prove J.

Maybe "negative hypothesis" would be a better term. The alternate term relative complement makes the word "complement" ambiguous.

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