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In research paradigm's post-positivism can I prove (verify) the hypothesis instead of falsifying it?

Guba, E.G. and Lincoln, Y.S., 1994. Competing paradigms in qualitative research. Handbook of qualitative research, 2(163-194), p.105. says, that in the methodology 

positivism's experimental/manipulative methodology
that focuses on verification of hypotheses;

postpositivism' s modified experimental/
manipulative methodology invested in critical
multiplism focusing on falsification of hypotheses;

But, can I just prove (verify) the hypothesis instead of falsifying it? I don't want to fully be on pure objectivism and don't want to be in pure subjectivism so I'm considering the nature of knowledge to be in post-positivism ..

Mainly, I want to gather data and do both qualitative and quantitative analysis and then triangulate the data to come up with a conclusion and prove (verify) the hypothesis. If I do that does it comes under positivism instead of post-positivism?

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  • When dealing with statistical data, you can only reject the null hypothesis, with certain confidence. For example, you cannot prove that two variables are totally uncorrelated, you can only show that if they are, it is smaller than your sensitivity. – Davidmh Aug 11 '16 at 15:15
  • @Davidmh : you mean I can't "verify" it with post-positivism. some how I should reject either the "hypothesis" or "null-hypothesis" and you mean, if I want to prove the hypothesis, I should consider the nature of knowledge as "positivism" instead of "post-positivism"? – Pretty_Girl Aug 11 '16 at 15:31
  • For instance, suppose I'm going to prove "medical practitioners have issues with co workers" hypothesis .. so I'll do a questionnaire survey as quantitative and interview them for qualitative data. ... so, must I consider the knowledge as "positivism" instead of "post-positivism"? .. Can't I consider it as "post-positivism"? – Pretty_Girl Aug 11 '16 at 15:35
  • @Pretty_Girl I am almost sure that the best you can do in the medical practitioners example is you can reject the null hypothesis (which is "medical practitioners don't have issues with coworkers"). – svavil Aug 11 '16 at 16:18
  • I do not think there is something strict system called "positivism" for proving something. However, yes, in computer science, we can find an alternative proof to a certain theorem using the concept of "proof by refutation". – Coder Aug 11 '16 at 16:38
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In short, post-positivism takes the stance that answers will change with more data and therefore prefers to reject standing assumptions rather than accepting alternatives. Instead of accepting your can say failed to reject. This leaves it in the realm of tentative working belief until more data is presented.

In length, if you are viewing the world through the lens of post-positivism then you believe that though there is a Reality out there it is not perfectly knowable. An example of this is in the moment of this writing there were an exact number of grains of sand within a given radius of the center of the planet. The quantity however is unknowable. Though it is unknowable we can easily reject the hypothesis that there were exactly ten grains of sand within a thousand kilometers of the earth's center. We have rejected a hypothesis without accepting any alternative. Let us say that an alternative hypothesis was put forward that there were 1 * 10 ^ 15 grains of sand. This alternative though certainly not accurate is much less easy to dismiss. Though I imagine a few quick calculations would be sufficient to reject it as well. We allow to stand a hypothesis that we can not bring enough evidence against to reject but we do not ever say that it is the final and true answer.

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