I would like to hear your thoughts on the topic. You see most of the text books tend to argue that the null hypothesis can never be proven because of falsifiability etc. So i have several questions on this:
1. If there are non-significant results should the whole survey become invaluable and be considered as a failure? My personal opinion for this is that if many papers show non-significance they only add support that the null is highly likely and therefore each non-significant result is still valuable.
2. Could qualitative data add in the completeness of a quantitative survey to the point that claims can be made that the null is highly likely whenever statistical significance is not achieved for the alternative hypothesis?
3. Is it appropriate to use noninferiority testing in social sciences in order to evaluate if indeed there is no difference? I've never used this analysis and before i go into that i want to know if it is relevant to the social sciences. In medical statistics it seems to be quite revolutionary.
I think these questions can be better answered using a Bayesian approach. These methods address better your ideas of "highly likely" hypothesis...
Are there many social researchers using Bayesian statistics? And what about equivalence testing?
I'm sure about the social researchers (I do more medical stats), but probably there aren't many because Bayesian Stats is less "popular" than classical frequentist inference. Largely due to the lack of teaching of bayesian methods. Any people should be using Bayesian methods much more.
And yes you can do equivalence analysis with bayesian methods.
On item #1, environmental data sets frequently have a preponderance of non-detects which are sometimes individually assigned a value of 'zero.' This can make the data set lead to the conclusion that the data cannot be used for statistical purposes except in a limited way. If, however, the uncensored data are available, non-detects are as statistically valid as the detects when included in the complete data set. See http://misterkenblog.blogspot.com/2010/03/twenty-random-points-resolved.html for an example of using uncensored data for statistical decision making.
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