Rejecting or revising hypotheses involves reasoned arguments.

Rejecting Measurable Hypotheses involves evidence that the experimental data do NOT match the predictions of the Measurable Hypotheses. 

Null Hypotheses can be rejected with statistical tests. For example, if a model mathematically predicts that a value will not change over a set of conditions, then finding significant differences among conditions could provide evidence to reject the model (e.g. Qiao et al., 2014). 

Rejecting Measurable Hypotheses may require arguments in the Discussion.

Rejecting Measurable Hypotheses that are not posed as Null Hypotheses is far less straightforward. For example, if a Measurable Hypothesis predicts significant differences among groups, failing to find statistically significant differences among groups does not necessarily provide sufficient evidence to reject a Measurable Hypothesis. There are many reasons that statistical tests can fail, and the true absence of differences among groups is only one reason for failure.

Imagine that we are interested in testing the General Hypothesis,

"Soda consumption is one cause of childhood obesity in the United States," by making the Measurable prediction,

"Removing soda machines from Central High School at the start of the school year will result in significantly lower average Body Mass Index (BMI) for students at the end of the school year relative to BMI at the start of the school year."

Does the experiment seem a reasonable test of the General Hypothesis? If we perform the experiment and fail to find a significant difference in BMI between the start and end of the school year, can we conclusively reject our Measurable Hypothesis? 

Not yet. Rejecting the Measurable Hypothesis may require arguments in the Discussion. Addressing the experimental limitations and arguing that the limitations are not likely to affect the conclusions of the study can be a useful start and provide initial arguments. However, we may need to provide additional arguments. For example, we may need to argue that we measured enough students to have statistical power sufficient to resolve potential differences in BMI. We also may need to argue that one school year is sufficient time for differences in BMI to be measurably large (potentially based on other studies that successfully found changes to BMI over a 9-month period). 

Therefore, rejecting Measurable Hypotheses that are not posed as Null Hypotheses can require arguments in the Discussion. 

Revising Measurable Hypotheses can result in stronger hypotheses.

If the data of a study do not support a Measurable Hypotheses, or if the data reject the Measurable Hypotheses, then the Discussion can propose ways to revise the Measurable Hypotheses.

For example, even if we convincingly reject our Measurable Hypotheses that removing soda machines from school significantly decreases BMI, the bulk of evidence from many other studies may still support the General Hypothesis that soda contributes to childhood obesity. Therefore, we may choose to make different measurable predictions: to revise our Measurable Hypotheses. For example, students could document (through food logs) their soda consumption, and we could test for positive correlations between soda consumption and BMI. 

Revising or developing new Measurable Hypotheses can involve re-visiting the assumptions of the study.

Whereas defending the assumptions of a study can be important for supporting Hypotheses, questioning assumptions can lead to reasonable approaches to revise Measurable Hypotheses. Therefore, identifying and discussing assumptions made in a study can provide a reasonable starting point for arguments for revised Measurable Hypotheses.

For example, our study on soda consumption was based on the assumption that school vending machines are a major source of sugary drinks in the diet of High School students. Questioning our assumption would require us to revise the Measurable Hypothesis -- i.e. to generate a hypothesis that is NOT based on the assumption that students primarily drink sugary drinks at school. Although the testing the new Measurable Hypothesis is outside the scope of the Discussion, the Discussion can present arguments that the revised Measurable Hypothesis is reasonable, and propose subsequent experiments to test the revised hypothesis.

Rejecting General Hypotheses typically requires many studies.

Imagine that we were able to convincingly reject our Measurable Hypothesis that removing soda machines from Central High School would result in significantly lower BMI among students. Based on the rejection of our Measurable Hypothesis, can we therefore reject our General Hypothesis that soda consumption contributes to childhood obesity?

Again, not yet. It is easy to think of many reasons that removing soda machines would not change BMI, even if overall soda consumption does in fact contribute to obesity. Students could bring soda from home, or buy soda elsewhere, or simply increase soda consumption outside of school. Because it is seldom possible to be confident that an experiment has controlled for all necessary variables, rejecting a single Measurable Hypotheses may not provide convincing evidence to reject a General Hypothesis. 

Therefore, rejecting a General Hypothesis typically requires evidence from many studies that all conflict with the General Hypothesis. Constructing arguments against General Hypotheses can involve the same types of reasoned arguments as supporting General Hypotheses. Hill's Criteria (or other frameworks) could likewise contribute to rejecting hypotheses. For example, paragraphs of the Discussion could argue that there is not a diversity of studies that support the General Hypothesis, or that there are not plausible mechanisms for the hypothesized explanation, or that there is not an association between variables strong enough to be important.

If a General Hypothesis consistently fails to make successful predictions, then it may be necessary to revise the General Hypothesis. Revision may involve creating an entirely new General Hypothesis. A revised or new General Hypothesis should lead to a different set of predictions that can subsequently be tested. A reasonable objective for a Discussion section would therefore be to present and defend the revised General Hypothesis.

Appropriate statistical tests can be sufficient evidence to reject Null Hypotheses. However, reasoned arguments are typically necessary to reject BOTH Measurable Hypotheses and General Hypotheses. Revising Measurable Hypotheses can start with questioning assumptions that led to the [rejected] Measurable Hypothesis. Arguments to revise General Hypotheses can employ frameworks such as Hill's Criteria.