What happens if you do not reject the null hypothesis?
Rejecting the null hypothesis, or not, is a normal part of quantitative research. For doctoral students, rejection of the null is not necessary for dissertation approval, but rather, only that doctoral level research is demostrated, which can apply, regardless. Failure to reject the null for correlation testing, simply means that the independent variable tested is not a statistically significant predictor of the dependent (outcome) variable. Such a result is valuable, in that, it contributes new findings to the body of knowledge, which may lead to further research of other potential IVs as predictors of the DV.
Source: https://www.quora.com/What-happens-if-you-do-not-reject-the-null-hypothesis/answer/Lawrence-Ness-4
For further research on this topic, see:
Lawrence Ness's answer to How do you accept or reject the null hypothesis in regression?
Lawrence Ness's answer to Will the researcher reject the null hypothesis?
Lawrence Ness's answer to How do you write a null hypothesis in quantitative research?
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