"A method of procedure that has characterized natural science since the 17th century, consisting in systematic observation, measurement, and experiment, and the formulation, testing, and modification of hypotheses." 
The practice of scientific research -- whether quantitative, qualitative, or mixed methods -- demands that the researcher's work is intellectually rigorous, accurate on all points, ethical, and dispassionately executed.
The steps of the scientific method vary slightly according to field (see the 1st video below) but the list below outlines the general approach. 
"Rigor in quantitative research is judged by how narrow, concise, and objective the design and analysis techniques are and how scrupulously the rules have been adhered to and applied to all decisions.
Rigor in qualitative research is defined by quite the opposite set of criteria and is associated with being open to the data, scrupulously adhering to a specific philosophical perspective, and thoroughness in collecting data.
Rigor is also judged by the logic of the emerging theory and whether the results are adding to what is known about a phenomenon.” 
Scientific rigor is the concept more typically applied to qualitative research because this type of research is not experimental in nature. The steps of a qualitative study must comply with the fundamental trustworthiness of the investigation. The criteria for this have been outlined by Guba, E.G.(1981). Criteria for assessing the trustworthiness of naturalistic inquiries. Educational Resources Information Center Annual Review Paper, 29, 75-91. 
 Definitions from the University of North Carolina at Chapel Hill, School of Nursing: Course site for Research for Nursing Practice: Introduction to Qualitative Research. URL: http://www.unc.edu/courses/2005fall/nurs/077/960/qualitative/topic1.html
 Krefting, L. (1991). Rigor in Qualitative Research: The Assessment of Trustworthiness. The American Journal of Occupational Therapy, 45(3), 214-222.
Scientific rigor addresses the quality, credibility, and authoritativeness of sources. The issue of fake news is something to be aware of as these fake stories may report false data and misrepresent research. Fake news is "a story that's completely false, usually invented for traffic and ad revenue, or to advance a political agenda — or both." [From TechCrunch]
SOURCE: The International Federation of Library Associations and Institutions (IFLA)
"How to Spot Fake News"