Reproducibility in the context of Empirical law

Early Islamic philosophy or classical Islamic philosophy is a period of intense philosophical development beginning in the 2nd century AH of the Islamic calendar (early 9th century CE) and lasting until the 6th century AH (late 12th century CE). The period is known as the Islamic Golden Age, and the achievements of this period had a crucial influence in the development of modern philosophy and science. For Renaissance Europe, "Muslim maritime, agricultural, and technological innovations, as well as much East Asian technology via the Muslim world, made their way to western Europe in one of the largest technology transfers in world history." This period starts with al-Kindi in the 9th century and ends with Averroes (Ibn Rushd) at the end of 12th century. The death of Averroes effectively marks the end of a particular discipline of Islamic philosophy usually called the Peripatetic Arabic School, and philosophical activity declined significantly in Western Islamic countries, namely in Islamic Spain and North Africa, though it persisted for much longer in the Eastern countries, in particular Persia and India where several schools of philosophy continued to flourish: Avicennism, Illuminationist philosophy, Mystical philosophy, and Transcendent theosophy.

Intellectual innovations, achievements, and advancements of this period included, within jurisprudence, the development of ijtihad, a method or methodological approach to legal reasoning, interpretation, and argument based on independent inquiry and analogical deduction; within science and the philosophy of science, the development of empirical research methods emphasizing controlled experimentation, observational evidence, and reproducibility, as well as early formulations of empiricist epistemologies; commentaries and developments in Aristotelian logic, as well as innovations in non-Aristotelian temporal modal logic and inductive logic; and developments in research practice and methodology, including, within medicine, the first documented peer review process and within jurisprudence and theology, a strict science of citation, the isnad or "backing".

Scientific laws or laws of science are statements, based on repeated experiments or observations, that describe or predict a range of natural phenomena. The term law has diverse usage in many cases (approximate, accurate, broad, or narrow) across all fields of natural science (physics, chemistry, astronomy, geoscience, biology). Laws are developed from data and can be further developed through mathematics; in all cases they are directly or indirectly based on empirical evidence. It is generally understood that they implicitly reflect, though they do not explicitly assert, causal relationships fundamental to reality, and are discovered rather than invented.

Scientific laws summarize the results of experiments or observations, usually within a certain range of application. In general, the accuracy of a law does not change when a new theory of the relevant phenomenon is worked out, but rather the scope of the law's application, since the mathematics or statement representing the law does not change. As with other kinds of scientific knowledge, scientific laws do not express absolute certainty, as mathematical laws do. A scientific law may be contradicted, restricted, or extended by future observations.

Natural science or empirical science is a branch of science concerned with the description, understanding, and prediction of natural phenomena, based on empirical evidence from observation and experimentation. Mechanisms such as peer review and reproducibility of findings are used to try to ensure the validity of scientific advances.

Natural science can be divided into two main branches: life science and physical science. Life science is alternatively known as biology. Physical science is subdivided into physics, astronomy, Earth science, and chemistry. These branches of natural science may be further divided into more specialized branches, also known as fields. As empirical sciences, natural sciences use tools from the formal sciences, such as mathematics and logic, converting information about nature into measurements that can be explained as clear statements of the "laws of nature".

A scientific theory is an explanation of an aspect of the natural world that can be or that has been repeatedly tested and has corroborating evidence in accordance with the scientific method, using accepted protocols of observation, measurement, and evaluation of results. Where possible, theories are tested under controlled conditions in an experiment. In circumstances not amenable to experimental testing, theories are evaluated through principles of abductive reasoning. Established scientific theories have withstood rigorous scrutiny and embody scientific knowledge.

A scientific theory differs from a scientific fact: a fact is an observation, while a theory connects and explains multiple observations. Furthermore, a theory is expected to make predictions which could be confirmed or refuted with additional observations. Stephen Jay Gould wrote that "...facts and theories are different things, not rungs in a hierarchy of increasing certainty. Facts are the world's data. Theories are structures of ideas that explain and interpret facts."A theory differs from a scientific law in that a law is an empirical description of a relationship between facts and/or other laws. For example, Newton's Law of Gravity is a mathematical equation that can be used to predict the attraction between bodies, but it is not a theory to explain how gravity works.

Testability is a primary aspect of science and the scientific method. There are two components to testability:

1. Falsifiability or defeasibility, which means that counterexamples to the hypothesis are logically possible.
2. The practical feasibility of observing a reproducible series of such counterexamples if they do exist.

In short, a hypothesis is testable if there is a possibility of deciding whether it is true or false based on experimentation by anyone. This allows anyone to decide whether a theory can be supported or refuted by data. However, the interpretation of experimental data may be also inconclusive or uncertain. Karl Popper introduced the concept that scientific knowledge had the property of falsifiability as published in The Logic of Scientific Discovery.

In natural and social science research, a protocol is most commonly a predefined procedural method in the design and implementation of an experiment. Protocols are written whenever it is desirable to standardize a laboratory method to ensure successful replication of results by others in the same laboratory or by other laboratories. Additionally, and by extension, protocols have the advantage of facilitating the assessment of experimental results through peer review. In addition to detailed procedures, equipment, and instruments, protocols will also contain study objectives, reasoning for experimental design, reasoning for chosen sample sizes, safety precautions, and how results were calculated and reported, including statistical analysis and any rules for predefining and documenting excluded data to avoid bias.

Similarly, a protocol may refer to the procedural methods of health organizations, commercial laboratories, manufacturing plants, etc. to ensure their activities (e.g., blood testing at a hospital, testing of certified reference materials at a calibration laboratory, and manufacturing of transmission gears at a facility) are consistent to a specific standard, encouraging safe use and accurate results.

The problem of philosophical objectivity is contrasted with personal subjectivity, sometimes exacerbated by the overgeneralization of a hypothesis to the whole. For example, Newton's law of universal gravitation appears to be the norm for the attraction between celestial bodies, but it was later refined and extended—and philosophically superseded—by the more general theory of relativity.

Metascience (also known as meta-research) is the use of scientific methodology to study science itself. Metascience seeks to increase the quality of scientific research and enhance its efficiency. It is also known as "research on research" and "the science of science", as it uses research methods to study how research is done and find where improvements can be made. Metascience concerns itself with all fields of research and has been described as "a bird's eye view of science". In the words of John Ioannidis, "Science is the best thing that has happened to human beings ... but we can do it better."

In 1966, an early meta-research paper examined the statistical methods of 295 papers published in ten high-profile medical journals. It found that "in almost 73% of the reports read ... conclusions were drawn when the justification for these conclusions was invalid." Meta-research in the following decades found many methodological flaws, inefficiencies, and poor practices in research across numerous scientific fields. Many scientific studies could not be reproduced, particularly in medicine and the soft sciences. The term "replication crisis" was coined in the early 2010s as part of a growing awareness of the problem.

Clinical trials are prospective biomedical or behavioral research studies on human participants designed to answer specific questions about biomedical or behavioral interventions, including new treatments (such as novel vaccines, drugs, dietary choices, dietary supplements, and medical devices) and known interventions that warrant further study and comparison. Clinical trials generate data on dosage, safety and efficacy. They are conducted only after they have received health authority/ethics committee approval in the country where approval of the therapy is sought. These authorities are responsible for vetting the risk/benefit ratio of the trial—their approval does not mean the therapy is 'safe' or effective, only that the trial may be conducted.

Depending on product type and development stage, investigators initially enroll volunteers or patients into small pilot studies, and subsequently conduct progressively larger scale comparative studies. Clinical trials can vary in size and cost, and they can involve a single research center or multiple centers, in one country or in multiple countries. Clinical study design aims to ensure the scientific validity and reproducibility of the results.

Accuracy and precision are measures of observational error; accuracy is how close a given set of measurements is to the true value and precision is how close the measurements are to each other.

The International Organization for Standardization (ISO) defines a related measure:trueness, "the closeness of agreement between the arithmetic mean of a large number of test results and the true or accepted reference value."