Search results
Results from the WOW.Com Content Network
A random experiment is described or modeled by a mathematical construct known as a probability space. A probability space is constructed and defined with a specific kind of experiment or trial in mind. A mathematical description of an experiment consists of three parts: A sample space, Ω (or S), which is the set of all possible outcomes.
Probability theory or probability calculus is the branch of mathematics concerned with probability. Although there are several different probability interpretations , probability theory treats the concept in a rigorous mathematical manner by expressing it through a set of axioms .
Randomization is a statistical process in which a random mechanism is employed to select a sample from a population or assign subjects to different groups. [1] [2] [3] The process is crucial in ensuring the random allocation of experimental units or treatment protocols, thereby minimizing selection bias and enhancing the statistical validity. [4]
For any given event, only one of two possibilities may hold: It occurs or it does not. The relative frequency of occurrence of an event, observed in a number of repetitions of the experiment, is a measure of the probability of that event. This is the core conception of probability in the frequentist interpretation.
Random assignment or random placement is an experimental technique for assigning human participants or animal subjects to different groups in an experiment (e.g., a treatment group versus a control group) using randomization, such as by a chance procedure (e.g., flipping a coin) or a random number generator. [1]
This can be represented mathematically as follows: If a random experiment can result in N mutually exclusive and equally likely outcomes and if N A of these outcomes result in the occurrence of the event A, the probability of A is defined by =. There are two clear limitations to the classical definition. [18]
In the statistical theory of design of experiments, randomization involves randomly allocating the experimental units across the treatment groups.For example, if an experiment compares a new drug against a standard drug, then the patients should be allocated to either the new drug or to the standard drug control using randomization.
A random process is a sequence of random variables whose outcomes do not follow a deterministic pattern, but follow an evolution described by probability distributions. These and other constructs are extremely useful in probability theory and the various applications of randomness .