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Odds Ratio
An odds ratio (OR) is a statistic that quantifies the strength of the association between two events, A and B. The odds ratio is defined as the ratio of the odds of A in the presence of B and the odds of A in the absence of B, or equivalently (due to symmetry), the ratio of the odds of B in the presence of A and the odds of B in the absence of A. Two events are independent if and only if the OR equals 1, i.e., the odds of one event are the same in either the presence or absence of the other event. If the OR is greater than 1, then A and B are associated (correlated) in the sense that, compared to the absence of B, the presence of B raises the odds of A, and symmetrically the presence of A raises the odds of B. Conversely, if the OR is less than 1, then A and B are negatively correlated, and the presence of one event reduces the odds of the other event. Note that the odds ratio is symmetric in the two events, and there is no causal direction implied (correlation does not imply causat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistic
A statistic (singular) or sample statistic is any quantity computed from values in a sample which is considered for a statistical purpose. Statistical purposes include estimating a population parameter, describing a sample, or evaluating a hypothesis. The average (or mean) of sample values is a statistic. The term statistic is used both for the function and for the value of the function on a given sample. When a statistic is being used for a specific purpose, it may be referred to by a name indicating its purpose. When a statistic is used for estimating a population parameter, the statistic is called an ''estimator''. A population parameter is any characteristic of a population under study, but when it is not feasible to directly measure the value of a population parameter, statistical methods are used to infer the likely value of the parameter on the basis of a statistic computed from a sample taken from the population. For example, the sample mean is an unbiased estimator of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prevalence
In epidemiology, prevalence is the proportion of a particular population found to be affected by a medical condition (typically a disease or a risk factor such as smoking or seatbelt use) at a specific time. It is derived by comparing the number of people found to have the condition with the total number of people studied and is usually expressed as a fraction, a percentage, or the number of cases per 10,000 or 100,000 people. Prevalence is most often used in questionnaire studies. Difference between prevalence and incidence Prevalence is the number of disease cases ''present ''in a particular population at a given time, whereas incidence is the number of new cases that ''develop '' during a specified time period. Prevalence answers "How many people have this disease right now?" or "How many people have had this disease during this time period?". Incidence answers "How many people acquired the disease uring a specified time period". However, mathematically, prevalence is propor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logit
In statistics, the logit ( ) function is the quantile function associated with the standard logistic distribution. It has many uses in data analysis and machine learning, especially in data transformations. Mathematically, the logit is the inverse of the standard logistic function \sigma(x) = 1/(1+e^), so the logit is defined as :\operatorname p = \sigma^(p) = \ln \frac \quad \text \quad p \in (0,1). Because of this, the logit is also called the log-odds since it is equal to the logarithm of the odds \frac where is a probability. Thus, the logit is a type of function that maps probability values from (0, 1) to real numbers in (-\infty, +\infty), akin to the probit function. Definition If is a probability, then is the corresponding odds; the of the probability is the logarithm of the odds, i.e.: :\operatorname(p)=\ln\left( \frac \right) =\ln(p)-\ln(1-p)=-\ln\left( \frac-1\right)=2\operatorname(2p-1) The base of the logarithm function used is of little importance in t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Odds Ratio Map
Odds provide a measure of the likelihood of a particular outcome. They are calculated as the ratio of the number of events that produce that outcome to the number that do not. Odds are commonly used in gambling and statistics. Odds also have a simple relation with probability: the odds of an outcome are the ratio of the probability that the outcome occurs to the probability that the outcome does not occur. In mathematical terms, where p is the probability of the outcome: :\text = \frac where 1-p is the probability that the outcome does not occur. Odds can be demonstrated by examining rolling a six-sided die. The odds of rolling a 6 is 1:5. This is because there is 1 event (rolling a 6) that produces the specified outcome of "rolling a 6", and 5 events that do not (rolling a 1,2,3,4 or 5). The odds of rolling either a 5 or 6 is 2:4. This is because there are 2 events (rolling a 5 or 6) that produce the specified outcome of "rolling either a 5 or 6", and 4 events that do ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistical Independence
Independence is a fundamental notion in probability theory, as in statistics and the theory of stochastic processes. Two events are independent, statistically independent, or stochastically independent if, informally speaking, the occurrence of one does not affect the probability of occurrence of the other or, equivalently, does not affect the odds. Similarly, two random variables are independent if the realization of one does not affect the probability distribution of the other. When dealing with collections of more than two events, two notions of independence need to be distinguished. The events are called pairwise independent if any two events in the collection are independent of each other, while mutual independence (or collective independence) of events means, informally speaking, that each event is independent of any combination of other events in the collection. A similar notion exists for collections of random variables. Mutual independence implies pairwise independence ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binary Data
Binary data is data whose unit can take on only two possible states. These are often labelled as 0 and 1 in accordance with the binary numeral system and Boolean algebra. Binary data occurs in many different technical and scientific fields, where it can be called by different names including ''bit'' (binary digit) in computer science, ''truth value'' in mathematical logic and related domains and ''binary variable'' in statistics. Mathematical and combinatoric foundations A discrete variable that can take only one state contains zero information, and is the next natural number after 1. That is why the bit, a variable with only two possible values, is a standard primary unit of information. A collection of bits may have states: see binary number for details. Number of states of a collection of discrete variables depends exponentially on the number of variables, and only as a power law on number of states of each variable. Ten bits have more () states than three decimal digits ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conditional Probabilities
In probability theory, conditional probability is a measure of the probability of an event occurring, given that another event (by assumption, presumption, assertion or evidence) has already occurred. This particular method relies on event B occurring with some sort of relationship with another event A. In this event, the event B can be analyzed by a conditional probability with respect to A. If the event of interest is and the event is known or assumed to have occurred, "the conditional probability of given ", or "the probability of under the condition ", is usually written as or occasionally . This can also be understood as the fraction of probability B that intersects with A: P(A \mid B) = \frac. For example, the probability that any given person has a cough on any given day may be only 5%. But if we know or assume that the person is sick, then they are much more likely to be coughing. For example, the conditional probability that someone unwell (sick) is coughing might be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Random Variable
A random variable (also called random quantity, aleatory variable, or stochastic variable) is a mathematical formalization of a quantity or object which depends on random events. It is a mapping or a function from possible outcomes (e.g., the possible upper sides of a flipped coin such as heads H and tails T) in a sample space (e.g., the set \) to a measurable space, often the real numbers (e.g., \ in which 1 corresponding to H and -1 corresponding to T). Informally, randomness typically represents some fundamental element of chance, such as in the roll of a dice; it may also represent uncertainty, such as measurement error. However, the interpretation of probability is philosophically complicated, and even in specific cases is not always straightforward. The purely mathematical analysis of random variables is independent of such interpretational difficulties, and can be based upon a rigorous axiomatic setup. In the formal mathematical language of measure theory, a random var ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probability Distribution
In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment. It is a mathematical description of a random phenomenon in terms of its sample space and the probabilities of events (subsets of the sample space). For instance, if is used to denote the outcome of a coin toss ("the experiment"), then the probability distribution of would take the value 0.5 (1 in 2 or 1/2) for , and 0.5 for (assuming that the coin is fair). Examples of random phenomena include the weather conditions at some future date, the height of a randomly selected person, the fraction of male students in a school, the results of a survey to be conducted, etc. Introduction A probability distribution is a mathematical description of the probabilities of events, subsets of the sample space. The sample space, often denoted by \Omega, is the set of all possible outcomes of a random phe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dichotomy
A dichotomy is a partition of a whole (or a set) into two parts (subsets). In other words, this couple of parts must be * jointly exhaustive: everything must belong to one part or the other, and * mutually exclusive: nothing can belong simultaneously to both parts. If there is a concept A, and it is split into parts B and not-B, then the parts form a dichotomy: they are mutually exclusive, since no part of B is contained in not-B and vice versa, and they are jointly exhaustive, since they cover all of A, and together again give A. Such a partition is also frequently called a bipartition. The two parts thus formed are complements. In logic, the partitions are opposites if there exists a proposition such that it holds over one and not the other. Treating continuous variables or multi categorical variables as binary variables is called dichotomization. The discretization error inherent in dichotomization is temporarily ignored for modeling purposes. Etymology The term '' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Control Group
In the design of experiments, hypotheses are applied to experimental units in a treatment group. In comparative experiments, members of a control group receive a standard treatment, a placebo, or no treatment at all. There may be more than one treatment group, more than one control group, or both. A placebo control group can be used to support a double-blind study, in which some subjects are given an ineffective treatment (in medical studies typically a sugar pill) to minimize differences in the experiences of subjects in the different groups; this is done in a way that ensures no participant in the experiment (subject or experimenter) knows to which group each subject belongs. In such cases, a third, non-treatment control group can be used to measure the placebo effect directly, as the difference between the responses of placebo subjects and untreated subjects, perhaps paired by age group or other factors (such as being twins). For the conclusions drawn from the results of an e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Insensitivity To The Type Of Sampling
Sensory processing is the process that organizes sensation from one's own body and the environment, thus making it possible to use the body effectively within the environment. Specifically, it deals with how the brain processes multiple sensory modality inputs, such as proprioception, vision, auditory system, tactile, olfactory, vestibular system, interoception, and taste into usable functional outputs. It has been believed for some time that inputs from different sensory organs are processed in different areas in the brain. The communication within and among these specialized areas of the brain is known as functional integration. Newer research has shown that these different regions of the brain may not be solely responsible for only one sensory modality, but could use multiple inputs to perceive what the body senses about its environment. Multisensory integration is necessary for almost every activity that we perform because the combination of multiple sensory inputs is essen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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