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Fisher's Method
In statistics, Fisher's method, also known as Fisher's combined probability test, is a technique for data fusion or "meta-analysis" (analysis of analyses). It was developed by and named for Ronald Fisher. In its basic form, it is used to combine the results from several independence tests bearing upon the same overall hypothesis (''H''0). Application to independent test statistics Fisher's method combines extreme value probabilities from each test, commonly known as " p-values", into one test statistic (''X''2) using the formula :X^2_ \sim -2\sum_^k \log(p_i), where ''p''''i'' is the p-value for the ''i''th hypothesis test. When the p-values tend to be small, the test statistic ''X''2 will be large, which suggests that the null hypotheses are not true for every test. When all the null hypotheses are true, and the ''p''''i'' (or their corresponding test statistics) are independent, ''X''2 has a chi-squared distribution with 2''k'' degrees of freedom, where ''k'' is the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
False Discovery Rate
In statistics, the false discovery rate (FDR) is a method of conceptualizing the rate of type I errors in null hypothesis testing when conducting multiple comparisons. FDR-controlling procedures are designed to control the FDR, which is the expected proportion of "discoveries" (rejected null hypotheses) that are false (incorrect rejections of the null). Equivalently, the FDR is the expected ratio of the number of false positive classifications (false discoveries) to the total number of positive classifications (rejections of the null). The total number of rejections of the null include both the number of false positives (FP) and true positives (TP). Simply put, FDR = FP / (FP + TP). FDR-controlling procedures provide less stringent control of Type I errors compared to family-wise error rate (FWER) controlling procedures (such as the Bonferroni correction), which control the probability of ''at least one'' Type I error. Thus, FDR-controlling procedures have greater power, at the co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cumulative Distribution Function
In probability theory and statistics, the cumulative distribution function (CDF) of a real-valued random variable X, or just distribution function of X, evaluated at x, is the probability that X will take a value less than or equal to x. Every probability distribution supported on the real numbers, discrete or "mixed" as well as continuous, is uniquely identified by an ''upwards continuous'' ''monotonic increasing'' cumulative distribution function F : \mathbb R \rightarrow ,1/math> satisfying \lim_F(x)=0 and \lim_F(x)=1. In the case of a scalar continuous distribution, it gives the area under the probability density function from minus infinity to x. Cumulative distribution functions are also used to specify the distribution of multivariate random variables. Definition The cumulative distribution function of a real-valued random variable X is the function given by where the right-hand side represents the probability that the random variable X takes on a value less th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Samuel A
Samuel ''Šəmūʾēl'', Tiberian: ''Šămūʾēl''; ar, شموئيل or صموئيل '; el, Σαμουήλ ''Samouḗl''; la, Samūēl is a figure who, in the narratives of the Hebrew Bible, plays a key role in the transition from the biblical judges to the United Kingdom of Israel under Saul, and again in the monarchy's transition from Saul to David. He is venerated as a prophet in Judaism, Christianity, and Islam. In addition to his role in the Hebrew scriptures, Samuel is mentioned in Jewish rabbinical literature, in the Christian New Testament, and in the second chapter of the Quran (although Islamic texts do not mention him by name). He is also treated in the fifth through seventh books of ''Antiquities of the Jews'', written by the Jewish scholar Josephus in the first century. He is first called "the Seer" in 1 Samuel 9:9. Biblical account Family Samuel's mother was Hannah and his father was Elkanah. Elkanah lived at Ramathaim in the district of Zuph. His gene ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistical Power
In statistics, the power of a binary hypothesis test is the probability that the test correctly rejects the null hypothesis (H_0) when a specific alternative hypothesis (H_1) is true. It is commonly denoted by 1-\beta, and represents the chances of a true positive detection conditional on the actual existence of an effect to detect. Statistical power ranges from 0 to 1, and as the power of a test increases, the probability \beta of making a type II error by wrongly failing to reject the null hypothesis decreases. Notation This article uses the following notation: * ''β'' = probability of a Type II error, known as a "false negative" * 1 − ''β'' = probability of a "true positive", i.e., correctly rejecting the null hypothesis. "1 − ''β''" is also known as the power of the test. * ''α'' = probability of a Type I error, known as a "false positive" * 1 − ''α'' = probability of a "true negative", i.e., correctly not rejecting the null hypothesis Description For a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Diabetes
Diabetes, also known as diabetes mellitus, is a group of metabolic disorders characterized by a high blood sugar level ( hyperglycemia) over a prolonged period of time. Symptoms often include frequent urination, increased thirst and increased appetite. If left untreated, diabetes can cause many health complications. Acute complications can include diabetic ketoacidosis, hyperosmolar hyperglycemic state, or death. Serious long-term complications include cardiovascular disease, stroke, chronic kidney disease, foot ulcers, damage to the nerves, damage to the eyes, and cognitive impairment. Diabetes is due to either the pancreas not producing enough insulin, or the cells of the body not responding properly to the insulin produced. Insulin is a hormone which is responsible for helping glucose from food get into cells to be used for energy. There are three main types of diabetes mellitus: * Type 1 diabetes results from failure of the pancreas to produce enough insulin due ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Effect Size
In statistics, an effect size is a value measuring the strength of the relationship between two variables in a population, or a sample-based estimate of that quantity. It can refer to the value of a statistic calculated from a sample of data, the value of a parameter for a hypothetical population, or to the equation that operationalizes how statistics or parameters lead to the effect size value. Examples of effect sizes include the correlation between two variables, the regression coefficient in a regression, the mean difference, or the risk of a particular event (such as a heart attack) happening. Effect sizes complement statistical hypothesis testing, and play an important role in power analyses, sample size planning, and in meta-analyses. The cluster of data-analysis methods concerning effect sizes is referred to as estimation statistics. Effect size is an essential component when evaluating the strength of a statistical claim, and it is the first item (magnitude) in the MA ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harmonic Mean P-value
The harmonic mean ''p''-value (HMP) is a statistical technique for addressing the multiple comparisons problem that controls the strong-sense family-wise error rate (this claim has been disputed). It improves on the power of Bonferroni correction by performing combined tests, i.e. by testing whether ''groups'' of ''p''-values are statistically significant, like Fisher's method. However, it avoids the restrictive assumption that the ''p''-values are independent, unlike Fisher's method. Consequently, it controls the false positive rate when tests are dependent, at the expense of less power (i.e. a higher false negative rate) when tests are independent. Besides providing an alternative to approaches such as Bonferroni correction that controls the stringent family-wise error rate, it also provides an alternative to the widely-used Benjamini-Hochberg procedure (BH) for controlling the less-stringent false discovery rate. This is because the power of the HMP to detect significant '' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
T Approximation
T, or t, is the twentieth letter in the Latin alphabet, used in the modern English alphabet, the alphabets of other western European languages and others worldwide. Its name in English is ''tee'' (pronounced ), plural ''tees''. It is derived from the Semitic Taw 𐤕 of the Phoenician and Paleo-Hebrew script (Aramaic and Hebrew Taw ת/𐡕/, Syriac Taw ܬ, and Arabic ت Tāʼ) via the Greek letter τ (tau). In English, it is most commonly used to represent the voiceless alveolar plosive, a sound it also denotes in the International Phonetic Alphabet. It is the most commonly used consonant and the second most commonly used letter in English-language texts. History '' Taw'' was the last letter of the Western Semitic and Hebrew alphabets. The sound value of Semitic ''Taw'', Greek alphabet Tαυ (''Tau''), Old Italic and Latin T has remained fairly constant, representing in each of these; and it has also kept its original basic shape in most of these alphabets. Use in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Extensions Of Fisher's Method
In statistics, extensions of Fisher's method are a group of approaches that allow approximately valid statistical inferences to be made when the assumptions required for the direct application of Fisher's method are not valid. Fisher's method is a way of combining the information in the p-values from different statistical tests so as to form a single overall test: this method requires that the individual test statistics (or, more immediately, their resulting p-values) should be statistically independent. Dependent statistics A principal limitation of Fisher's method is its exclusive design to combine independent p-values, which renders it an unreliable technique to combine dependent p-values. To overcome this limitation, a number of methods were developed to extend its utility. Known covariance Brown's method Fisher's method showed that the log-sum of ''k'' independent p-values follow a ''χ''2-distribution with 2''k'' degrees of freedom: : X = -2\sum_^k \log_e(p_i) \sim \chi^ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
