A histogram is an approximate representation of the distribution of numerical or categorical data. It was first introduced by Karl Pearson. To construct a histogram, the first step is to "bin" the range of values—that is, divide the entire range of values into a series of intervals—and then count how many values fall into each interval. The bins are usually specified as consecutive, non-overlapping intervals of a variable. The bins (intervals) must be adjacent, and are often of equal size.
There are several kinds of means in various branches of mathematics.
In statistics, stratified sampling is a method of sampling from a population which can be partitioned into subpopulations.
In statistics, an effect size is a quantitative measure of the magnitude of a phenomenon. It can refer to the value of a statistic calculated from a sample of data, the value of a parameter of a hypothetical statistical 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 happening. Effect sizes complement statistical hypothesis testing, and play an important role in power analyses, sample size planning, and in meta-analyses.
The t-test is any statistical hypothesis test in which the test statistic follows a Student's t-distribution under the null hypothesis.
Sample size determination is the act of choosing the number of observations or replicates to include in a statistical sample. The sample size is an important feature of any empirical study in which the goal is to make inferences about a population from a sample. In practice, the sample size used in a study is usually determined based on the cost, time, or convenience of collecting the data, and the need for it to offer sufficient statistical power. In complicated studies there may be several different sample sizes: for example, in a stratified survey there would be different sizes for each stratum. In a census, data is sought for an entire population, hence the intended sample size is equal to the population. In experimental design, where a study may be divided into different treatment groups, there may be different sample sizes for each group.
In statistical process monitoring (SPM), the and R chart is a type of scheme, popularly known as control chart, used to monitor the mean and range of a normally distributed variables simultaneously, when samples are collected at regular intervals from a business or industrial process.. It is often used to monitor the variables data but the performance of the and R chart may suffer when the normality assumption is not valid. This is connected traditional statistical quality control (SQC) and statistical process control (SPC). However, Woodall noted that "I believe that the use of control charts and other monitoring methods should be referred to as “statistical process monitoring,” not “statistical process control (SPC).”"
In statistical quality control, the p-chart is a type of control chart used to monitor the proportion of nonconforming units in a sample, where the sample proportion nonconforming is defined as the ratio of the number of nonconforming units to the sample size, n.
An index of qualitative variation (IQV) is a measure of statistical dispersion in nominal distributions. There are a variety of these, but they have been relatively little-studied in the statistics literature. The simplest is the variation ratio, while more complex indices include the information entropy.
The combination of quality control and genetic algorithms led to novel solutions of complex quality control design and optimization problems. Quality control is a process by which entities review the quality of all factors involved in production. Quality is the degree to which a set of inherent characteristics fulfils a need or expectation that is stated, general implied or obligatory. Genetic algorithms are search algorithms, based on the mechanics of natural selection and natural genetics.
In statistical quality control, the individual/moving-range chart is a type of control chart used to monitor variables data from a business or industrial process for which it is impractical to use rational subgroups.
In statistical quality control, the np-chart is a type of control chart used to monitor the number of nonconforming units in a sample. It is an adaptation of the p-chart and used in situations where personnel find it easier to interpret process performance in terms of concrete numbers of units rather than the somewhat more abstract proportion.
In statistical quality control, the and s chart is a type of control chart used to monitor variables data when samples are collected at regular intervals from a business or industrial process. This is connected traditional statistical quality control (SQC) and statistical process control (SPC). However, Woodall noted that "I believe that the use of control charts and other monitoring methods should be referred to as “statistical process monitoring,” not “statistical process control (SPC).”"
In statistical quality control, the c-chart is a type of control chart used to monitor "count"-type data, typically total number of nonconformities per unit. It is also occasionally used to monitor the total number of events occurring in a given unit of time.
In statistical quality control, the EWMA chart is a type of control chart used to monitor either variables or attributes-type data using the monitored business or industrial process's entire history of output. While other control charts treat rational subgroups of samples individually, the EWMA chart tracks the exponentially-weighted moving average of all prior sample means. EWMA weights samples in geometrically decreasing order so that the most recent samples are weighted most highly while the most distant samples contribute very little.
Acceptance sampling uses statistical sampling to determine whether to accept or reject a production lot of material. It has been a common quality control technique used in industry. It is usually done as products leaves the factory, or in some cases even within the factory. Most often a producer supplies a consumer a number of items and a decision to accept or reject the items is made by determining the number of defective items in a sample from the lot. The lot is accepted if the number of defects falls below where the acceptance number or otherwise the lot is rejected.
Taylor's power law is an empirical law in ecology that relates the variance of the number of individuals of a species per unit area of habitat to the corresponding mean by a power law relationship. It is named after the ecologist who first proposed it in 1961, Lionel Roy Taylor (1924–2007). Taylor's original name for this relationship was the law of the mean.
In statistics, the Jonckheere trend test is a test for an ordered alternative hypothesis within an independent samples (between-participants) design. It is similar to the Kruskal–Wallis test in that the null hypothesis is that several independent samples are from the same population. However, with the Kruskal–Wallis test there is no a priori ordering of the populations from which the samples are drawn. When there is an a priori ordering, the Jonckheere test has more statistical power than the Kruskal–Wallis test. The test was developed by A. R. Jonckheere, who was a psychologist and statistician at University College London.
High-temperature operating life (HTOL) is a reliability test applied to integrated circuits (ICs) to determine their intrinsic reliability. This test stresses the IC at an elevated temperature, high voltage and dynamic operation for a predefined period of time. The IC is usually monitored under stress and tested at intermediate intervals. This reliability stress test is sometimes referred to as a "lifetime test", "device life test" or "extended burn in test" and is used to trigger potential failure modes and assess IC lifetime.
A variables sampling plan is an acceptance sampling technique. Plans for variables are intended for quality characteristics that are measured in a continuous scale. This plan requires the knowledge of the statistical model e.g. normal distribution. The historical evolution of this technique dates back to the seminal work of Wallis (1943). The purpose of a plan for variables is to assess whether the process is operating far enough from the specification limit. Plans for variables may produce a similar OC curve to attribute plans with significantly less sample size.
