Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model to be studied. Populations can be diverse groups of people or objects such as "all people living in a country" or "every atom composing a crystal". Statistics deals with every aspect of data, including the planning of data collection in terms of the design of surveys and experiments.
In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean of the set, while a high standard deviation indicates that the values are spread out over a wider range.
Uncertainty refers to epistemic situations involving imperfect or unknown information. It applies to predictions of future events, to physical measurements that are already made, or to the unknown. Uncertainty arises in partially observable and/or stochastic environments, as well as due to ignorance, indolence, or both. It arises in any number of fields, including insurance, philosophy, physics, statistics, economics, finance, psychology, sociology, engineering, metrology, meteorology, ecology and information science.
In statistical hypothesis testing, a result has statistical significance when it is very unlikely to have occurred given the null hypothesis. More precisely, a study's defined significance level, denoted by , is the probability of the study rejecting the null hypothesis, given that the null hypothesis was assumed to be true; and the p-value of a result, , is the probability of obtaining a result at least as extreme, given that the null hypothesis is true. The result is statistically significant, by the standards of the study, when . The significance level for a study is chosen before data collection, and is typically set to 5% or much lower—depending on the field of study.
In statistics, a confidence interval (CI) is a type of estimate computed from the statistics of the observed data. This gives a range of values for an unknown parameter. The interval has an associated confidence level that gives the probability with which the estimated interval will contain the true value of the parameter. The confidence level is chosen by the investigator. For a given estimation in a given sample, using a higher confidence level generates a wider confidence interval. In general terms, a confidence interval for an unknown parameter is based on sampling the distribution of a corresponding estimator.
Significant figures of a number in positional notation are digits in the number that are reliable and absolutely necessary to indicate the quanity of something. If a number expressing the result of measurement of something has more digits than the digits allowed by the measurement resolution, then the only digits allowed by the measurement resolution are reliable so only these can be significant figures; For example, if a length measurement gives 11.48 mm while the smallest interval between marks on the ruler used in the measurment is 1 mm, then the first three digits are ony reliable so can be significant figures. Among these digits, there is uncertainty in the last digit but it is also considered as a significant figure since digits that are uncertain but reliable are considered significant figures. Another example is a volume measurement of 2.98 L with the uncertainty of ± 0.05 L. The actual volume is somewhere between 2.93 L and 3.03 L. Even if all three digits are not certain but reliable as these indicate to the actual volume with the acceptable uncertainty. So, these are significant figures.
The plus–minus sign, ±, is a mathematical symbol with multiple meanings.
In statistics, an effect size is a number measuring the strength of the relationship between two variables in a statistical 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 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 cluster of data-analysis methods concerning effect sizes is referred to as estimation statistics.
The standard error (SE) of a statistic is the standard deviation of its sampling distribution or an estimate of that standard deviation. If the statistic is the sample mean, it is called the standard error of the mean (SEM).
In statistics, propagation of uncertainty is the effect of variables' uncertainties on the uncertainty of a function based on them. When the variables are the values of experimental measurements they have uncertainties due to measurement limitations which propagate due to the combination of variables in the function.
In probability theory and statistics, the coefficient of variation (CV), also known as relative standard deviation (RSD), is a standardized measure of dispersion of a probability distribution or frequency distribution. It is often expressed as a percentage, and is defined as the ratio of the standard deviation to the mean . The CV or RSD is widely used in analytical chemistry to express the precision and repeatability of an assay. It is also commonly used in fields such as engineering or physics when doing quality assurance studies and ANOVA gauge R&R. In addition, CV is utilized by economists and investors in economic models.
Significance arithmetic is a set of rules for approximating the propagation of uncertainty in scientific or statistical calculations. These rules can be used to find the appropriate number of significant figures to use to represent the result of a calculation. If a calculation is done without analysis of the uncertainty involved, a result that is written with too many significant figures can be taken to imply a higher precision than is known, and a result that is written with too few significant figures results in an avoidable loss of precision. Understanding these rules requires a good understanding of the concept of significant and insignificant figures.
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 analytical chemistry, the detection limit, lower limit of detection, or LOD, often mistakenly confused with the analytical sensitivity, is the lowest quantity of a substance that can be distinguished from the absence of that substance with a stated confidence level. The detection limit is estimated from the mean of the blank, the standard deviation of the blank, the slope of the calibration plot and a defined confidence factor. Another consideration that affects the detection limit is the accuracy of the model used to predict concentration from the raw analytical signal.
In metrology, measurement uncertainty is the expression of the statistical dispersion of the values attributed to a measured quantity. All measurements are subject to uncertainty and a measurement result is complete only when it is accompanied by a statement of the associated uncertainty, such as the standard deviation. By international agreement, this uncertainty has a probabilistic basis and reflects incomplete knowledge of the quantity value. It is a non-negative parameter.
A Bland–Altman plot in analytical chemistry or biomedicine is a method of data plotting used in analyzing the agreement between two different assays. It is identical to a Tukey mean-difference plot, the name by which it is known in other fields, but was popularised in medical statistics by J. Martin Bland and Douglas G. Altman.
The minimal important difference (MID) or minimal clinically important difference (MCID) is the smallest change in a treatment outcome that an individual patient would identify as important and which would indicate a change in the patient's management.
Estimation statistics, or simply estimation, is a data analysis framework that uses a combination of effect sizes, confidence intervals, precision planning, and meta-analysis to plan experiments, analyze data and interpret results. It is distinct from null hypothesis significance testing (NHST), which is considered to be less informative. Estimation statistics is also known as the new statistics in the fields of psychology, medical research, life sciences and other experimental sciences, where NHST still remains prevalent, despite contrary recommendations for several decades.
Radiocarbon dating measurements produce ages in "radiocarbon years", which must be converted to calendar ages by a process called calibration. Calibration is needed because the atmospheric 14
C/12
C ratio, which is a key element in calculating radiocarbon ages, has not been constant historically.
