What are reliability intervals?

In statistics, reliability intervals are used as estimates of the interval for population parameters. They are often used in science and engineering to test hypotheses, statistical processes management and data analysis. Although it is possible to calculate reliability intervals manually, it is usually easier and much faster to use specialized statistical programs or advanced graphics calculators.

If the statement of the p (l <θ ≤) = 1 - α and a and and a a and a a a a a a a a a a and a and and and a a a and a and and and and and and the parameter, then the interval between l and u . This definition can be given in a more intuitive and practical way by the statement that the θ parameter is in the reliability interval will be true 100 (1 - α) she will make her. The term (1 - α) is known as trust. Calculated by the Equation x - Z _{α/2 σ/√n ≤ μ ≤ x + Z and/2 σ/√n} , in which and/2 is the upper 100 curves. This is a simple case, because the actual diameter and dispersion of the whole population is usually not known.

Reliability intervals

are most often used to determine how well a certain parameter fits into a given data file. For example, if the reliability interval for a given data set covers from 45 to 55 with a 0.95 reliability coefficient, it can be argued that any data point that falls within this Belongs area in the populationwith 95 % confidence. Increasing the reliability coefficient will complete the interval, which means that a smaller range of variables can be explained with greater certainty. The decrease in the confidence coefficient extends the interval but reduces trust.

In some applications, such as normally distributed populations with known means and deviations, equations are used to calculate the reliability intervals easily available. Statistical tables can be used to find values ​​for z _and/2 . Other applications such as data analysis in engineering require more sophisticated calculation methods. It is usually more practical to use the statistical program to determine the reliability intervals in these cases. Statistical programs can be particularly useful if data files are extremely large and the results must be presented graphically.