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Degrees of freedom
...of a statistical data set. It is a fundamental concept in the fields of [[statistics]], [[physics]], and [[engineering]]. ...ution. In other words, it is the number of values in the final calculation of a statistic that are free to vary without violating any given constraints.

2 KB (229 words) - 15:35, 22 February 2024
Welch–Satterthwaite equation
...pothesis testing or constructing [[confidence intervals]] for the variance of a combined population. The Welch–Satterthwaite equation is named after B. ...zes are unequal. The equation provides a way to approximate the degrees of freedom for the combined variance estimate, which is crucial for further statistica

3 KB (404 words) - 12:26, 22 March 2024
Chi-squared distribution
...nstruction of [[confidence intervals]] for a population standard deviation of a normal distribution from a sample standard deviation. ...y χ²(k), where ''k'' is the number of degrees of freedom (i.e., the number of independent standard normal variables in the sum).

2 KB (333 words) - 03:57, 24 April 2024
Inverse-chi-squared distribution
...ng]]. It is especially important in the context of estimating the variance of a normally distributed population when the mean is known. ...where \( X \) follows a chi-squared distribution with \( \nu \) degrees of freedom. Mathematically, if \( X \sim \chi^2(\nu) \), then \( \frac{1}{X} \) follow

2 KB (305 words) - 08:27, 19 March 2024
Student's t-distribution
...rucial role in many areas of [[statistics]], especially in the development of [[t-tests]] for hypothesis testing and in constructing confidence intervals ...rewing. The distribution is defined by a parameter known as the degrees of freedom, which is related to the sample size.

3 KB (404 words) - 20:52, 16 April 2024
Jarque–Bera test
...approximated using Monte Carlo simulation in Matlab)[[Category:Dictionary of medicine]].

668 bytes (106 words) - 05:41, 6 April 2024
T distribution
'''t-distribution''' or '''Student's t-distribution''' is a type of [[probability distribution]] that is symmetric and bell-shaped, like the [[ ...ed in the problems of small samples – for example, the chemical properties of barley where sample sizes might be as low as 3. To account for the uncertai

2 KB (325 words) - 22:20, 4 March 2024
Scaled inverse chi-squared distribution
...Bayesian inference]] and hierarchical models. It is a two-parameter family of continuous probability distributions and is closely related to the [[Invers ...scale parameter \( \sigma^2 > 0 \). The probability density function (pdf) of the scaled inverse chi-squared distribution for \( x > 0 \) is given by:

2 KB (295 words) - 00:33, 22 March 2024
Noncentral chi-squared distribution
...alternative hypothesis]], and in the study of [[power (statistics)|power]] of statistical tests. ...the noncentrality parameter ''λ''. The probability density function (pdf) of the noncentral chi-squared distribution for ''x'' > 0 is given by:

2 KB (318 words) - 04:34, 22 March 2024
Statistical mechanics
...d in everyday life, therefore explaining [[thermodynamics]] as a result of statistics. ...for the fundamental study of any physical system that has many degrees of freedom. The approach is based on statistical methods, probability theory and the m

2 KB (289 words) - 23:11, 4 March 2024
Multivariate t-distribution
...variance is unknown. This distribution is particularly useful in the field of [[multivariate analysis]], where it helps in making inferences about a popu The multivariate t-distribution describes the distribution of a random vector. Let \(X\) be a \(p\)-dimensional random vector. \(X\) foll

2 KB (328 words) - 12:32, 21 March 2024
Blocking (statistics)
...for these external variables, thereby increasing the [[statistical power]] of the test and reducing the [[experimental error]]. ...can more accurately isolate the effect of the treatments from the effects of the blocking factors.

4 KB (633 words) - 01:38, 18 April 2024
Residuals
...in [[regression analysis]], where they help in validating the assumptions of the linear model. * Assess the fit of a model: Large residuals indicate that the model does not fit the data well

3 KB (372 words) - 19:22, 22 March 2024
95% CI
...hich we can be 95% certain that the true value (for example, the true mean of a population) lies. It is a key concept in [[statistical inference]], allow ...amples and build a confidence interval from each sample, approximately 95% of these intervals would contain the true population parameter.

2 KB (381 words) - 04:03, 30 March 2024
Behrens–Fisher problem
...her problem''' is a statistical issue that arises when comparing the means of two [[normal distribution|normal distributions]] that have unknown and uneq ...rld data analysis, making the Behrens–Fisher problem a critical topic in [[statistics]].

3 KB (438 words) - 20:11, 17 March 2024
F-test
...f Variance (ANOVA)]], [[regression analysis]], and the testing of equality of variances. ...late the F-statistic. The basic formula for the F-statistic in the context of comparing two sample variances is:

3 KB (440 words) - 02:33, 25 March 2024
Prediction interval
...y of a population parameter, prediction intervals focus on the uncertainty of individual future observations. A prediction interval provides an upper and lower bound on the expected value of a new observation based on a fitted statistical model. The interval is calc

4 KB (524 words) - 03:00, 18 April 2024
Log rank test
...ovascular diseases]]. The test is non-parametric and is based on the ranks of survival times, making no assumptions about the underlying survival distrib ...served minus expected events across all observed event times. It is a type of [[Kaplan-Meier estimator|Kaplan-Meier]] survival curve comparison.

3 KB (431 words) - 03:52, 28 March 2024
Monte Carlo method
...matics]], allowing for the modeling of complex systems and the computation of difficult integrals. ...tatistical properties as the system under study. By analyzing the outcomes of these simulations, researchers can approximate solutions to problems such a

3 KB (437 words) - 16:16, 23 March 2024
Likelihood-ratio test
...e test is based on the likelihood function, which measures the probability of observing the data given a specific model. ...improves the fit compared to a simpler model. It compares the likelihoods of the two models and calculates a test statistic, known as the likelihood rat

4 KB (536 words) - 15:55, 22 January 2024