Independent T Test

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{\displaystyle {\begin{matrix}{\frac {1}{2}}+x\Gamma \left({\frac {\nu +1}{2}}\right)\times \\[0.5em]{\frac {\,_{2}F_{1}\left({\frac {1}{2}},{\frac {\nu +1}{2}};{\frac {3}{2}};-{\frac {x^{2}}{\nu }}\right)}{{\sqrt {\pi \nu }}\,\Gamma \left({\frac {\nu }{2}}\right)}}\end{matrix}}}

In statistics, the number of degrees of freedom is the number of values in the final calculation of a statistic that are free to vary.[1]

Analysis of variance (ANOVA) is a collection of statistical models and their associated estimation procedures (such as the "variation" among and between groups) used to analyze the differences among group means in a sample. ANOVA was developed by statistician and evolutionary biologist Ronald Fisher. The ANOVA is based on the law of total variance, where the observed variance in a particular variable is partitioned into components attributable to different sources of variation. In its simplest form, ANOVA provides a statistical test of whether two or more population means are equal, and therefore generalizes the t-test beyond two means.

How to test the difference between two means on a TI calculator by performing a Two Sample T-Test.

A scientific calculator is a type of electronic calculator, usually but not always handheld, designed to calculate problems in science, engineering, and mathematics. They have completely replaced slide rules in traditional applications, and are widely used in both education and professional settings.

An electronic calculator is typically a portable electronic device used to perform calculations, ranging from basic arithmetic to complex mathematics.

In statistics, a confidence interval (CI) is a type of estimate computed from the statistics of the observed data. This proposes a range of plausible values for an unknown parameter (for example, the mean). The interval has an associated confidence level that the true parameter is in the proposed range. Given observations

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{\displaystyle x_{1},\ldots ,x_{n}}

and a confidence level

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{\displaystyle \gamma }

, a valid confidence interval has a

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{\displaystyle \gamma }

probability of containing the true underlying parameter. The level of confidence can be chosen by the investigator. In general terms, a confidence interval for an unknown parameter is based on sampling the distribution of a corresponding estimator.[1]

The t-test is any statistical hypothesis test in which the test statistic follows a Student's t-distribution under the null hypothesis.

A correlation coefficient is a numerical measure of some type of correlation, meaning a statistical relationship between two variables.[a] The variables may be two columns of a given data set of observations, often called a sample, or two components of a multivariate random variable with a known distribution.[citation needed]

In statistics, a confidence interval (CI) is a type of estimate computed from the statistics of the observed data. This proposes a range of plausible values for an unknown parameter (for example, the mean). The interval has an associated confidence level that the true parameter is in the proposed range. Given observations x 1 , … , x n {\displaystyle x_{1},\ldots ,x_{n}} and a confidence level γ {\displaystyle \gamma } , a valid confidence interval has a γ {\displaystyle \gamma } probability of containing the true underlying parameter. The level of confidence can be chosen by the investigator. In general terms, a confidence interval for an unknown parameter is based on sampling the distribution of a corresponding estimator.[1]

In statistics and in probability theory, distance correlation or distance covariance is a measure of dependence between two paired random vectors of arbitrary, not necessarily equal, dimension. The population distance correlation coefficient is zero if and only if the random vectors are independent. Thus, distance correlation measures both linear and nonlinear association between two random variables or random vectors. This is in contrast to Pearson's correlation, which can only detect linear association between two random variables.

Two events are independent, statistically independent, or stochastically independent[1] if the occurrence of one does not affect the probability of occurrence of the other (equivalently, does not affect the odds). Similarly, two random variables are independent if the realization of one does not affect the probability distribution of the other.

In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values.[1] A low standard deviation indicates that the values tend to be close to the mean (also called the expected value) of the set, while a high standard deviation indicates that the values are spread out over a wider range.