RESUMEN
Student's t test (t test), analysis of variance (ANOVA), and analysis of covariance (ANCOVA) are statistical methods used in the testing of hypothesis for comparison of means between the groups. The Student's t test is used to compare the means between two groups, whereas ANOVA is used to compare the means among three or more groups. In ANOVA, first gets a common P value. A significant P value of the ANOVA test indicates for at least one pair, between which the mean difference was statistically significant. To identify that significant pair(s), we use multiple comparisons. In ANOVA, when using one categorical independent variable, it is called one-way ANOVA, whereas for two categorical independent variables, it is called two-way ANOVA. When using at least one covariate to adjust with dependent variable, ANOVA becomes ANCOVA. When the size of the sample is small, mean is very much affected by the outliers, so it is necessary to keep sufficient sample size while using these methods.
RESUMEN
La prueba t-Student se fundamenta en dos premisas; la primera: en la distribución de normalidad, y la segunda: en que las muestras sean independientes. Permite comparar muestras, N ≤ 30 y/o establece la diferencia entre las medias de las muestras. El análisis matemático y estadístico de la prueba con frecuencia se minimiza para N > 30, utilizando pruebas no paramétricas, cuando la prueba tiene suficiente poder estadístico.
Student's t test is based on two premises; first: normality of distribution and second: the independence of the samples. This allows comparing samples N ≤ 30 and/or establishes the differences between the means of the two samples. The mathematical and statistical analysis of the test is frequently minimalized N > 30, using non parametric tests, when the test has enough statistical power.
RESUMEN
Los grados de libertad representan un tema central en la estadística moderna, sin embargo su concepto se explica poco en los libros de texto. A pesar de que Gauss los usó por primera vez al estimar las distancias entre las estrellas, no aparece formalmente hasta los escritos de Gosset (Student) en 1908. El concepto de grados de libertad se puede entender desde un punto de vista geométrico, algebraico e incluso intuitivo. La geometría nos describe a los grados de libertad como espacios e hiperespacios de libertad através de los cuales una medida de resumen puede moverse y tomar diferentes valores. El punto de vista algebraico los describe como el número de ecuaciones que se establecen usando los datos. Ambos puntos de vista est n relacionados y ayudan a comprender con mayor profundidad el concepto de grados de libertad. La aplicaciones de los grados de libertad está n extendidas através de toda la estadstica, el calculo de la desviación estándar y la prueba t de Student son solo algunos ejemplos.
Degrees of freedom is a central topic in modern statistics, however is poor explained in textbooks. Gauss used it for first time in estimates of astronomic distances but it appears formally in Gosset (Student) manuscripts in 1908. Degrees of freedom can be understood from geometric, algebraic or even intuitive point of view. Geometrics shows degrees of freedom as spaces through a summary measure can move freely assuming different values. Algebra describes degrees of freedom as number of unknown variables in respect of number of equations we can establish using data. Both algebraic and geometric points of view are related and help us to understand better the meaning of degrees of freedom. Applications in statistics are widely spread but standard deviation and Student t are just some examples.