Statistical test methods

Comparison of two mean values ​​(Student's t-test)

  • Comparison of two mean values xa¯ and xb¯ from or nb Data points with homogeneous variance. It should be checked whether the difference between the mean values ​​is due solely to a random error (both mean values ​​come from the population with the same mean value). If the test shows a significant difference, the two mean values ​​must not be compared with one another.
  • First, after the error propagation, the standard deviation of the difference between two mean values ​​with the degrees of freedom f=n1+n22 calculated:sx1¯x2¯=s12n1+s22n2=sdv¯xn1+n2n1n2
  • The differences xa¯xb¯ are random variables which, with the mostly available number, only follow a few measurements of a t-distribution. You will still be with sdv¯x normalized and one obtains:tˆ=xa¯xb¯sdv¯xnanbna+nb
  • The tested hypothesis m1=m2=m is with α (possible error 1st type) to be discarded if calculated tˆ larger than tabulated t-Is worth. Then there is a significant difference between the two mean values.
  • The difference between the two mean values ​​is considered inconclusive, if tber.<ttab.fails. If applies t>tα2f, the mean values ​​are different within the given probability of error.
  • The prerequisite for the calculation, however, is that the two standard deviations do not show any difference, otherwise they cannot be "pooled". An F-test must always be placed in front of it.
  • Pooled variance:var¯x=na1varxa¯+nb1varxb¯na+nb2

Video: Testování statistických hypotéz - Statistika část (December 2021).