The goodness–of–fit test can be used to decide whether a population fits a given distribution, but it will not suffice to decide whether two populations follow the same unknown distribution. A different test, called the test for homogeneity, can be used to conclude whether two populations have the same distribution. To calculate the test statistic for a test for homogeneity, follow the same procedure as with the test of independence. The hypotheses for the test for homogeneity can be stated as follows:

H0: The distributions of the two populations are the same.

H1: The distributions of the two populations are not the same.

This test uses a chi-square test Statistic and is computed in the same way as the test for independence. The degrees of freedom for this test are given as df = number of columns - 1

The most common use for this test is comparing two populations. For example, men vs. women, before vs. after, and east vs. west. The variable is categorical, with more than two possible response values.

The expected frequency values for this test are required to be at least 5, similar to the chi-square-based tests. However, if any value is below five, one can use a Fischer Exact Test. It is helpful for all chi-square-based tests and provides an exact P-value. However, since the calculations involved in this test are complex, computer software such as Minitab and STATDISK are used.

This text is adapted from Openstax, Introductory Statistics, Section 11.4 Test for Homogeneity.

Tags
Test For HomogeneityGoodness of fit TestChi square Test StatisticIndependence TestNull HypothesisAlternative HypothesisDegrees Of FreedomCategorical VariableExpected FrequencyFischer Exact TestMinitabSTATDISK

Dal capitolo 8:

article

Now Playing

8.14 : Test for Homogeneity

Distributions

1.9K Visualizzazioni

article

8.1 : Distribuzioni per stimare il parametro della popolazione

Distributions

3.8K Visualizzazioni

article

8.2 : Gradi di libertà

Distributions

2.8K Visualizzazioni

article

8.3 : Distribuzione t degli studenti

Distributions

5.5K Visualizzazioni

article

8.4 : Scegliere tra la distribuzione z e t

Distributions

2.5K Visualizzazioni

article

8.5 : Distribuzione del chi-quadrato

Distributions

3.2K Visualizzazioni

article

8.6 : Trovare i Valori Critici per il Chi-Quadrato

Distributions

2.7K Visualizzazioni

article

8.7 : Stima della deviazione standard della popolazione

Distributions

2.9K Visualizzazioni

article

8.8 : Test di bontà dell'adattamento

Distributions

3.2K Visualizzazioni

article

8.9 : Frequenze attese nei test di bontà dell'adattamento

Distributions

2.4K Visualizzazioni

article

8.10 : Tabella di contingenza

Distributions

2.3K Visualizzazioni

article

8.11 : Introduzione alla Prova di Indipendenza

Distributions

2.0K Visualizzazioni

article

8.12 : Test di ipotesi per il test di indipendenza

Distributions

3.3K Visualizzazioni

article

8.13 : Determinazione della frequenza prevista

Distributions

2.0K Visualizzazioni

article

8.15 : F Distribuzione

Distributions

3.5K Visualizzazioni

JoVE Logo

Riservatezza

Condizioni di utilizzo

Politiche

Ricerca

Didattica

CHI SIAMO

Copyright © 2025 MyJoVE Corporation. Tutti i diritti riservati