ANOVA

Reference: http://home.ubalt.edu/ntsbarsh/stat-data/Topics.htm

• According to Field (2006), ANOVA refers to a family of statistical procedures that use F-test to test the overall fit of a linear model to the observed data. The result of F-test is an overall test whether group means differ accross levels of the categorical independent variable(s).
• "Simply, if there is one independent variable then the ANOVA is called a one-way ANOVA. If two independent variables have been manipulated in the the research, then a two-way ANOVA could be used to anayse the data." (Field, 2006)

Reference:
Foster, Kelly N., and Leah Melani Christian. " F-Test." Encyclopedia of Survey Research Methods.2008. SAGE Publications. 4 Mar. 2009. http://sage-ereference.com/survey/Article_n197.html.

• Foster and Christian (2008) writes, the F test is frequently associated with analysis of variance (ANOVA) and is most commonly used to test the null hypotheis that the means of normally distributed groups are equal.
• The F test was devised as an extension to the Z-test. Although the F test produces the same information as the Z test, when testing one independent variable with a nondirectional hypothesis, the F test has a distinct advantage over the Z test because multiple independent groups can easily be compared.
• The F test compares the observed value to the critical value of F. If the observed value of F (which is derived by dividing the mean squared error) is larger than the critical vlaue of F (obtained using the F distribution tabel) then the ralationship is deemed statistically significant and the null hypothesis is rejected.
• According to Foster and Christian (2008), there are two types of degree of freedom associated with the F test. The first is derived by subtrcting 1 from the numebr of independent variables and the second by subtracting the number of independent variables from the total number of cases. In output tables from software packages such as SPSS, SAS, and STATA the F value is listed with the degree of freedom and a P value. If the P value is less than the alpha valuechose (e.g. P<.05) then the relationship is statistically significant and the null hypotheis is rejected.