Page 92 - Quantitative Data Analysis

Quantitative Data Analysis
Simply Explained Using SPSS

o 5% chance of being sig by chance

 About 30% for all six test…

6
 1 – (1 – 0.05) = 0.265, actually 26%

Which means your chances of incorrectly rejecting the null
hypothesis (a type I error) is about 1 in 4 instead of 1 in 20!!

Assumptions of ANOVA

ANOVA has similar assumptions like independent t-test. Like

1. The population sample must be normal
2. The observations must be independent in each sample
3. Homogeneity of variance

ANOVA compares all means simultaneously and maintains
the type I error probability at the designated level.

The ANOVA results do not tell you which group is different,
only whether a difference exists.
Once ANOVA is significant then we can test significance
differences among all possible pair wise comparisons.
If ANOVA is not significant then pair wise group tests are
less meaningful.

In conclusion it is necessary to use the ANOVA when the design
of a study has more than 2 conditions or groups to compare. The t-
test is simple and less daunting especially when you see a 2 x 3 x 4
factorial ANOVA is needed, but the risk of committing a type I error

The Theory and Applications of Statistical Inferences 76