Analysis of Variance (ANOVA)

F distribution

• a continuous right-skewed distribution used in an analysis of variance

• this distribution depends on on two-degreed-of-freedom values

Analysis of Variance (ANOVA)

• an extension of t-test

• there is a direct relationship between the t test and the F statistic

F statistic

It is generally used for determining differences for more than two means

One-way analysis of variance

It is a method used to compare two or more group means simultaneously in the light of single variable

Variance homogeneity

In One-way ANOVA, it means that within-group variance is constant across groups

Mean square error (MSE)

In ANOVA, s2 is called the _____________

SS

Represent the sum of squared deviations associated with the factor listed under 'Source'

Total Sum of Squares (SST)

Reflects the overall variation in all the given observations

Sum of squares between-group (SSB)

• reflects the variations between groups due to treatment effect

• also called between-column sum of squared (SSC)

Sum of squares within-group (SSW)

• reflects the differences in the observations within the same group due to sampling error

• also called the error sum of squares (SSE)

Sum of squares between-group (SSB) Sum of squares within group (SSW)

The SST of one-way ANOVA is further partitioned into to sums of square:

Mean squares

The obtained result when the SSC and SSE are divided by their corresponding degrees of freedom

Significant

Any test statistic having probability of less than 0.05 indicates ______________

Scheffe Bonferroni Sidak

STATA software has three built-in pairwise methods:

Scheffe

• Performs pairwise comparisons for all possible pairwise combinations of means

• uses F test to perform the said pairwise means comparison

Bonferroni

• it is used after obtaining a significant ANOVA F test

• it uses t-test to perform pairwise comparisons between group means

Sidak

• it is based in an t statistic

• this test can be applied to groups where the sample in each group may be equal or not

Turkey HSD Turkey-Kramer Fisher Hayter

Studentized Range distribution:

Turkey HSD

• this is used for testing the significance of all pairwise comparison based on studentized range distribution

• It is one of several methods of ensuring that the chance of finding a significant difference in any comparison is maintained at the alpha level of the test

• it preserves "family-wise type I"

Turkey-Kramer

This is another post-hoc pairwise means comparison based on the studentized range distribution

Fisher-Hayter

This is also a post-hoc technique that test all pairwise comparisons of means based on the studentized range distribution

Two-Way Analysis of Variance (ANOVA)

It is a method for simultaneously analyzing more mean in the light if two variables

Blocking variable

variation can be separated form the error variation to give more precise group comparisons

Two-way ANOVA without Interaction

It implies that there are only two possible hypotheses that can be formulated in this case, i.e., one for each variable