Glass & Hopkins (1984) ANOVA - Chapter 16

Question 1

What is the probability of at least 1 type-1 error when conducting more than 1 t-test?

Answer 1

p = 1 - (1 - a)^k

Where K is the number of comparisons being made

Question 2

What is an omnibus hypothesis?

Answer 2

Tests are referred to as omnibus if after rejecting the null hypothesis you do not know where the differences assessed by the statistical test are. In the case of F tests they are omnibus when there is more than one df in the numerator (3 or more groups) it is omnibus. In the case of Chi-square tests, when there is more than one df it is omnibus.

Question 3

What is SS_Total?

Answer 3

SS_T is defined as the sum of the squared deviation of every score from the grand mean: x̄

Where the grand mean is the mean of all the n. observations

Question 4

What does a hat (^) over a symbol mean?

Answer 4

An estimate of

Question 5

What is a_j?

Answer 5

a_j is the difference between the mean of group j, µ_j, and the grand mean, µ

That is, a_j can be said to be the effect of treatment j.

It is estimated by: â_j = X̄_j - X̄

Question 6

What is the F ratio?

Answer 6

the F ratio is computed by dividing SSb and SSw by their reprective degrees of freedom - this gives us MSb and MSw, and the F ratio is as follows:

F = MSb/MSw

Question 7

How do we reject H0 with an F ratio?

Answer 7

When H0 is true the value of F will be approximately 1.0 (i.e., the denominator will be larger than the numerator)

When H0 is false, the numerator will tend to be larger than the denominator.