Multivariate Statistical Methods

Two-way ANOVA with and without replication

Imad Feneir

Q1. Test for a difference between the two schedules of injection and

to determine whether there are differences between four drug

mixtures.

a) Is this a randomized block design or repeated design? ExplainIt is repeated design. Because there are more than one observation per cell.

b) What are the factors in this experiment?Drug mix and injection schedule.

c) Identify the levels of each factor Drug mix 4Injection schedule 2

The Two-way ANOVA EXCEL outputAt the 5 % significance level we need to determine:1) There are differences in the

improvement in the headache index between the schedules.

2) There are differences in the improvement in the headache index between the four drug mixtures.

3) There is interaction between schedules and drug mixtures

(1) H0: The two injection schedules

means are same. H1: The means are different.

Fstatistical < Fcrit 0.940 < 4.150 p-value > α 0.340 > 0.05

There is no sufficient statistical evidence to infer that there are differences in the improvement in the headache index between the

schedules.

(2) H0: The four drug mixtures means are

the same. H1: At least one of the means is different.

Fstatistical > Fcrit 8.05 > 2.90 p-value < α 0.0004 < 0.05

There is sufficient statistical evidence to infer that there are differences in the improvement in the headache index between the

four drug mixtures.

(3) H0: The interaction between schedules and drug mixtures

equal to zeroH1: There is an interaction between injection schedules

and drug mixtures.

Fstatistical > Fcrit 6.61 > 2.90 p-value < α 0.001 < 0.05

There is sufficient statistical evidence to infer that there are interaction between schedules and drug mixtures.

Q2. Test for a difference between the four diets.

a) What type of experimental ANOVA design does this set up represent?Randomized block design.

b) How many observations are there in each cell? One observation per Cell.

c) What are the factors in this experiment?Age groups and diet forms.

d) Identify the levels of factorsAge groups 5Diet forms 4

e) What is the dependent variable measured in this experiment?The number of pounds that each person lost (Weight loss).

The Two-way ANOVA EXCEL output

At the 1 % significance level we need to determine

that there are differences between

the four diets.

H0: The four diets group means are all the same H1: At least one pair of means is not equal

Fstatistical < Fcrit 1.65 < 5.95 p-value > α 0.23 > 0.01

There is no sufficient statistical evidence to infer that there are differences between the four diets.

(They are all the same)