imad feneir - two-way anova - replication
TRANSCRIPT
![Page 1: Imad Feneir - Two-way ANOVA - replication](https://reader036.vdocuments.net/reader036/viewer/2022062523/58cec04d1a28ab09548b4c8f/html5/thumbnails/1.jpg)
Multivariate Statistical Methods
Two-way ANOVA with and without replication
Imad Feneir
![Page 2: Imad Feneir - Two-way ANOVA - replication](https://reader036.vdocuments.net/reader036/viewer/2022062523/58cec04d1a28ab09548b4c8f/html5/thumbnails/2.jpg)
Q1. Test for a difference between the two schedules of injection and
to determine whether there are differences between four drug
mixtures.
![Page 3: Imad Feneir - Two-way ANOVA - replication](https://reader036.vdocuments.net/reader036/viewer/2022062523/58cec04d1a28ab09548b4c8f/html5/thumbnails/3.jpg)
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
![Page 4: Imad Feneir - Two-way ANOVA - replication](https://reader036.vdocuments.net/reader036/viewer/2022062523/58cec04d1a28ab09548b4c8f/html5/thumbnails/4.jpg)
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
![Page 5: Imad Feneir - Two-way ANOVA - replication](https://reader036.vdocuments.net/reader036/viewer/2022062523/58cec04d1a28ab09548b4c8f/html5/thumbnails/5.jpg)
(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.
![Page 6: Imad Feneir - Two-way ANOVA - replication](https://reader036.vdocuments.net/reader036/viewer/2022062523/58cec04d1a28ab09548b4c8f/html5/thumbnails/6.jpg)
(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.
![Page 7: Imad Feneir - Two-way ANOVA - replication](https://reader036.vdocuments.net/reader036/viewer/2022062523/58cec04d1a28ab09548b4c8f/html5/thumbnails/7.jpg)
(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.
![Page 8: Imad Feneir - Two-way ANOVA - replication](https://reader036.vdocuments.net/reader036/viewer/2022062523/58cec04d1a28ab09548b4c8f/html5/thumbnails/8.jpg)
Q2. Test for a difference between the four diets.
![Page 9: Imad Feneir - Two-way ANOVA - replication](https://reader036.vdocuments.net/reader036/viewer/2022062523/58cec04d1a28ab09548b4c8f/html5/thumbnails/9.jpg)
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.
![Page 10: Imad Feneir - Two-way ANOVA - replication](https://reader036.vdocuments.net/reader036/viewer/2022062523/58cec04d1a28ab09548b4c8f/html5/thumbnails/10.jpg)
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).
![Page 11: Imad Feneir - Two-way ANOVA - replication](https://reader036.vdocuments.net/reader036/viewer/2022062523/58cec04d1a28ab09548b4c8f/html5/thumbnails/11.jpg)
The Two-way ANOVA EXCEL output
At the 1 % significance level we need to determine
that there are differences between
the four diets.
![Page 12: Imad Feneir - Two-way ANOVA - replication](https://reader036.vdocuments.net/reader036/viewer/2022062523/58cec04d1a28ab09548b4c8f/html5/thumbnails/12.jpg)
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)
![Page 13: Imad Feneir - Two-way ANOVA - replication](https://reader036.vdocuments.net/reader036/viewer/2022062523/58cec04d1a28ab09548b4c8f/html5/thumbnails/13.jpg)