1. ANOVA
ANalysis Of VAriance
(Single Factor/One way)
Purpose
1. For experiments where the variance of the treatments are the same.
2. For experiments where the total number of replicates and treatments are the same.
3. For experiments where there are more than 3 different types of treatments.
a. This is to avoid the inherent error in calculating multiple times using t tests on 3 or more
treatments. The more times a t-test is done, the subsequent tries decrease in
probability.
Shortcut Procedure
A. State the hypothesis.
B. Calculate Variance
a. Total Variance
b. Between groups
c. Within groups
C. Calculate for the Mean Squares
D. Calculate the F-ratio
E. Calculate effect size
Not so Short step-by-step Procedure
A. State The Hypothesis of your experiment.
a. Either
i. Ho where all the means of the various treatments are the same.
ii. Ha Where there is at least one mean that differs from the rest.

2. B. Tabulate Scores
a. The scores are in this format: Leftmost are treatments, Upmost are replicates.
1 2 3 4 Row Total Row Total
Squared
A A1 A2 A3 A4 Summation
A
B B1 B2 B3 B4 Summation
B
C C1 C3 C3 C4 Summation
C
…Z Z1 Z2 Z3 Z4 Summation
Z
C. Create an ANOVA table
a. Here we Calculate for important values that will give us the answer.
Source of
Variation
Sum of
Squares
Degrees of
Freedom
Mean
Square
F calc F tab or
crit
Between
Treatments
SSBT DFBT MSBT
Within
Treatments
SSWT DFWT MSWT
TOTAL SST DFT
b. The values of each entry in the ANOVA table is :

3. i. Where I represents a treatment, and j a replicate…
ii. SSBT = summation (XI
2
)/r – (XT
2
/N)
iii. SSWT = Summation (XIj
2
) – (XALLTREATMENTS
2
)/r
iv. SST = SSWT + SSBT
v. DFBT = t – 1
vi. DFWT = t(r – 1)
vii. DFT = DFBT + DFWT
viii. MSBT = SSBT/DFBT
ix. MSWT = SSWT/DFWT
x. Fcalc =MSBT/MSWT
xi. The F Critical is found by Looking at the F table, where DFBT is V1 and DFWT is V2
and they intersect at the previously stated level of significance.
D. Formulate a Conclusion
a. If the calculated F ratio is within the region of acceptance, accept Ho and reject Ha.
b. If the calculated F ratio is within the region of rejection, accept Ha and reject Ho.
c. A rejected Ho means that there is a treatment where the mean has differed. An
accepted Ho means all the means of all treatments are alike.
http://dspace.lib.uoguelph.ca/xmlui/bitstream/handle/10214/1866/A_About%20Single
%20Factor%20ANOVA.pdf?sequence=2