Question

The following ANOVA table and accompanying information are the result of a randomized block ANOVA test.

Summary           Count                 Sum                    Average             Variance

1                         4                         443                     110.8                           468.9

2                         4                         275                     68.8                           72.9

3                         4                         1,030                  257.5                           1891.7

4                          4                         300                     75.0                           433.3

5                         4                         603                     150.8                           468.9

6                         4                         435                     108.8                           72.9

7                         4                         1,190                  297.5                           1891.7

8                         4                         460                     115.0                           433.3

Sample 1           8                         1,120                  140.0                           7142.9

Sample 2            8                         1,236                  154.5                           8866.6

Sample 3           8                         1,400                  175.0                           9000.0

Sample 4           8                         980                     122.5                           4307.1

ANOVA

Source of

Variation            SS                        df          MS                      F                          p-value               F-crit

Rows                  199,899              7            28557.0              112.8                  0.0000                2.488

Columns             11,884                3            3961.3               15.7                    0.0000                3.073

Error                   5,317                  21         253.2

Total                   217,100              31        

1. How many blocks were used in this study?
2. How many populations are involved in this test?
3. Test to determine whether blocking is effective using an alpha level equal to 0.05
4. Test the main hypothesis of interest using α=0.05.
5. If warranted, conducted an LSD test with α=0.05 to determine which population mean are different.

Answer 1

a) blocks = 8

b) population = 8*4 =32

c)

F test statistic = 112.8

p value=0.0000 <α=0.05, reject ho

so, blocking is effective

d)

F test statistic = 15.7

p value=0.00 <α=0.05, so test is significant

conclusion :    there is enough evidence of significance difference among four treatments

e)

Level of significance=   0.0500
no. of treatments,k=   4
DF error =N-k=   21
MSE=   253.20
t-critical value,t(α/2,df)=   2.0796

Fishers LSD critical value=tα/2,df √(MSE(1/ni+1/nj)) = 16.55
if absolute difference of means > critical value,means are significnantly different ,otherwise not

population mean difference		critical value			result
µ1-µ2	14.000	16.55			means are not different
µ1-µ3	35.000	16.55			means are different
µ1-µ4	17.500	16.55			means are different
µ2-µ3	21.000	16.55			means are different
µ2-µ4	31.500	16.55			means are different
µ3-µ4	52.500	16.55			means are different