Friedman Test
Friedman Test for a random Block Design
-The Friedman Test is used when compairing more than two populations or treatments randomly assigned within blocks. This is the counterpart of the F test or ANOVA used in parametric statistics. Unlike the F test or ANOVA which is used with the assumption that the observations taken from each of the populations are normally distributed, the Friedman test is used when no distrubutional assumptions are necessary.
The following are the steps in doing the Friedman Test:
a. State the null hypothesis.
b. State the alternative hypothesis.
c. Let t represent the treatment and b represent the blocks. Arrange the recorded observation for each treatment-block combination in a two-way table in which the treatments are placed in columns and the blocks in rows. Treatment
Block
t1
t2
t3 b1 b2
b3
b4
T1
T2
T3
d. Rank the data within the blocks, giving the lowest rank 1 and tied values the average of the two ranks.
e. Get the sum of the ranks in each column or per treatment.
f. Compute the Friedman test statistics, Fr, using the following formula.
g. Test the null hypothesis by comparing Fr with the critical value of X2 from the X2 distribution table at d.f. = t-1 and α=0.05. If Fr is greater than or equal to , the null hypothesis is rejected.
-The Friedman Test is used when compairing more than two populations or treatments randomly assigned within blocks. This is the counterpart of the F test or ANOVA used in parametric statistics. Unlike the F test or ANOVA which is used with the assumption that the observations taken from each of the populations are normally distributed, the Friedman test is used when no distrubutional assumptions are necessary.
The following are the steps in doing the Friedman Test:
a. State the null hypothesis.
b. State the alternative hypothesis.
c. Let t represent the treatment and b represent the blocks. Arrange the recorded observation for each treatment-block combination in a two-way table in which the treatments are placed in columns and the blocks in rows. Treatment
Block
t1
t2
t3 b1 b2
b3
b4
T1
T2
T3
d. Rank the data within the blocks, giving the lowest rank 1 and tied values the average of the two ranks.
e. Get the sum of the ranks in each column or per treatment.
f. Compute the Friedman test statistics, Fr, using the following formula.
g. Test the null hypothesis by comparing Fr with the critical value of X2 from the X2 distribution table at d.f. = t-1 and α=0.05. If Fr is greater than or equal to , the null hypothesis is rejected.