# Friedman Test

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introductio n The Friedman Test is used when comparing 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 distributional assumption are necessary.

c

j

discussio n g
STEP
ONE

State the null hypothesis.
HO: The probability distributions for the treatment groups are identical. c

j

discussio n g
STEP
TWO

State the alternative.
HA: At least two of the treatment groups are identical.

cg

Let t represent the treatments, and b represent the blocks. Arrange the recorded observations for each treatment-block combination in a twoway table in which the treatments are placed in columns and the blocks in rows.

discussio
STEP
3 n j

g g STEP
4

STEP
5

Rank the data within the blocks,

giving the lowest value rank 1.

Get the sum of the ranks in each column or per treatment.

j g STEP
6

Compute the Friedman test statistic using the ff. formula.

Fr=

g
STEP
7

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
2critical,

X

the null hypothesis is rejected.

c

EXample

A nutritionist compared three treatments of squash-malunggay-banana baby food preparations with the three main ingredients in different proportions per treatment. The three treatments were subjected to a sensory evaluation tests using
10 evaluators. The following data were obtained.

sOLUTIO
N
a. HO: The three elements are identical. b. HA: Al least two treatments are different from one another.

c. Computations:

sOLUTIO
N

d. Calculate the test statistic Fr

sOLUTIO
N

e. Test the null hypothesis.
Compare Fr = 3.05 with X20.05 = 5.99 at d.f. = 3-1 = 2 and α = 0.05
Since Fr = 3.04

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