1. Nonparametric Statistics
Previously we have done inferences relative to a population parameter
Quantitative data - Population Mean - µ
Qualitative data - Population Proportion - p
Now we infer location in a general sense without a parameter
We have Ordinal data or Quantitative data not normally distributed.
Rank-Sum Tests - Use the observations only to assign ranks to the data
Ex: "Dance Fever"
Couple
Judge 1 2 3 A B C
Total

2. Two-Sample Rank-Sum Test
Wilcoxon - Rank Observations from Low to High - Assign 1 to Min Obs
Mann-Whitney - Rank Observations from High to Low - Assign 1 to Max Obs
(Note: The author ranks from Low to High which is incorrect)
WSU St Mary
95 91
78 76
Wwsu =
93 75
86 88
WStMary =
92 83
79 90
89 72
94 82

3. Mann-Whitney U Test:
If n1 ≥ 10 and n2 ≥ 10, the Rank Sums are Normally Distributed
H0: Loc(WSU) = Loc(StMary)
HA: Loc(WSU) > Loc(StMary)
R: Z > 1.645

4. Ordinal Data: Likert Scale -
1-Strongly Favor Favor Neutral Oppose Strongly Oppose
Likert Male M-Rank F-Rank Female Rank Ave Rank
1 SF
2 F
3 N
4 O
5 SO
H0: Loc(M) = Loc (F)
HA: Loc(M) ≠ Loc (F)
R: Z > 1.96
Z < -1.96

5. Correction for Ties: (More then 25% Obs Involved in Ties)
For this type data we should also do a second test: Homogenity of Data
Male Female
SA 10 30
A 20 20
N 40 0
D 20 20
SD 10 30
H0: Data Homogeneous
HA: Data Not Homogeneous
R: χ2 > χ2α,df=k-1
χ2 > 9.49

6. Kruskal-Wallis Test - k groups of Observations
1 2 3 … k Use Observations to
X11 X12 X13 X1k Assign Ranks to Data
X21 X22 X23 X2k
… … … …
W1 W2 W3 Wk Rank Sums
H0: All Group Locations Equal
HA: Not All Locations Equal
R: K > χ2α,df=k-1

7. Example 3:
H0: Loc(1)=Loc(2)=Loc(3)
HA: Not All Loc Equal
R: K > χ2.05,df=2
K > 5.99

8. WSU-StMary Example
Wwsu = 83 WStMary = 127
H0: Loc(WSU)=Loc(StMary)
HA: Loc(WSU)≠Loc(StMary)
R: K > χ2.10,df=1
K > 2.706

9. Cookie Mix Example:
Income Pre-Mix Mix Own Ranks Ave Rank
<30K
30-60K
>60K
H0: Both Locations Equal
HA: Not Equal
R: K > χ2.05,df=1
K > 3.84