Mann Whitney Wilcoxon Tables


Nondirectionalα=.05 (Directional α=.025)


n1












n2









1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

1

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

2

-

-

-

-

-

-

-

0

0

0

0

1

1

1

1

1

2

2

2

2

3

-

-

-

-

0

1

1

2

2

3

3

4

4

5

5

6

6

7

7

8

4

-

-

-

0

1

2

3

4

4

5

6

7

8

9

10

11

11

12

13

13

5

-

-

0

1

2

3

5

6

7

8

9

11

12

13

14

15

17

18

19

20

6

-

-

1

2

3

5

6

8

10

11

13

14

16

17

19

21

22

24

25

27

7

-

-

1

3

5

6

8

10

12

14

16

18

20

22

24

26

28

30

32

34

8

-

0

2

4

6

8

10

13

15

17

19

22

24

26

29

31

34

36

38

41

9

-

0

2

4

7

10

12

15

17

21

23

26

28

31

34

37

39

42

45

48

10

-

0

3

5

8

11

14

17

20

23

26

29

33

36

39

42

45

48

52

55

11

-

0

3

6

9

13

16

19

23

26

30

33

37

40

44

47

51

55

58

62

12

-

1

4

7

11

14

18

22

26

29

33

37

41

45

49

53

57

61

65

69

13

-

1

4

8

12

16

20

24

28

33

37

41

45

50

54

59

63

67

72

76

14

-

1

5

9

13

17

22

26

31

36

40

45

50

55

59

64

67

74

78

83

15

-

1

5

10

14

19

24

29

34

39

44

49

54

59

64

70

75

80

85

90

16

-

1

6

11

15

21

26

31

37

42

47

53

59

64

70

75

81

86

92

98

17

-

2

6

11

17

22

28

34

39

45

51

57

63

67

75

81

87

93

99

105

18

-

2

7

12

18

24

30

36

42

48

55

61

67

74

80

86

93

99

106

112

19

-

2

7

13

19

25

32

38

45

52

58

65

72

78

85

92

99

106

113

119

20

-

2

8

14

20

27

34

41

48

55

62

69

76

83

90

98

105

112

119

127








Nondirectionalα=.01 (Directional α=.005)






n1












n2









1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

1

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

2

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

0

0

3

-

-

-

-

-

-

-

-

0

0

0

1

1

1

2

2

2

2

3

3

4

-

-

-



0

0

1

1

2

2

3

3

4

5

5

6

6

7

8

5

-

-

-


0

1

1

2

3

4

5

6

7

7

8

9

10

11

12

13

6

-

-

-

0

1

2

3

4

5

6

7

9

10

11

12

13

15

16

17

18

7

-

-

-

0

1

3

4

6

7

9

10

12

13

15

16

18

19

21

22

24

8

-

-

-

1

2

4

6

7

9

11

13

15

17

18

20

22

24

26

28

30

9

-

-

0

1

3

5

7

9

11

13

16

18

20

22

24

27

29

31

33

36

10

-

-

0

2

4

6

9

11

13

16

18

21

24

26

29

31

34

37

39

42

11

-

-

0

2

5

7

10

13

16

18

21

24

27

30

33

36

39

42

45

46

12

-

-

1

3

6

9

12

15

18

21

24

27

31

34

37

41

44

47

51

54

13

-

-

1

3

7

10

13

17

20

24

27

31

34

38

42

45

49

53

56

60

14

-

-

1

4

7

11

15

18

22

26

30

34

38

42

46

50

54

58

63

67

15

-

-

2

5

8

12

16

20

24

29

33

37

42

46

51

55

60

64

69

73

16

-

-

2

5

9

13

18

22

27

31

36

41

45

50

55

60

65

70

74

79

17

-

-

2

6

10

15

19

24

29

34

39

44

49

54

60

65

70

75

81

86

18

-

-

2

6

11

16

21

26

31

37

42

47

53

58

64

70

75

81

87

92

19

-

0

3

7

12

17

22

28

33

39

45

51

56

63

69

74

81

87

93

99

20

-

0

3

8

13

18

24

30

36

42

46

54

60

67

73

79

86

92

99

105

Uobtis the lesser of the twocalculated test statistics (U1& U2).If Uobt≤ Ucrit,reject H0.

Dashes(-) indicate that the sample size is too small to reject the NullHypothesis at the chosen α level.

If n > 20 this table cannot be used. A pcan be computed for U, using the normal distribution approximation: