Procformat; Value Fax 0='Not Giants'1='Giants'5='Not Finished'6='Finished';Run ;

optionspageno=min;

ProcFormat; Value fax 0='Not_Giants'1='Giants'5='Not_Finished'6='Finished';run;

Data PDS; Infile'C:\Users\Vati\Documents\_XYZZY\_Stats\6430\HW-30\PDS\2016_PDS/Sager_TerraMystica.dat';

Input Faction Finished Score Place_Finish;

Score_log = LOG10(Score);

title'Online Terra Mystica Scores for David Sager'; Format Faction Finished fax.;

ProcSort; By Finished;

ProcPrint; Var Score; By Finished; run;

ProcMeansNmeanstddevskewnesskurtosis; Var Score Score_log; By Finished; run;

ProcFreq; Tables Faction*Finished; run;

ProcGLM; Class Faction Finished; Model Score = Faction|Finished/ss3; Run; Quit;

ProcGLM; Class Faction Finished; Model Score = Faction Finished/ss3; Run; Quit;

ProcNPAR1WAYWilcoxon; Class Finished; Var Score; run;

Online Terra Mystica Scores for David Sager

Finished=Not_Finished

Obs / Score
1 / 41
2 / 47
3 / 39

Only three scores not finished, and one of them is considerably higher than the other two.

Finished=Finished

Obs / Score
4 / 99
5 / 122
6 / 126
7 / 102
8 / 78
9 / 113
10 / 89
11 / 102
12 / 109
13 / 123
14 / 104
15 / 118
16 / 102
17 / 108
18 / 121
19 / 102
20 / 131
21 / 88
22 / 102
23 / 81
24 / 116
25 / 103
26 / 87
27 / 106
28 / 107
29 / 98
30 / 126
31 / 107
32 / 95
33 / 75
34 / 89
35 / 131
36 / 83
37 / 115
38 / 137
39 / 138
40 / 136
41 / 126
42 / 99
43 / 113
44 / 118
45 / 122
46 / 90
47 / 81
48 / 103
49 / 103
50 / 136
51 / 111
52 / 107
53 / 135
54 / 117
55 / 99
56 / 108
57 / 113
58 / 104
59 / 102
60 / 121
61 / 111
62 / 136
63 / 138
64 / 91
65 / 139
66 / 106
67 / 117
68 / 121
69 / 128
70 / 148
71 / 137
72 / 128
73 / 131
74 / 120
75 / 102
76 / 121
77 / 127
78 / 133
79 / 108
80 / 117
Online Terra Mystica Scores for David Sager

The MEANS Procedure

Finished=Not_Finished

Variable / N / Mean / Std Dev / Skewness / Kurtosis
Score
Score_log
/ 3
3
/ 42.3333333
1.6253154
/ 4.1633320
0.0419449
/ 1.2933428
1.2244295
/ .
.

In that small set of scores, there is troublesome skewness and transforming the data does not much help.

Finished=Finished

Variable / N / Mean / Std Dev / Skewness / Kurtosis
Score
Score_log
/ 77
77
/ 112.1558442
2.0448454
/ 16.7631056
0.0669413
/ -0.1130352
-0.4416680
/ -0.6081299
-0.2917595
Online Terra Mystica Scores for David Sager

The FREQ Procedure

Frequency
Percent
Row Pct
Col Pct
/ TableofFactionbyFinished
Faction / Finished
Not_Finished / Finished / Total
Not_Giants / 3
3.75
5.17
100.00
/ 55
68.75
94.83
71.43
/ 58
72.50
Giants / 0
0.00
0.00
0.00
/ 22
27.50
100.00
28.57
/ 22
27.50
Total / 3
3.75
/ 77
96.25
/ 80
100.00

Oh my, there is a cell with no data. The marginal Ns are nonzero, so we can test the main effects, but we cannot test the interaction.

Online Terra Mystica Scores for David Sager

The GLM Procedure

Class Level Information
Class / Levels / Values
Faction / 2 / Giants Not_Giants
Finished / 2 / Finished Not_Finished
Number of Observations Read / 80
Number of Observations Used / 80
Online Terra Mystica Scores for David Sager

The GLM Procedure

Dependent Variable: Score

Source / DF / Sum of Squares / Mean Square / F Value / PrF
Model / 2 / 14317.22083 / 7158.61042 / 26.06 / <.0001
Error / 77 / 21150.66667 / 274.68398
Corrected Total / 79 / 35467.88750
R-Square / CoeffVar / Root MSE / ScoreMean
0.403667 / 15.13052 / 16.57359 / 109.5375
Source / DF / Type III SS / Mean Square / F Value / PrF
Faction / 1 / 240.12987 / 240.12987 / 0.87 / 0.3527
Finished / 1 / 14316.30355 / 14316.30355 / 52.12 / <.0001
Faction*Finished / 0 / 0.00000 / . / . / .

So, just drop the interaction from the model.

Online Terra Mystica Scores for David Sager
Online Terra Mystica Scores for David Sager

The GLM Procedure

Dependent Variable: Score

This, above, is the source table to put into the discussion board.

But, wait a minute, we have not resolved the problem with the skewness of the one group. Accordingly, we shift to an analysis on ranks.

Online Terra Mystica Scores for David Sager

The NPAR1WAY Procedure

Wilcoxon Scores (Rank Sums) for Variable Score
Classified by Variable Finished
Finished / N / Sum of
Scores / Expected
Under H0 / Std Dev
Under H0 / Mean
Score
Not_Finished / 3 / 6.0 / 121.50 / 39.461414 / 2.0
Finished / 77 / 3234.0 / 3118.50 / 39.461414 / 42.0
Average scores were used for ties.
Wilcoxon Two-Sample Test
Statistic (S) / 6.0000
Normal Approximation
Z / -2.9142
One-Sided Pr < Z / 0.0018
Two-Sided Pr > |Z| / 0.0036
t Approximation
One-Sided Pr < Z / 0.0023
Two-Sided Pr > |Z| / 0.0046
Exact Test
One-Sided Pr <= S / 1.217E-05
Two-Sided Pr >= |S - Mean| / 1.217E-05
Z includes a continuity correction of 0.5.

p = .00001217