http://www.ats.ucla.edu/stat/sas/whatstat/whatstat.htm
Pendahuluan
Dalam memutuskan pilihan pengujian yang tepat untuk digunakan, penting untuk mempertimbangkan jenis variabelnya. Apakah variabelnya berbentuk kategorikal, ordinal atau interval, dan apakah variabel tersebut terdistribusi secara normal ? (lihat link).
Seputar Data File ”hsb”
Pengujian Satu Sampel
proc ttest data = "c:\mydata\hsb2" h0 = 50;
var write;
run;
Hasilnya ditampilkan sebagai berikut :
The TTEST Procedure
Statistics
Lower CL Upper CL Lower CL Upper CL
Variable N Mean Mean Mean Std Dev Std Dev Std Dev Std Err
write 200 51.453 52.775 54.097 8.6318 9.4786 10.511 0.6702
T-Tests
Variable DF t Value Pr > |t|
write 199 4.14 <.0001
Pengujian Satu Median Sampel
proc univariate data = "c:\mydata\hsb2" loccount mu0 = 50;
var write;
run;
Hasilnya ditampilkan sebagai berikut :
Basic Statistical Measures
Location Variability
Mean 52.77500 Std Deviation 9.47859
Median 54.00000 Variance 89.84359
Mode 59.00000 Range 36.00000
Interquartile Range 14.50000
Tests for Location: Mu0=50
Test -Statistic- -----p Value------
Student's t t 4.140325 Pr > |t| <.0001
Sign M 27 Pr >= |M| 0.0002
Signed Rank S 3326.5 Pr >= |S| <.0001
Location Counts: Mu0=50.00
Count Value
Num Obs > Mu0 12
Num Obs ^= Mu0 198
Num Obs < Mu0 72
Uji Binomial
proc freq data = "c:\mydata\hsb2";
tables female / binomial(p=.5);
exact binomial;
run;
Hasilnya ditampilkan sebagai berikut :
The FREQ Procedure
Cumulative Cumulative
female Frequency Percent Frequency Percent
-----------------------------------------------------------
0 91 45.50 91 45.50
1 109 54.50 200 100.00
Binomial Proportion for female = 0
-----------------------------------
Proportion (P) 0.4550
ASE 0.0352
95% Lower Conf Limit 0.3860
95% Upper Conf Limit 0.5240
Exact Conf Limits
95% Lower Conf Limit 0.3846
95% Upper Conf Limit 0.5267
Test of H0: Proportion = 0.5
ASE under H0 0.0354
Z -1.2728
One-sided Pr < Z 0.1015
Two-sided Pr > |Z| 0.2031
Exact Test
One-sided Pr <= P 0.1146
Two-sided = 2 * One-sided 0.2292
Sample Size = 200
Chi-square goodness of fit
tables race / chisq testp=(10 10 10 70);
run;
Hasil estimasinya adalah
The FREQ Procedure
Test Cumulative Cumulative
race Frequency Percent Percent Frequency Percent
--------------------------------------------------------------------
1 24 12.00 10.00 24 12.00
2 11 5.50 10.00 35 17.50
3 20 10.00 10.00 55 27.50
4 145 72.50 70.00 200 100.00
Chi-Square Test
for Specified Proportions
-------------------------
Chi-Square 5.0286
DF 3
Pr > ChiSq 0.1697
Sample Size = 200
Hasilnya menunjukkan bahwa komposisi rasial dalam sampel tidak berbeda signifikan dari nilai yang ditetapkan dalam hipotesis (chi-square dengan derajat kebebasan = 5.0286, p = .1697).
Pengujian Dua Sampel Independen
proc ttest data = "c:\mydata\hsb2";
class female;
var write;
run;
Hasilnya disajikan sebagai berikut
The TTEST Procedure
Statistics
Lower CL Upper CL Lower CL Upper CL
Variable female N Mean Mean Mean Std Dev Std Dev Std Dev Std Err
write 0 91 47.975 50.121 52.267 8.9947 10.305 12.066 1.0803
write 1 109 53.447 54.991 56.535 7.1786 8.1337 9.3843 0.7791
write Diff (1-2) -7.442 -4.87 -2.298 8.3622 9.1846 10.188 1.3042
T-Tests
Variable Method Variances DF t Value Pr > |t|
write Pooled Equal 198 -3.73 0.0002
write Satterthwaite Unequal 170 -3.66 0.0003
Equality of Variances
Variable Method Num DF Den DF F Value Pr > F
write Folded F 90 108 1.61 0.0187
Hasilnya menunjukkan bahwa terdapat perbedaan signifikan antara skor nilai menulis pria dan wanita (t = -3.73, p = .0002). Dengan perkataan lain, wanita memiliki skor nilai menulis In other words, females have a statistically significantly higher mean score on writing (54.991) than males (50.121).
Pengujian Wilcoxon-Mann-Whitney test
proc npar1way data = "c:\mydata\hsb2" wilcoxon;
class female;
var write;
run;
The NPAR1WAY Procedure
Wilcoxon Scores (Rank Sums) for Variable write
Classified by Variable female
Sum of Expected Std Dev Mean
female N Scores Under H0 Under H0 Score
----------------------------------------------------------------------
0 91 7792.0 9145.50 406.559086 85.626374
1 109 12308.0 10954.50 406.559086 112.917431
Average scores were used for ties.
Wilcoxon Two-Sample Test
Statistic 7792.0000
Normal Approximation
Z -3.3279
One-Sided Pr < Z 0.0004
Two-Sided Pr > |Z| 0.0009
t Approximation
One-Sided Pr < Z 0.0005
Two-Sided Pr > |Z| 0.0010
Z includes a continuity correction of 0.5.
Pengujian Chi-square
proc freq data = "c:\mydata\hsb2";
tables schtyp*female / chisq;
run;
Hasilnya disajikan sebagai berikut :
The FREQ Procedure
Table of schtyp by female
schtyp(type of school)
female
Frequency|
Percent |
Row Pct |
Col Pct | 0| 1| Total
---------+--------+--------+
1 | 77 | 91 | 168
| 38.50 | 45.50 | 84.00
| 45.83 | 54.17 |
| 84.62 | 83.49 |
---------+--------+--------+
2 | 14 | 18 | 32
| 7.00 | 9.00 | 16.00
| 43.75 | 56.25 |
| 15.38 | 16.51 |
---------+--------+--------+
Total 91 109 200
45.50 54.50 100.00
Statistics for Table of schtyp by female
Statistic DF Value Prob
------------------------------------------------------
Chi-Square 1 0.0470 0.8283
Likelihood Ratio Chi-Square 1 0.0471 0.8281
Continuity Adj. Chi-Square 1 0.0005 0.9815
Mantel-Haenszel Chi-Square 1 0.0468 0.8287
Phi Coefficient 0.0153
Contingency Coefficient 0.0153
Cramer's V 0.0153
Sample Size = 200
Mari kita lihat contoh lainnya yang melihat hubungan antara jenis kelamin (female) dan status sosial ekonomi (ses). Poin pada contoh ini adalah satu atau setiap variabel dapat memiliki lebih dari dua level, dan variabel tersebut tidak memiliki jumlah level yang sama. Dalam contoh ini, variabel female memiliki dua level (pria dan wanita), dan variabel ses memiliki tiga level (rendah, menengah dan tinggi).
proc freq data = "c:\mydata\hsb2";
tables female*ses / chisq;
run;
Hasilnya disajikan sebagai berikut :
The FREQ Procedure
Table of female by ses
female ses
Frequency|
Percent |
Row Pct |
Col Pct | 1| 2| 3| Total
---------+--------+--------+--------+
0 | 15 | 47 | 29 | 91
| 7.50 | 23.50 | 14.50 | 45.50
| 16.48 | 51.65 | 31.87 |
| 31.91 | 49.47 | 50.00 |
---------+--------+--------+--------+
1 | 32 | 48 | 29 | 109
| 16.00 | 24.00 | 14.50 | 54.50
| 29.36 | 44.04 | 26.61 |
| 68.09 | 50.53 | 50.00 |
---------+--------+--------+--------+
Total 47 95 58 200
23.50 47.50 29.00 100.00
Statistics for Table of female by ses
Statistic DF Value Prob
------------------------------------------------------
Chi-Square 2 4.5765 0.1014
Likelihood Ratio Chi-Square 2 4.6789 0.0964
Mantel-Haenszel Chi-Square 1 3.1098 0.0778
Phi Coefficient 0.1513
Contingency Coefficient 0.1496
Cramer's V 0.1513
Sample Size = 200
Penguian Fisher's exact
tables schtyp*race / fisher;
run;
Hasilnya disajikan sebagai berikut :
The FREQ Procedure
Table of schtyp by race
schtyp(type of school) race
Frequency|
Percent |
Row Pct |
Col Pct | 1| 2| 3| 4| Total
---------+--------+--------+--------+--------+
1 | 22 | 10 | 18 | 118 | 168
| 11.00 | 5.00 | 9.00 | 59.00 | 84.00
| 13.10 | 5.95 | 10.71 | 70.24 |
| 91.67 | 90.91 | 90.00 | 81.38 |
---------+--------+--------+--------+--------+
2 | 2 | 1 | 2 | 27 | 32
| 1.00 | 0.50 | 1.00 | 13.50 | 16.00
| 6.25 | 3.13 | 6.25 | 84.38 |
| 8.33 | 9.09 | 10.00 | 18.62 |
---------+--------+--------+--------+--------+
Total 24 11 20 145 200
12.00 5.50 10.00 72.50 100.00
Statistics for Table of schtyp by race
Statistic DF Value Prob
------------------------------------------------------
Chi-Square 3 2.7170 0.4373
Likelihood Ratio Chi-Square 3 2.9985 0.3919
Mantel-Haenszel Chi-Square 1 2.3378 0.1263
Phi Coefficient 0.1166
Contingency Coefficient 0.1158
Cramer's V 0.1166
WARNING: 38% of the cells have expected counts less
than 5. Chi-Square may not be a valid test.
Fisher's Exact Test
----------------------------------
Table Probability (P) 0.0077
Pr <= P 0.5975
Sample Size = 200
One-way ANOVA
proc glm data = "c:\mydata\hsb2";
class prog;
model write = prog;
means prog;
run;
quit;
Hasilnya disajikan sebagai berikut :
The GLM Procedure
Class Level Information
Class Levels Values
prog 3 1 2 3
Number of observations 200
Dependent Variable: write writing score
Sum of
Source DF Squares Mean Square F Value Pr > F
Model 2 3175.69786 1587.84893 21.27 <.0001
Error 197 14703.17714 74.63542
Corrected Total 199 17878.87500
R-Square Coeff Var Root MSE write Mean
0.177623 16.36983 8.639179 52.77500
Source DF Type I SS Mean Square F Value Pr > F
prog 2 3175.697857 1587.848929 21.27 <.0001
Source DF Type III SS Mean Square F Value Pr > F
prog 2 3175.697857 1587.848929 21.27 <.0001
Level of ------------write------------
prog N Mean Std Dev
1 45 51.3333333 9.39777537
2 105 56.2571429 7.94334333
3 50 46.7600000 9.31875441
Pengujian Kruskal Wallis
Metode ini digunakan ketika kita memiliki variabel independen dengan dua atau lebih tingkat dan variabel dependen yang bersifat ordinal. Dengan perkataan lain, pengujian tersebut merupakan versi non-parametrik dari ANOVA.
class prog;
var write;
run;
The NPAR1WAY Procedure
Wilcoxon Scores (Rank Sums) for Variable write
Classified by Variable prog
Sum of Expected Std Dev Mean
prog N Scores Under H0 Under H0 Score
--------------------------------------------------------------------
1 45 4079.0 4522.50 340.927342 90.644444
3 50 3257.0 5025.00 353.525185 65.140000
2 105 12764.0 10552.50 407.705133 121.561905
Average scores were used for ties.
Kruskal-Wallis Test
Chi-Square 34.0452
DF 2
Pr > Chi-Square <.0001
Pengujian Pasangan (Paired t-test)
proc ttest data = "c:\mydata\hsb2";
paired write*read;
run;
The TTEST Procedure
Statistics
Lower CL Upper CL Lower CL Upper CL
Difference N Mean Mean Mean Std Dev Std Dev Std Dev Std Err
write - read 200 -0.694 0.545 1.7841 8.0928 8.8867 9.8546 0.6284
T-Tests
Difference DF t Value Pr > |t|
write - read 199 0.87 0.3868
*Semoga bermanfaat*