18. 통계분석

1. SAS
2. SPSS
3. R-PROJECT
4. S-PLUS
5. PROC SQL


1. SAS	MAIN

* 기초 통계 테스트를 위한 SAS 프로그램.;

data temp;

set BACK.mydata;

myDiff=q2-q1;

run;

* 간단한 결과 산출의 기초 통계;

proc means data=temp;

var q1-q4;

run;

변수 N 평균값 표준편차 최소값 최대값

-------------------------------------------------------------------------

q1 8 3.2500000 1.4880476 1.0000000 5.0000000

q2 8 2.7500000 1.7525492 1.0000000 5.0000000

q3 7 4.1428571 1.0690450 2.0000000 5.0000000

q4 8 3.2500000 1.5811388 1.0000000 5.0000000

-------------------------------------------------------------------------

* 기초 통계 산출;

proc univariate data=temp;

var q1-q4;

run;

UNIVARIATE 프로시저

변수: q1

적률

N 8 가중합 8

평균 3.25 관측치 합 26

표준편차 1.48804762 분산 2.21428571

왜도 -0.2167811 첨도 -1.4101977

제곱합 100 수정 제곱합 15.5

변동계수 45.7860806 평균의 표준오차 0.52610428

기본 통계 측도

위치측도 변이측도

평균 3.250000 표준편차 1.48805

중위수 3.500000 분산 2.21429

최빈값 2.000000 범위 4.00000

사분위 범위 2.50000

NOTE: 표시된 모드는 3 모드(2 도수를 가지는) 중에 가장 작습니다.

위치모수 검정: Mu0=0

검정 --통계량--- -------p-값-------

스튜던트의 t t 6.177483 Pr > |t| 0.0005

부호 M 4 Pr >= |M| 0.0078

부호 순위 S 18 Pr >= |S| 0.0078

* 빈도와 백분율;

proc freq data=temp;

tables workshop--q4;

run;

FREQ 프로시저

누적 누적

workshop 빈도 백분율 빈도 백분율

----------------------------------------------------

1 4 50.00 4 50.00

2 4 50.00 8 100.00

누적 누적

gender 빈도 백분율 빈도 백분율

--------------------------------------------------

f 4 50.00 4 50.00

m 4 50.00 8 100.00

누적 누적

q1 빈도 백분율 빈도 백분율

----------------------------------------------

1 1 12.50 1 12.50

2 2 25.00 3 37.50

3 1 12.50 4 50.00

4 2 25.00 6 75.00

5 2 25.00 8 100.00

*---관계 측도.;

* 피어슨 상관계수;

proc corr data=temp;

var q1-q4;

run;

피어슨 상관 계수

H0: Rho=0 검정에 대한 Prob > |r|

관측치 개수

q1 q2 q3 q4

q1 1.00000 0.73952 -0.12500 0.88041

0.0360 0.7894 0.0039

8 8 7 8

q2 0.73952 1.00000 -0.27003 0.85064

0.0360 0.5581 0.0074

8 8 7 8

q3 -0.12500 -0.27003 1.00000 -0.02614

0.7894 0.5581 0.9556

7 7 7 7

q4 0.88041 0.85064 -0.02614 1.00000

0.0039 0.0074 0.9556

8 8 7 8

* 스피어만 상관계수;

proc corr data=temp spearman;

var q1-q4;

run;

스피어만 상관 계수

H0: Rho=0 검정에 대한 Prob > |r|

관측치 개수

q1 q2 q3 q4

q1 1.00000 0.70005 -0.03965 0.86958

0.0532 0.9327 0.0050

8 8 7 8

q2 0.70005 1.00000 -0.07857 0.88052

0.0532 0.8670 0.0039

8 8 7 8

q3 -0.03965 -0.07857 1.00000 0.25774

0.9327 0.8670 0.5768

7 7 7 7

q4 0.86958 0.88052 0.25774 1.00000

0.0050 0.0039 0.5768

8 8 7 8

* 선형 회귀 분석;

proc reg data=temp;

model q4=q1-q3;

run;

The REG Procedure

Model: MODEL1

Dependent Variable: q4

Number of Observations Read 8

Number of Observations Used 7

Number of Observations with Missing Values 1

Analysis of Variance

Sum of Mean

Source DF Squares Square F Value Pr > F

Model 3 16.20684 5.40228 13.27 0.0308

Error 3 1.22173 0.40724

Corrected Total 6 17.42857

Root MSE 0.63816 R-Square 0.9299

Dependent Mean 3.28571 Adj R-Sq 0.8598

Coeff Var 19.42214

Parameter Estimates

Parameter Standard

Variable DF Estimate Error t Value Pr > |t|

Intercept 1 -1.32426 1.28774 -1.03 0.3794

q1 1 0.42975 0.26233 1.64 0.1999

q2 1 0.63101 0.25027 2.52 0.0861

q3 1 0.31498 0.25570 1.23 0.3058

*---그룹 비교;

* Chi-square;

proc freq data=temp;

tables workshop*gender/chisq;

run;

FREQ 프로시저

workshop * gender 테이블

workshop gender

빈도|

백분율|

행 백분율|

칼럼 백분율|f |m | 총합

-----------+--------+--------+

1 | 2 | 2 | 4

| 25.00 | 25.00 | 50.00

| 50.00 | 50.00 |

-----------+--------+--------+

2 | 2 | 2 | 4

| 25.00 | 25.00 | 50.00

| 50.00 | 50.00 |

-----------+--------+--------+

총합 4 4 8

50.00 50.00 100.00

workshop * gender 테이블에 대한 통계량

통계량 자유도 값 확률

----------------------------------------------------------

카이제곱 1 0.0000 1.0000

우도비 카이제곱 1 0.0000 1.0000

연속성 수정 카이제곱 1 0.0000 1.0000

Mantel-Haenszel 카이제곱 1 0.0000 1.0000

파이 계수 0.0000

우발성 계수 0.0000

크래머의 V 0.0000

* 독립 samples t-test;

proc ttest data=temp;

class gender;

var q4;

run;

The TTEST Procedure

Statistics

Lower CL Upper CL Lower CL Upper CL

Variable gender N Mean Mean Mean Std Dev Std Dev Std Dev Std Err

q4 f 4 0.1626 2 3.8374 0.6541 1.1547 4.3054 0.5774

q4 m 4 3.5813 4.5 5.4187 0.3271 0.5774 2.1527 0.2887

q4 Diff (1-2) -4.079 -2.5 -0.921 0.5882 0.9129 2.0102 0.6455

T-Tests

Variable Method Variances DF t Value Pr > |t|

q4 Pooled Equal 6 -3.87 0.0082

q4 Satterthwaite Unequal 4.41 -3.87 0.0149

Equality of Variances

Variable Method Num DF Den DF F Value Pr > F

q4 Folded F 3 3 4.00 0.2848

* Wilcoxon/Mann-Whitney test 을 이용한 위 예제의 비모수 버전;

proc npar1way data=temp;

class gender;

var q4;

run;

The NPAR1WAY Procedure

Kolmogorov-Smirnov Test for Variable q4

Classified by Variable gender

EDF at Deviation from Mean

gender N Maximum at Maximum

---------------------------------------------------

f 4 1.00 1.0

m 4 0.00 -1.0

Total 8 0.50

Maximum Deviation Occurred at Observation 4

Value of q4 at Maximum = 3.0

Kolmogorov-Smirnov Two-Sample Test (Asymptotic)

KS 0.500000 D 1.000000

KSa 1.414214 Pr > KSa 0.0366

Cramer-von Mises Test for Variable q4

Classified by Variable gender

Summed Deviation

gender N from Mean

--------------------------------------

f 4 0.3750

m 4 0.3750

Cramer-von Mises Statistics (Asymptotic)

CM 0.093750 CMa 0.750000

Kuiper Test for Variable q4

Classified by Variable gender

Deviation

gender N from Mean

------------------------------

f 4 1.0

m 4 0.0

Kuiper Two-Sample Test (Asymptotic)

K 1.000000 Ka 1.414214 Pr > Ka 0.2564

* Paired samples t-test (silly one);

proc ttest data=temp;

paired q1*q2;

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

q1 - q2 8 -0.499 0.5 1.4992 0.7903 1.1952 2.4326 0.4226

T-Tests

Difference DF t Value Pr > |t|

q1 - q2 7 1.18 0.2753

* 부호 순위 검정을 이용한 위 예제의 비모수 버전.;

proc univariate data=temp;

var myDiff;

run;

UNIVARIATE 프로시저

변수: myDiff

적률

N 8 가중합 8

평균 -0.5 관측치 합 -4

표준편차 1.19522861 분산 1.42857143

왜도 0 첨도 -1.456

제곱합 12 수정 제곱합 10

변동계수 -239.04572 평균의 표준오차 0.42257713

기본 통계 측도

위치측도 변이측도

평균 -0.50000 표준편차 1.19523

중위수 -0.50000 분산 1.42857

최빈값 -2.00000 범위 3.00000

사분위 범위 2.00000

* Oneway Analysis of Variance (ANOVA);

proc glm data=temp;

class workshop;

model q4=workshop;

means workshop gender / tukey;

run;

The GLM Procedure

Dependent Variable: q4

Sum of

Source DF Squares Mean Square F Value Pr > F

Model 1 0.50000000 0.50000000 0.18 0.6891

Error 6 17.00000000 2.83333333

Corrected Total 7 17.50000000

R-Square Coeff Var Root MSE q4 Mean

0.028571 51.79233 1.683251 3.250000

Source DF Type I SS Mean Square F Value Pr > F

workshop 1 0.50000000 0.50000000 0.18 0.6891

Source DF Type III SS Mean Square F Value Pr > F

workshop 1 0.50000000 0.50000000 0.18 0.6891

* Kruskal-Wallis test 을 이용한 위 예제의 비모수 버전;

proc npar1way data=temp;

class workshop;

var q4;

run;

The NPAR1WAY Procedure

Analysis of Variance for Variable q4

Classified by Variable workshop

workshop N Mean

------------------------------------

1 4 3.00

2 4 3.50

Source DF Sum of Squares Mean Square F Value Pr > F

-------------------------------------------------------------------

Among 1 0.50 0.500000 0.1765 0.6891

Within 6 17.00 2.833333

Average scores were used for ties.

Wilcoxon Scores (Rank Sums) for Variable q4

Classified by Variable workshop

Sum of Expected Std Dev Mean

workshop N Scores Under H0 Under H0 Score

------------------------------------------------------------------------

1 4 16.0 18.0 3.380617 4.0

2 4 20.0 18.0 3.380617 5.0

Average scores were used for ties.

Wilcoxon Two-Sample Test

Statistic 16.0000

Normal Approximation

Z -0.4437

One-Sided Pr < Z 0.3286

Two-Sided Pr > |Z| 0.6573

t Approximation

One-Sided Pr < Z 0.3353

Two-Sided Pr > |Z| 0.6706

Z includes a continuity correction of 0.5.

Kruskal-Wallis Test

Chi-Square 0.3500

DF 1

Pr > Chi-Square 0.5541


2. SPSS	MAIN

* SPSS Program of Basic Statistical Tests.

GET FILE='C:\mydata.sav'.

DATASET NAME DataSet2 WINDOW=FRONT.

* Descriptive stats in compact form.

DESCRIPTIVES VARIABLES=q1 q2 q3 q4

/STATISTICS=MEAN STDDEV VARIANCE MIN MAX SEMEAN .

* Descriptive stats of every sort.

EXAMINE VARIABLES=q1 q2 q3 q4

/PLOT BOXPLOT STEMLEAF NPPLOT

/COMPARE GROUP

/STATISTICS DESCRIPTIVES EXTREME

/CINTERVAL 95

/MISSING PAIRWISE

/NOTOTAL.

EXECUTE.

* Frequencies and percents.

FREQUENCIES VARIABLES=workshop gender q1 q2 q3 q4

/ORDER= ANALYSIS .

EXECUTE.

*---Measures of association.

* Person correlations.

CORRELATIONS

/VARIABLES=q1 q2 q3 q4

/PRINT=TWOTAIL NOSIG

/MISSING=PAIRWISE .

EXECUTE.

* Spearman correlations.

NONPAR CORR

/VARIABLES=q1 q2 q3 q4

/PRINT=SPEARMAN TWOTAIL NOSIG

/MISSING=PAIRWISE .

EXECUTE.

* Linear regression.

REGRESSION

/MISSING LISTWISE

/STATISTICS COEFF OUTS R ANOVA

/CRITERIA=PIN(.05) POUT(.10)

/NOORIGIN

/DEPENDENT q4

/METHOD=ENTER q1 q2 q3 .

EXECUTE.

*---Group comparisons;

* Chisquare.

CROSSTABS

/TABLES=workshop BY gender

/FORMAT= AVALUE TABLES

/STATISTIC=CHISQ

/CELLS= COUNT ROW

/COUNT ROUND CELL .

EXECUTE.

* Independent samples t-test.

T-TEST

GROUPS = gender('m' 'f')

/MISSING = ANALYSIS

/VARIABLES = q4

/CRITERIA = CI(.95) .

EXECUTE.

* Nonparametric version of above using

Wilcoxon/Mann-Whitney test.

* SPSS requires a numeric form of gender for this procedure.

AUTORECODE

VARIABLES=gender /INTO genderN

/PRINT.

NPAR TESTS

/M-W= q4 BY genderN(1 2)

/MISSING ANALYSIS.

EXECUTE.

* Paired samples t-test.

T-TEST

PAIRS = q1 WITH q2 (PAIRED)

/CRITERIA = CI(.95)

/MISSING = ANALYSIS.

EXECUTE.

* Nonparametric version of above using

Wilcoxon Signed Rank test.

NPAR TEST

/WILCOXON=q1 WITH q2 (PAIRED)

/MISSING ANALYSIS.

EXECUTE.

* Oneway analysis of variance (ANOVA).

UNIANOVA q4 BY workshop

/METHOD = SSTYPE(3)

/INTERCEPT = INCLUDE

/POSTHOC = workshop ( TUKEY )

/PRINT = ETASQ HOMOGENEITY

/CRITERIA = ALPHA(.05)

/DESIGN = workshop .

* Nonparametric version of above using

Kruskal Wallis test.

NPAR TESTS

/K-W=q4 BY workshop(1 3)

/MISSING ANALYSIS.

EXECUTE.


3. R-PROJECT	MAIN

mydata<-read.table ("c:/data/mydata.csv",header=TRUE,

sep=",",row.names="id")

print(mydata)

# 실행전 Hmisc와 prettyR을 인스톨.

library(foreign)

library(Hmisc)

install.packages("prettyR")

library(prettyR)

# 기술 통계와 빈도;

summary(mydata)

workshop gender q1 q2 q3 q4

Min. :1.0 f:4 Min. :1.00 Min. :1.00 Min. :2.000 Min. :1.00

1st Qu.:1.0 m:4 1st Qu.:2.00 1st Qu.:1.00 1st Qu.:4.000 1st Qu.:2.50

Median :1.5 Median :3.50 Median :2.50 Median :4.000 Median :3.50

Mean :1.5 Mean :3.25 Mean :2.75 Mean :4.143 Mean :3.25

3rd Qu.:2.0 3rd Qu.:4.25 3rd Qu.:4.25 3rd Qu.:5.000 3rd Qu.:4.25

Max. :2.0 Max. :5.00 Max. :5.00 Max. :5.000 Max. :5.00

NA's :1.000

# Hmisc 패키지의 describe함수를 이용하여 평균,빈도,백분율 계산;

describe(mydata)

Description of mydata

Numeric

mean median var sd valid.n

workshop 1.5 1.5 0.2857 0.5345 8

q1 3.25 3.5 2.214 1.488 8

q2 2.75 2.5 3.071 1.753 8

q3 4.143 4 1.143 1.069 7

q4 3.25 3.5 2.5 1.581 8

Factor

f m

gender 4 4

mode = >1 mode Valid n = 8

# prettyR 패키지로부터 freq함수를 이용한 빈도, 백분율 계산.

freq(mydata)

Frequencies for workshop

1 2

4 4

% 50 50

Frequencies for gender

f m

4 4

% 50 50

Frequencies for q1

1 2 3 4 5

1 2 1 2 2

% 12.5 25 12.5 25 25

Frequencies for q2

1 2 3 4 5

3 1 1 1 2

% 37.5 12.5 12.5 12.5 25

Frequencies for q3

2 4 5 NA

1 3 3 1

% 12.5 37.5 37.5 12.5

%!NA 14.3 42.9 42.9

Frequencies for q4

1 3 4 5

2 2 2 2

% 25 25 25 25

#---연관성 측도.

# 피어슨 상관계수.

# Hmisc 패키지의 rcorr함수는 SAS 나 SPSS와 비슷한 결과 산출. 상관계수,n,p-value 산출.

rcorr( cbind(mydata$q1,mydata$q2,mydata$q3,mydata$q4) )

[,1] [,2] [,3] [,4]

[1,] 1.00 0.74 -0.12 0.88

[2,] 0.74 1.00 -0.27 0.85

[3,] -0.12 -0.27 1.00 -0.03

[4,] 0.88 0.85 -0.03 1.00

[,1] [,2] [,3] [,4]

[1,] 8 8 7 8

[2,] 8 8 7 8

[3,] 7 7 7 7

[4,] 8 8 7 8

[,1] [,2] [,3] [,4]

[1,] 0.0360 0.7894 0.0039

[2,] 0.0360 0.5581 0.0074

[3,] 0.7894 0.5581 0.9556

[4,] 0.0039 0.0074 0.9556

# cor function은 기본 제공 함수지만, 유의성 검증 결과를 제공하지 않는다.

cor(data.frame(mydata$q1,mydata$q2,mydata$q3,mydata$q4),method="pearson",use="pairwise")

mydata.q1 mydata.q2 mydata.q3 mydata.q4

mydata.q1 1.0000000 0.7395179 -0.12500000 0.88040627

mydata.q2 0.7395179 1.0000000 -0.27003086 0.85063978

mydata.q3 -0.1250000 -0.2700309 1.00000000 -0.02613542

mydata.q4 0.8804063 0.8506398 -0.02613542 1.00000000

# cor.test함수는 상관계수, p-value, 신뢰구간을 제공하지만, 단지 2개의 변수만 검증.

cor.test(mydata$q1,mydata$q2,use="pairwise")

Pearson's product-moment correlation

data: mydata$q1 and mydata$q2

t = 2.691, df = 6, p-value = 0.036

alternative hypothesis: true correlation is not equal to 0

95 percent confidence interval:

0.0727632 0.9494271

sample estimates:

cor

0.7395179

# Hmisc패키지의 rcorr함수를 이용하여 스피어만 상관계수 산출.

rcorr( cbind(mydata$q1,mydata$q2,mydata$q3,mydata$q4), type='spearman')

[,1] [,2] [,3] [,4]

[1,] 1.00 0.70 -0.04 0.87

[2,] 0.70 1.00 -0.08 0.88

[3,] -0.04 -0.08 1.00 0.26

[4,] 0.87 0.88 0.26 1.00

[,1] [,2] [,3] [,4]

[1,] 8 8 7 8

[2,] 8 8 7 8

[3,] 7 7 7 7

[4,] 8 8 7 8

[,1] [,2] [,3] [,4]

[1,] 0.0532 0.9327 0.0050

[2,] 0.0532 0.8670 0.0039

[3,] 0.9327 0.8670 0.5768

[4,] 0.0050 0.0039 0.5768

# 선형 회귀분석.

myRegModel<-lm(q4~q1+q2+q3,data=mydata)

summary(myRegModel)

Call:

lm(formula = q4 ~ q1 + q2 + q3, data = mydata)

Residuals:

1 2 3 5 6 7 8

-0.31139 -0.42616 0.94283 -0.17975 0.07658 0.02257 -0.12468

Coefficients:

Estimate Std. Error t value Pr(>|t|)

(Intercept) -1.3243 1.2877 -1.028 0.379

q1 0.4297 0.2623 1.638 0.200

q2 0.6310 0.2503 2.521 0.086 .

q3 0.3150 0.2557 1.232 0.306

---

Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.6382 on 3 degrees of freedom

(1 observation deleted due to missingness)

Multiple R-Squared: 0.9299, Adjusted R-squared: 0.8598

F-statistic: 13.27 on 3 and 3 DF, p-value: 0.03084

* 분산분석

anova(myRegModel)

Analysis of Variance Table

Response: q4

Df Sum Sq Mean Sq F value Pr(>F)

q1 1 13.4934 13.4934 33.1335 0.01042 *

q2 1 2.0955 2.0955 5.1456 0.10809

q3 1 0.6180 0.6180 1.5174 0.30576

Residuals 3 1.2217 0.4072

---

Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

plot(myRegModel)

termplot(myRegModel)

#---그룹 비교.

# prettyR 패키지의 xtab 함수를 이용하여 교차분석,chi-square 계산.

xtab(~workshop+gender,data=mydata,chisq=TRUE)

Crosstabulation of workshop by gender

gender

workshop f m

1 2 2 4

50 50 50

50 50

2 2 2 4

50 50 50

50 50

4 4 8

50 50

X2[1] = 0.5, p = 0.4795001

Warning message:

카이 자승 근사는 부정확할지도 모릅니다 in: chisq.test(x$counts, ...)

# R의 기본함수인 table를 이용하여 교차분석, chi-square 계산.

myWG<-table(mydata$workshop,mydata$gender)

print(myWG)

chisq.test(myWG)

Pearson's Chi-squared test with Yates' continuity correction

data: myWG

X-squared = 0.5, df = 1, p-value = 0.4795

Warning message:

카이 자승 근사는 부정확할지도 모릅니다 in: chisq.test(myWG)

# Independent samples t-test.

t.test(mydata$q4[mydata$gender=='m'],mydata$q4[mydata$gender=='f'] )

Welch Two Sample t-test

data: mydata$q4[mydata$gender == "m"] and mydata$q4[mydata$gender == "f"]

t = 3.873, df = 4.412, p-value = 0.01491

alternative hypothesis: true difference in means is not equal to 0

95 percent confidence interval:

0.7718919 4.2281081

sample estimates:

mean of x mean of y

4.5 2.0

# Wilcoxon/Mann-Whitney test를 이용한 위 예제의 비모수 버전.

wilcox.test(mydata$q4[mydata$gender=='m'],mydata$q4[mydata$gender=='f'] )

Wilcoxon rank sum test with continuity correction

data: mydata$q4[mydata$gender == "m"] and mydata$q4[mydata$gender == "f"]

W = 16, p-value = 0.02652

alternative hypothesis: true location shift is not equal to 0

Warning message:

ties가 있기때문에, 정확한 p값을 돌려줍니다 in: wilcox.test.default(mydata$q4[mydata$gender == "m"], mydata$ gender=='f'] )

# Paired samples t-test (silly one).

t.test(mydata$q1,mydata$q2,paired=TRUE)

Paired t-test

data: mydata$q1 and mydata$q2

t = 1.1832, df = 7, p-value = 0.2753

alternative hypothesis: true difference in means is not equal to 0

95 percent confidence interval:

-0.4992361 1.4992361

sample estimates:

mean of the differences

0.5

# 위 예제의 비모수 버전.

wilcox.test(mydata$q1,mydata$q2,paired=TRUE)

Wilcoxon signed rank test with continuity correction

data: mydata$q1 and mydata$q2

V = 16, p-value = 0.2795

alternative hypothesis: true location shift is not equal to 0

Warning messages:

1: ties가 있기때문에, 정확한 p값을 돌려줍니다 in: wilcox.test.default(mydata$q1, mydata$q2, paired = TRUE)

2: zeroes 값 때문에 수가 없습니다, 정확한 p 값을 계산할 수가 없습니다 in: wilcox.test.default(mydata$q1, mydata$q2, paired = TRUE)

# Oneway Analysis of Variance (ANOVA).

myModel<-aov(q4~workshop,data=mydata)

summary(myModel)

Df Sum Sq Mean Sq F value Pr(>F)

workshop 1 0.5000 0.5000 0.1765 0.689

Residuals 6 17.0000 2.8333

anova(myModel)

Analysis of Variance Table

Response: q4

Df Sum Sq Mean Sq F value Pr(>F)

workshop 1 0.5000 0.5000 0.1765 0.689

Residuals 6 17.0000 2.8333

plot(myModel)

termplot(myModel)

# Kruskal-Wallis test 를 이용한 위 예제의 비모수 일원분산분석.(Nonparametric oneway ANOVA)

kruskal.test(mydata$q4,mydata$workshop)

Kruskal-Wallis rank sum test

data: mydata$q4 and mydata$workshop

Kruskal-Wallis chi-squared = 0.35, df = 1, p-value = 0.5541


4. S-PLUS	MAIN

mydata<-read.table ("c:/data/mydata.csv",header=TRUE,

sep=",",row.names="id")

print(mydata)

# 기술 통계와 빈도.

summary(mydata)

workshop gender q1 q2 q3 q4

Min. :1.0 f:4 Min. :1.00 Min. :1.00 Min. :2.000 Min. :1.00

1st Qu.:1.0 m:4 1st Qu.:2.00 1st Qu.:1.00 1st Qu.:4.000 1st Qu.:2.50

Median :1.5 Median :3.50 Median :2.50 Median :4.000 Median :3.50

Mean :1.5 Mean :3.25 Mean :2.75 Mean :4.143 Mean :3.25

3rd Qu.:2.0 3rd Qu.:4.25 3rd Qu.:4.25 3rd Qu.:5.000 3rd Qu.:4.25

Max. :2.0 Max. :5.00 Max. :5.00 Max. :5.000 Max. :5.00

NA's :1.000

#---연관성 측도.

# 피어슨 상관계수.

# cor function은 기본 제공 함수지만, 유의성 검증 결과를 제공하지 않는다.

cor(cbind(mydata$q1,mydata$q2,mydata$q3,mydata$q4),na.method="available")

[,1] [,2] [,3] [,4]

[1,] 1.0000000 0.7395179 -0.13470398 0.88040627

[2,] 0.7395179 1.0000000 -0.26687250 0.85063978

[3,] -0.1347040 -0.2668725 1.00000000 -0.02817181

[4,] 0.8804063 0.8506398 -0.02817181 1.00000000

# cor.test함수는 상관계수, p-value, 신뢰구간을 제공하지만, 단지 2개의 변수만 검증.

cor.test(mydata$q1,mydata$q2,use="pairwise")

Pearson's product-moment correlation

data: mydata$q1 and mydata$q2

t = 2.691, df = 6, p-value = 0.036

alternative hypothesis: coef is not equal to 0

sample estimates:

cor

0.7395179

# 선형 회귀분석.

myRegModel<-lm(q4~q1+q2+q3,data=mydata,na.action=na.exclude)

summary(myRegModel)

Call: lm(formula = q4 ~ q1 + q2 + q3, data = mydata, na.action = na.exclude)

Residuals:

1 2 3 5 6 7 8

-0.3114 -0.4262 0.9428 -0.1797 0.07658 0.02257 -0.1247

Coefficients:

Value Std. Error t value Pr(>|t|)

(Intercept) -1.3243 1.2877 -1.0284 0.3794

q1 0.4297 0.2623 1.6382 0.1999

q2 0.6310 0.2503 2.5214 0.0861

q3 0.3150 0.2557 1.2318 0.3058

Residual standard error: 0.6382 on 3 degrees of freedom

Multiple R-Squared: 0.9299

F-statistic: 13.27 on 3 and 3 degrees of freedom, the p-value is 0.03084

1 observations deleted due to missing values

Correlation of Coefficients:

(Intercept) q1 q2

q1 -0.0969

q2 -0.2887 -0.7813

q3 -0.8895 -0.1422 0.2779

* 분산분석

anova(myRegModel)

Analysis of Variance Table

Response: q4

Terms added sequentially (first to last)

Df Sum of Sq Mean Sq F Value Pr(F)

q1 1 13.49339 13.49339 33.13347 0.0104181

q2 1 2.09550 2.09550 5.14557 0.1080859

q3 1 0.61795 0.61795 1.51741 0.3057616

Residuals 3 1.22173 0.40724

plot(myRegModel)

#---그룹 비교.

crosstabs(~mydata$workshop+mydata$gender)

Call:

crosstabs(formula = ~ mydata$workshop + mydata$gender)

8 cases in table

+----------+

|N |

|N/RowTotal|

|N/ColTotal|

|N/Total |

+----------+

mydata$workshop|mydata$gender

|f |m |RowTotl|

-------+-------+-------+-------+

1 |2 |2 |4 |

|0.5 |0.5 |0.5 |

|0.5 |0.5 | |

|0.25 |0.25 | |

-------+-------+-------+-------+

2 |2 |2 |4 |

|0.5 |0.5 |0.5 |

|0.5 |0.5 | |

|0.25 |0.25 | |

-------+-------+-------+-------+

ColTotl|4 |4 |8 |

|0.5 |0.5 | |

-------+-------+-------+-------+

Test for independence of all factors

Chi^2 = 0 d.f.= 1 (p=1)

Yates' correction not used

Some expected values are less than 5, don't trust stated p-value

# R의 기본함수인 table를 이용하여 교차분석, chi-square 계산.

myWG<-table(mydata$workshop,mydata$gender)

print(myWG)

f m

1 2 2

2 2 2

chisq.test(myWG)

Pearson's chi-square test with Yates' continuity correction

data: myWG

X-square = 0.5, df = 1, p-value = 0.4795

Warning messages:

Expected counts < 5. Chi-square approximation may not be appropriate. in:

chisq.test(myWG)

# Independent samples t-test.

t.test(mydata$q4[mydata$gender=='m'],mydata$q4[mydata$gender=='f'] )

Standard Two-Sample t-Test

data: mydata$q4[mydata$gender == "m"] and mydata$q4[mydata$gender == "f"]

t = 3.873, df = 6, p-value = 0.0082

alternative hypothesis: difference in means is not equal to 0

95 percent confidence interval:

0.9205252 4.0794748

sample estimates:

mean of x mean of y

4.5 2

# Wilcoxon/Mann-Whitney test를 이용한 위 예제의 비모수 버전.

wilcox.test(mydata$q4[mydata$gender=='m'],mydata$q4[mydata$gender=='f'] )

Wilcoxon rank-sum test

data: mydata$q4[mydata$gender == "m"] and mydata$q4[mydata$gender == "f"]

rank-sum normal statistic with correction Z = 2.2185, p-value = 0.0265

alternative hypothesis: mu is not equal to 0

Warning messages:

cannot compute exact p-value with ties in: wil.rank.sum(x, y, alternative,

exact, correct)

# Paired samples t-test (silly one).

t.test(mydata$q1,mydata$q2,paired=TRUE)

Paired t-Test

data: mydata$q1 and mydata$q2

t = 1.1832, df = 7, p-value = 0.2753

alternative hypothesis: mean of differences is not equal to 0

95 percent confidence interval:

-0.4992361 1.4992361

sample estimates:

mean of x - y

0.5

# 위 예제의 비모수 버전.

wilcox.test(mydata$q1,mydata$q2,paired=TRUE)

Wilcoxon signed-rank test

data: mydata$q1 and mydata$q2

signed-rank normal statistic with correction Z = 1.0064, p-value = 0.3142

alternative hypothesis: mu is not equal to 0

Warning messages:

1: cannot compute exact p-value with ties in: wil.sign.rank(dff, alternative,

exact, correct)

2: cannot compute exact p-value for zero differences in: wil.sign.rank(dff,

alternative, exact, correct)

# Oneway Analysis of Variance (ANOVA).

myModel<-aov(q4~workshop,data=mydata)

summary(myModel)

Df Sum of Sq Mean Sq F Value Pr(F)

workshop 1 0.5 0.500000 0.1764706 0.6890522

Residuals 6 17.0 2.833333

anova(myModel)

Analysis of Variance Table

Response: q4

Terms added sequentially (first to last)

Df Sum of Sq Mean Sq F Value Pr(F)

workshop 1 0.5 0.500000 0.1764706 0.6890522

Residuals 6 17.0 2.833333

plot(myModel)

# Kruskal-Wallis test 를 이용한 위 예제의 비모수 일원분산분석.(Nonparametric oneway ANOVA)

kruskal.test(mydata$q4,mydata$workshop)

Kruskal-Wallis rank sum test

data: mydata$q4 and mydata$workshop

Kruskal-Wallis chi-square = 0.35, df = 1, p-value = 0.5541

alternative hypothesis: two.sided


5. PROC SQL	MAIN

18. 통계분석

1. SAS

2. SPSS