[I]Description

1.overall description

summary()

> summary(data)        #min,lower quartile,median,upper quartile,max

sapply()

> sapply(x,FUN,options)        #mean,standard deviation,skewness,kurtosis#options:mean(),sd(),var(),min(),max(),median(),length(),range(),quantile(),fivenum()

describe() of Hmisc

> describe(data)        #variable and observation amount,missing value and unique value mean,                        #quantile,,five min,five max

stat.desc() of pastecs

> stat.desc(data)#- basic=TRUE(default)#variable,null value,missing value,min,max,range,summary#- desc=TRUE(default)#median,mean,mean standard deviation,mean confidence interval(confidence=95%)#- norm=TRUE#normal distribution,include skewness and kurtosis(and degree of statistics)

describe() of psych

> describe(data)        #missing value mean,standard deviation,madian,trimmed mean,                        #median absolute deviation,min,max,range,skewness,kurtosis,standard error of the mean

2.part description

aggregate()

> aggregate(data,by=list(INDICES),FUN)        #return single statistic

by()

> by(data,INDICES,FUN)        #return multiple statistics

summaryBy() of doBy

> summaryBy(formula,data=dataframe,FUN=function)          #single or multiple grouping variable layering#formula = var1 + var2 + var3 + ... + varN ~ groupvar1 + groupvar2 + ... + groupvarN#(varN is numerical variable,groupvar is grouping variable)

describeBy() of psych

> describeBy(data,list(INDICES))        #grouping variable are related

3.contingency table

traditional

Function	Describe
table(var1,var2, ... ,varN)	N dimensional table
xtabs(~formula,data)	N dimensional table is based on a formula,a matrix or data frame generating
prop.table(table,margins)	convert frequency to scale
margin.table(table,margin)	summary
addmargins(table,margins)	add margins to table
ftable(table)	tiled contingency table

CrossTable() of gmodels

> CrossTable(data1,data2)

---

[II]Test

1.known sample

- independence

Chi-square

> chis.test(data)        #p<0.01,related;p>0.05,unrelated

Fisher percision

> fisher.test(mytable)        #mytable is not a 2×2 table

Cochran-Mantel-Haenszel

> mantelhaen.test(mytable)        #no third-order interaction

- correlation

category type

(1)Phi/Contingency/Cramer's V

> assocstats(mytable)

(2)Pearson/Spearman/Kendall

> cor(x,use,method)        #default:use="everything",method="pearson"> cov(data)        #covariance> cor.test(x,y,alternative= ,method= )        #test a relationship at a time> corr.test(x,use,method)        #test multiple relationships at a time

use:

• all.obs:getting an error while getting wrong data;
• everything:missing is setting while missing data;
• complete.obs:line deletion
• pairwise.complete.obs:pairwise deletion

method:

• pearson:linear correlation between two variables
• spearman:degree of correlation between graded variables
• kendall:level related measure
  (3)partial correlation

> library(ggm)> pcor(u,S)        #u:numerical vetor;S:covariance> pcor.test(r,q,n)        #r:correlation coefficient;q:variable number;n:sample size

continuous type

(1)parameter

1)independent sample

> t.test(y~x,data)        #t.test(y1,y2)

2)dependent sample

> t.test(y1,y2,paired=TRUE)

3)more than two groups:ANOVA

• single factor varinance (y~A)

> aov(formula,data=dataframe)> TukeyHSD()        #pairwise comparison

• single factor covariance (y~x + A)
• double factors varinance (y~A * B)
• repeated measurement varinance (y~ B*W + Error(Subject/W))
• multiple varinance

> data->manova(y~A)> summary.aov(data)> Wilks.test(y,shelf,method="mcd")

• regression

> fit.lm<-lm(y~A,data)> summary(fit.lm)

(2)nonparameter

• two groups

> wilcox.test(y~x,data)        #wilco.text(y1,y2)

• more than two groups

#groups independent> kruskal.test(y~A,data)        #groups dependent>friedman.test(y~A|B,data)

2.random sample

Function	Description
oneway_test(y~A)	two samples and K samples
oneway_test(y~A | C)	containing a layering factor of two samples and K samples
wilcox_test(y~A)	Wilcoxon-Meann-Whitney
kruskal_test(y~A)	Kruskal-Wallis
chisq_test(A~B | C)	Pearson Chi-square
cmh_test(A~B | C)	Cochran-Mantel-Haenszel
lbl_test(D~E)	linear correlation
spearman_test(y~x)	Spearman
friendman_test(y~A | C)	Friendman
wilcoxsign_test(y1~y2)	Wilcoxon

• function_name(formula,data,distribution=)
• formula=variables relationship
• data=dataframe
• distribution="exact"/"asymptotic"/"approximate"

Function	Description
lmp(A~B,data=,perm=)	simple
lmp(A~B+I(height^2),data=,perm=)	polynomical
lmp(A~B+C+D+E,data=,perm=)	multiple
avop(A~B,data=,perm=)	single factor variance
avop(A~B+C,data=,perm=)	single factor covariance
avop(A~B*C,data=,perm=)	double factor variance

• perm="Exact"/"Prob"/"SPR"

---

[III]efficacy

Function	Description
pwr.2p.test(h=,n=,sig.level=,power=)	two(n is equal)
pwr.2p2n.test(h=,n1=,n2=,sig.level=,power=)	two(n are not equal)
pwr.anova.test(k=,n=,f=,sig.level=,power=)	balanced single factor ANOVA
pwr.chisq.test(w=,N=,df=,sig.level=,power=)	Chi-square test
pwr.f2.test(u=,v=,f2=,sig.level=,power=)	generalized linear model
pwr.p.test()	proportion(single sample)
pwr.r.test(n=,r=,sig.level=,power=,alternative=)	correlation coefficient
pwr.t.test(n=,d=,sig.level=,power=,type=,alternative=)	t est(single sample/two samples/pair)
pwr.t2n.test(n1=,n2=,d=,sig.level=,power=,alternative=)	t test(n are not equal of two samples)

• h=ES.h(p1,p2)
• n=sample size
• $\mu$=mean
• $\sigma^2$=error variance
• sig.level=significant level(default=0.05)
• power=efficacy level
• k=groups number
• f=$\sqrt{\frac{\sum_{i-1}^{k}{p_i * {(\mu_i -\mu)}^2}}{\sigma^2}}$,$p_i=\frac{n_i}{N}$
• w=$\sqrt{\sum_{i=1}^{m}{\frac{
  {(p0_i-p1_i)}^2}{p0_i}}}$,$p0_i=H_0$ for probability,$p1_i=H_1$ for probability
• N=total sample
• df=free degree
• u=N-B;N-k-1(k=forecast number)
• v=denominator free degree
• f2=$\frac{R^2}{1-R^2}$($R^2$=total squared value of multiple correlation);
  f2=$\frac{
  {R_{AB}}^2-{R_A}^2}{1-{R_{AB}}^2}$(${R_{A}}^2$=interpretation rate of A for total variance,${R_{AB}}^2$=interpretation rate of A and B for total variance)
• r=reference linear correlation coefficient
• alternative="two.sided"(default)/"less"/"greater"
• d=$\frac{\mu_1-\mu_2}{\sigma}$
• type="two.sample"(default)/"one.sample"/"paired"

  END!