(1)Ha:
sd(0)~=sd
(1)Ha:
sd(0)>sd
(1)
PF_U=0.8389P>F_obs=0.5805
P值=0.8389>>,因此可以认为两组方差齐性的。
正态性检验:
H0:
资料服从正态分布vsH1:
资料偏态分布
=0.05
每一组资料正态性检验
.swilkxifgroup==1
Shapiro-WilkWtestfornormaldata
Variable|ObsWVzProb>z
-------------+-------------------------------------------------
x|250.974030.722-0.6670.74747
.swilkxifgroup==0
Shapiro-WilkWtestfornormaldata
Variable|ObsWVzProb>z
-------------+-------------------------------------------------
x|250.971990.778-0.5130.69588
P值均大于,因此可以认为两组资料都服从正态分布
H0:
1=2vsH1:
12
=0.05
ttestx,by(group)
Two-samplettestwithequalvariances
------------------------------------------------------------------------------
Group|ObsMeanStd.Err.Std.Dev.[95%Conf.Interval]
---------+--------------------------------------------------------------------
0|2589.081.8229289.1146485.3176692.84234
1|25101.521.9009829.50491197.59657105.4434
---------+--------------------------------------------------------------------
combined|5095.31.57745611.154392.1299898.47002
---------+--------------------------------------------------------------------
diff|-12.442.633781-17.73557-7.144429
------------------------------------------------------------------------------
Degreesoffreedom:
48
Ho:
mean(0)-mean
(1)=diff=0
Ha:
diff<0Ha:
diff~=0Ha:
diff>0
t=-4.7232t=-4.7232t=-4.7232
P|t|=0.0000P>t=1.0000
P值(<0.0001)<,并且有0-1的95%可信区间为(-17.73557,-7.144429)可以知道,不接触组幼儿的平均智商高于接触组的幼儿平均智商,并且差别有统计学意义。
如果已知两组的样本量、样本均数和样本标准差,也可以用立即命令进行统计检验
ttesti样本量1样本均数1样本标准差1样本量2样本均数2样本标准差2
例如:
本例第1组n1=25均数1=89.08标准差1=9.115
第2组n2=25均数2=101.52标准差2=9.505
则ttesti2589.089.11525101.529.505
Two-samplettestwithequalvariances
------------------------------------------------------------------------------
|ObsMeanStd.Err.Std.Dev.[95%Conf.Interval]
---------+--------------------------------------------------------------------
x|2589.081.8239.11585.3175192.84249
y|25101.521.9019.50597.59653105.4435
---------+--------------------------------------------------------------------
combined|5095.31.57748211.1544892.1299398.47007
---------+--------------------------------------------------------------------
diff|-12.442.633843-17.7357-7.144303
------------------------------------------------------------------------------
Degreesoffreedom:
48
Ho:
mean(x)-mean(y)=diff=0
Ha:
diff<0Ha:
diff~=0Ha:
diff>0
t=-4.7231t=-4.7231t=-4.7231
P|t|=0.0000P>t=1.0000
结果解释同上。
方差不齐的情况,(小样本时,资料正态分布)还可以用t’检验
命令:
ttest观察变量名,by(分组变量名)unequal
立即命令为ttesti样本量1均数1标准差1样本量2均数2标准差2,unequal
假定本例的资料方差不齐(实际为方差不齐的),则要用t’检验如下
ttestx,by(group)unequal
Two-samplettestwithunequalvariances
------------------------------------------------------------------------------
Group|ObsMeanStd.Err.Std.Dev.[95%Conf.Interval]
---------+--------------------------------------------------------------------
0|2589.081.8229289.1146485.3176692.84234
1|25101.521.9009829.50491197.59657105.4434
---------+--------------------------------------------------------------------
combined|5095.31.57745611.154392.1299898.47002
---------+--------------------------------------------------------------------
diff|-12.442.633781-17.73581-7.144189
------------------------------------------------------------------------------
Satterthwaite'sdegreesoffreedom:
47.9159
Ho:
mean(0)-mean
(1)=diff=0
Ha:
diff<0Ha:
diff~=0Ha:
diff>0
t=-4.7232t=-4.7232t=-4.7232
P|t|=0.0000P>t=1.0000
结果解释同上。
t’检验有许多方法,这里介绍的Satterthwaite方法,主要根据两个样本方差差异的程度校正相应的自由度,由于本例的两个样本方差比较接近,故自由度几乎没有减少(t检验的自由度为48,而本例t’自由度为47.9159)。
由于t检验要求的两组总体方差相同(称为方差齐性),以及由于抽样误差的原因,样本方差一般不会相等,但是方差齐性的情况下,样本方差表现为两个样本方差之比1。
(注意:
两个样本方差之差很小,仍可能方差不齐。
如:
第一个样本标准差为0.1,样本量为100,第2个样本标准差为0.01,样本量为100,两个样本标准差仅差0.09,但是两个样本方差之比为100。
故用方差齐性检验的结果如下:
方差齐性的立即命令为sdtesti样本量1.标准差1样本量2.标准差2
sdtesti100.0.1100.0.01
Varianceratiotest
-----------------------------------------------------------------------------
|ObsMeanStd.Err.Std.Dev.[95%Conf.Interval]
---------+-------------------------------------------------------------------
x|100..01.1..
y|100..001.01..
---------+-------------------------------------------------------------------
combined|200.....
-----------------------------------------------------------------------------
Ho:
sd(x)=sd(y)
F(99,99)observed=F_obs=100.000
F(99,99)lowertail=F_L=1/F_obs=0.010
F(99,99)uppertail=F_U=F_obs=100.000
Ha:
sd(x)sd(x)~=sd(y)Ha:
sd(x)>sd(y)
PF_U=0.0000P>F_obs=0.0000
P值<0.0001,因此认为两组的方差不齐。
故方差齐性是考察两个样本方差之比是否接近1。
如果本例的资料不满足t检验要求(注:
实际是满足的,只是想用本例介绍成组秩和检验),则用秩和检验(WilcoxonRanksumtest)。
H0:
两组资料所在总体相同
H1:
两组资料所在总体不同
=0.05
命令:
ranksum观察变量名,by(分组变量)
本例为ranksumx,by(group)
.ranksumx,by(group)
Two-sampleWilcoxonrank-sum(Mann-Whitney)test
group|obsranksumexpected
-------------+---------------------------------
0|25437637.5
1|25838637.5
-------------+---------------------------------
combined|5012751275
unadjustedvariance2656.25
adjustmentforties-3.70
----------
adjustedvariance2652.55
Ho:
x(group==0)=