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lianxh
命令发布了:
随时搜索推文、Stata 资源。安装:
. ssc install lianxh
详情参见帮助文件 (有惊喜):
. help lianxh
连享会新命令:cnssc
,ihelp
,rdbalance
,gitee
,installpkg
⛳ Stata 系列推文:
编译:姜昊 (华东师范大学)
邮箱:HaoJiang0204@outlook.com
目录
tost
软件包提供了一套命令,包括 ttest
、ttesti
、prtest
、presti
、mcc
、mcci
、regress
、signrank
、ranksum
等。这些命令主要用于差异检验对应的两个单侧等值检验,从而解决一些配对和非配对、参数和非参数研究中的等值推断问题。
上述命令都将检验一个原假设,同时样本是从加减一些容忍度的不同总体中抽取。容忍度不仅可以用数据单位或等级单位 (tostrrp
和 tostrrpi
命令外) 用测试统计的分布单位 (
tost
软件包提供的所有命令都是基于
第一种,用
将绝对值符号打开,可以转化为下面两个单侧原假设:
当区间并非对称时,原假设变为:
将上式转化为下面两个单侧原假设:
第二种,用
将绝对值符号打开,可以转化为下面两个单侧原假设:
当区间并非对称时,原假设变为:
将上式转化为下面两个单侧原假设:
* 命令安装
net install tost.pkg, replace
tost
包含的命令如下:
tostt
:均值等价 tostpr
:比例等价 tostsignrank
:检验配对或匹配数据的分布是否等同于一个以零为中心的对称分布;tostranksum
:随机等价的双样本秩和检验;tostmcc
:二元数据中随机等价的配对 tostregress
:等价性的线性回归检验;tostrrp
:配对设计中相对风险的等价性检验。上述命令对应的即时命令:
tostti
:均值等价 tostt
对应;tostpri
:比例等价 tostpr
对应;tostmcci
:二元数据中随机等价的配对 tostmcc
对应;tostrrpi
:配对设计中相对风险的等价性检验的即时命令,与 tostrrp
对应。关于即使命令 (Immediate Commands),是指不依赖与内存数据集,而是依赖于直接输入的数字的一组命令,此时 Stata 类似于计算机功能,详见 help immed
。
* 单样本均值等值 t 检验
tostt varname == # [if] [in] [, eqvtype(type) eqvlevel(#)
uppereqvlevel(#) alpha(#)]
* 非配对双样本均值等值 t 检验
tostt varname1 == varname2 [if] [in], unpaired [eqvtype(type)
eqvlevel(#) uppereqvlevel(#) unequal welch alpha(#)]
* 配对双样本均值等值 t 检验
tostt varname1 == varname2 [if] [in] [, eqvtype(type) eqvlevel(#)
uppereqvlevel(#) alpha(#)]
* 双组非配对均值等值 t 检验
tostt varname [if] [in], by(groupvar) [eqvtype(type) eqvlevel(#)
uppereqvlevel(#) unequal welch alpha(#)]
上述命令中选项的含义:
eqvtype(string)
:指定等值阈值类型,包括 delta
或 epsilon
两种;eqvlevel(#)
:指定等值区间的容忍度水平;uppereqvlevel(#)
:指定对称等值区间的上限水平;uunpaired
:指定数据是非配对样本;by(groupvar)
:分组变量 (意味着样本为非配对样本);unequal
:非配对的样本具有不平等的变异性;alpha(#)
:设定第一类错误概率水平,默认为 0.05。* 单样本比例等值 z 检验
tostpr varname == # [if] [in] [, eqvtype(type) eqvlevel(#)
uppereqvlevel(#) alpha(#)]
* 双样本比例等值 z 检验
tostpr varname1 == varname2 [if] [in] [, eqvtype(type)
eqvlevel(#) yates ha uppereqvlevel(#) alpha(#)]
* 两组比例等值 z 检验
tostpr varname [if] [in] , by(groupvar) [eqvtype(type)
eqvlevel(#) uppereqvlevel(#) yates ha alpha(#)]
该命令选项与 tostt
命令基本一致,此处不再赘述。
* 配对符号秩检验,用于配对或匹配数据的分布,等价于对称且以零为中心的数据
tostsignrank varname = exp [if] [in] [, eqvtype(type) eqvlevel(#)
uppereqvlevel(#) ccontinuity alpha(#) relevance]
上述命令选项中,ccontinuity
指定数据是否需要对连续性进行修正。
. sysuse auto, clear
. tostt mpg==20, eqvt(delta) eqvl(2.5) upper(3)
One-sample t test for mean equivalence
------------------------------------------------------------------------------
Variable | Obs Mean Std. err. Std. dev. [95% conf. interval]
---------+--------------------------------------------------------------------
mpg | 74 21.2973 .6725511 5.785503 19.9569 22.63769
---------+--------------------------------------------------------------------
Δu-θ | 1.702703 .6725511 .3623103 3.043095
θ-Δl | 3.797297 .6725511 2.456905 5.13769
------------------------------------------------------------------------------
θ = mean(mpg) - 20
Δl = -2.5000 Δl expressed in same units as mpg
Δu = 3.0000 Δu expressed in same units as mpg
df = 73 using 74 - 1
Ho: θ <= Δl, or θ >= Δu:
t1 = 2.532 t2 = 5.646
Ho1: Δu-θ <= 0 Ho2: θ-Δl <= 0
Ha1: Δu-θ > 0 Ha2: θ-Δl > 0
Pr(T > t1) = 0.0068 Pr(T > t2) = 0.0000
根据上述检验结果可知,tostt
命令将该假设转换为两个单侧检验,并且都在 1% 的统计水平上拒绝原假设。
. webuse fuel, clear
. tostt mpg1==mpg2, eqvt(epsilon) eqvl(3) rel
Paired t test
------------------------------------------------------------------------------
Variable | Obs Mean Std. err. Std. dev. [95% conf. interval]
---------+--------------------------------------------------------------------
mpg1 | 12 21 .7881701 2.730301 19.26525 22.73475
mpg2 | 12 22.75 .9384465 3.250874 20.68449 24.81551
---------+--------------------------------------------------------------------
diff | 12 -1.75 .7797144 2.70101 -3.46614 -.0338602
------------------------------------------------------------------------------
mean(diff) = mean(mpg1 - mpg2) t = -2.2444
H0: mean(diff) = 0 Degrees of freedom = 11
Ha: mean(diff) < 0 Ha: mean(diff) != 0 Ha: mean(diff) > 0
Pr(T < t) = 0.0232 Pr(|T| > |t|) = 0.0463 Pr(T > t) = 0.9768
Paired t test for mean equivalence
------------------------------------------------------------------------------
Variable | Obs Mean Std. err. Std. dev. [95% conf. interval]
---------+--------------------------------------------------------------------
mpg1 | 12 21 .7881701 2.730301 19.26525 22.73475
mpg2 | 12 22.75 .9384465 3.250874 20.68449 24.81551
---------+--------------------------------------------------------------------
θ | 12 -1.75 .7797144 2.70101 -3.46614 -.0338602
------------------------------------------------------------------------------
mean(θ) = mean(mpg1 - mpg2)
ε = 3.0000 ε expressed in units of the t distribution
df = 11
Ho: |T| >= ε:
t1 = 5.244 t2 = .7556
Ho1: ε-T <= 0 Ho2: T+ε <= 0
Ha1: ε-T > 0 Ha2: T+ε > 0
Pr(T > t1) = 0.0001 Pr(T > t2) = 0.2329
Relevance test conclusion for α = 0.05, and ε = 3:
Ho test for difference: Reject
Ho test for equivalence: Fail to reject
Conclusion from combined tests: Relevant difference
对于配对双样本检验,由于两个单侧检验结果并非一致,因此需要在 tostt
命令中增加选项 relevance
,综合检验结果显示存在相对差异。
. sysuse auto, clear
. tostpr foreign==.4, eqvt(delta) eqvl(.15) upper(.2) rel
One-sample test of proportion Number of obs = 74
------------------------------------------------------------------------------
Variable | Mean Std. err. [95% conf. interval]
-------------+----------------------------------------------------------------
foreign | .2972973 .0531331 .1931583 .4014363
------------------------------------------------------------------------------
p = proportion(foreign) z = -1.8034
H0: p = 0.4
Ha: p < 0.4 Ha: p != 0.4 Ha: p > 0.4
Pr(Z < z) = 0.0357 Pr(|Z| > |z|) = 0.0713 Pr(Z > z) = 0.9643
One-sample test of proportion equivalence foreign: Number of obs = 74
------------------------------------------------------------------------------
Variable | Mean Std. Err. [95% Conf. Interval]
-------------+----------------------------------------------------------------
foreign | .2972973 .0531331 .1931583 .4014363
-------------+----------------------------------------------------------------
Δu-θ | .3027027 .0569495 .1910838 .4143216
θ-Δl | .0472973 .0569495 -.0643216 .1589162
------------------------------------------------------------------------------
θ = prop(foreign) - .4 = -.1027027
Δl = -0.1500 Δl expressed in same units as prop(foreign)
Δu = 0.2000 Δu expressed in same units as prop(foreign)
Ho: θ <= Δl, or θ >= Δu:
z1 = 5.315 z2 = .8305
Ho1: Δu-θ <= 0 Ho2: θ-Δl <= 0
Ha1: Δu-θ > 0 Ha2: θ-Δl > 0
Pr(Z > z1) = 0.0000 Pr(Z > z2) = 0.2031
Relevance test conclusion for α = 0.05, Δl = -0.15, and Δu = 0.2:
Ho test for difference: Fail to reject
Ho test for equivalence: Fail to reject
Conclusion from combined tests: Indeterminate (underpowered test)
通过上述检验可以发现,无论是绝对数量差异性检验,还是在选定的 delta
水平下,均无法拒绝原假设。
. webuse cure, clear
. tostpr cure1==cure2, eqvt(epsilon) eqvl(2.5) rel
Two-sample test of proportions cure1: Number of obs = 50
cure2: Number of obs = 59
------------------------------------------------------------------------------
Variable | Mean Std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
cure1 | .52 .0706541 .3815205 .6584795
cure2 | .7118644 .0589618 .5963013 .8274275
-------------+----------------------------------------------------------------
diff | -.1918644 .0920245 -.372229 -.0114998
| under H0: .0931155 -2.06 0.039
------------------------------------------------------------------------------
diff = prop(cure1) - prop(cure2) z = -2.0605
H0: diff = 0
Ha: diff < 0 Ha: diff != 0 Ha: diff > 0
Pr(Z < z) = 0.0197 Pr(|Z| > |z|) = 0.0394 Pr(Z > z) = 0.9803
Two-sample test of proportion equivalence cure1: Number of obs = 50
cure2: Number of obs = 59
------------------------------------------------------------------------------
Variable | Mean Std. Err. [95% Conf. Interval]
-------------+----------------------------------------------------------------
cure1 | .52 .0706541 .3815205 .6584795
cure2 | .7118644 .0589618 .5963013 .8274275
-------------+----------------------------------------------------------------
θ | -.1918644 .0931155 -.3743675 -.0093613
------------------------------------------------------------------------------
θ = prop(cure1) - prop(cure2) = -.19186441
ε = 2.5000 ε expressed in units of the z distribution
Ho: |Z| >= ε:
z1 = 4.56 z2 = .4395
Ho1: ε-Z <= 0 Ho2: Z+ε <= 0
Ha1: ε-Z > 0 Ha2: Z+ε > 0
Pr(Z > z1) = 0.0000 Pr(Z > z2) = 0.3301
Relevance test conclusion for α = 0.05, and ε = 2.5:
Ho test for difference: Reject
Ho test for equivalence: Fail to reject
Conclusion from combined tests: Relevant difference
通过上述检验可以发现,两组样本在绝对数量上存在显著差异,但在指定的 epsilon
范围内无法拒绝原假设。
. webuse fuel, clear
. tostsignrank mpg1 = mpg2, eqvt(epsilon) eqvl(2.46) rel
Relevance signed-rank test
Wilcoxon signed-rank test
Sign | Obs Sum ranks Expected
-------------+---------------------------------
Positive | 3 13.5 38.5
Negative | 8 63.5 38.5
Zero | 1 1 1
-------------+---------------------------------
All | 12 78 78
Unadjusted variance 162.50
Adjustment for ties -1.63
Adjustment for zeros -0.25
----------
Adjusted variance 160.63
H0: mpg1 = mpg2
z = -1.973
Prob > |z| = 0.0485
Exact prob = 0.0479
Signed-rank test for the distribution of paired or matched data being
equivalent to one that is symmetrical & centered on zero
sign | obs sum ranks expected
-------------+---------------------------------
positive | 3 13.5 38.5
negative | 8 63.5 38.5
zero | 1 1 1
-------------+---------------------------------
all | 12 78 78
unadjusted variance 162.5
adjustment for ties -1.625
adjustment for zeros -.25
----------
adjusted variance 160.625
ε = 2.4600 ε expressed in units of the z distribution
Ho: |Z| >= ε:
z1 = 4.433 z2 = .4874
Ho1: ε-Z <= 0 Ho2: Z+ε <= 0
Ha1: ε-Z > 0 Ha2: Z+ε > 0
Pr(Z > t1) = 0.0000 Pr(Z > t2) = 0.3130
Relevance test conclusion for α = 0.05, and ε = 2.46:
Ho test for difference: Reject
Ho test for equivalence: Fail to reject
Conclusion from combined tests: Relevant difference
通过上述检验可以发现,配对样本的符号秩检验在绝对数量上存在显著差异,但在指定的 epsilon
范围内无法拒绝原假设。
Note:产生如下推文列表的 Stata 命令为:
lianxh 差异检验, m
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New!
lianxh
和songbl
命令发布了:
随时搜索连享会推文、Stata 资源,安装命令如下:
. ssc install lianxh
使用详情参见帮助文件 (有惊喜):
. help lianxh