> x<-c(3.5, 3.6, 7.8, 9.6, 5.7, 8.9, 6.3)
> y<-c(1.0, 2.7, 8.9, 6.5, 8.9, 6.5,12.5,10.2, 1.2)
> t.test(x,y,alternative=c("two.sided"),var.equal=TRUE,conf.level=0.95)
Two Sample t-test
data: x and y
t = -0.0018, df = 14, p-value = 0.9986
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-3.760075 3.753726
sample estimates:
mean of x mean of y
6.485714 6.488889
t = -0.0018 ( ), 14.
p-value = 0.9986, .. , 99.86% .
95% (-3.760075, 3.753726). , 5% .
, , :
> t.test(x,y,alternative=c("two.sided"),var.equal=FALSE, conf.level=0.95)
Welch Two Sample t-test
data: x and y
t = -0.0019, df = 13.242, p-value = 0.9985
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-3.545004 3.538655
sample estimates:
mean of x mean of y
6.485714 6.488889
13.242 14, .
( ):
> x<-c(3.5, 3.6, 7.8, 9.6, 5.7, 8.9, 6.3, 8.3, 4.5)
> y<-c(1.0, 2.7, 8.9, 6.5, 8.9, 6.5,12.5,10.2, 1.2)
> t.test(x,y,alternative=c("two.sided"),var.equal=TRUE, paired=TRUE)
Paired t-test
data: x and y
t = -0.0202, df = 8, p-value = 0.9843
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-2.554391 2.509946
sample estimates:
mean of the differences
-0.02222222
:
t = -0.0202 ( ), 8.
p-value = 0.9943, .. , 99.86% .
95% (-2.554391, 2.509946). , 5% .
( ).
() , . , :
,
i - , - i - , - , - .
:
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,
,
,
, R bartlett.test()
bartlett.test (x, g...)
x | , , ( "lm"). |
g | , x. , x - . |
x - , g , bartlett.test(x). , bartlett.test(list (x...)).
( ) [2,.329] - qchisq(p,df).
> x1<-c(3.5, 3.6, 7.8, 9.6, 5.7, 8.9, 6.3)
> x2<-c(1.0, 2.7, 8.9, 6.5, 8.9, 6.5,12.5,10.2, 1.2)
> x3<-c(3.6,7.8,9.6,5.7,8.9)
> x4<-c(2.7,8.9,6.5,8.9)
5.86, 16.75, 6.05 8.57, H0 , 5%.
> bartlett.test(list(x1,x2,x3,x4))
Bartlett test of homogeneity of variances
data: list(x1, x2, x3, x4)
Bartlett's K-squared = 2.2368, df = 3, p-value = 0.5247
Bartlett's K-squared = 2.2368 ( ), 3,
p -value = 0.5247, .. H0 52.47%. , 5% .
() , (Cochran) outliers, cochran.test().
cochran.test(object,data)
object | , |
data | , |
qcochran(p, n, k) , p - , n ( , ), k .
, , 7, 9, 5 4 . H0 , 5%.
> cochran.test(object= c(var(x1),var(x2),var(x3),var(x4)), data=c(7,9,5,4))
Cochran test for outlying variance
data: c(var(x1), var(x2), var(x3), var(x4))
C = 0.4499, df = 6.25, k = 4.00, p-value = 0.3083
alternative hypothesis: Group 2 has outlying variance
Cochran C = 0.4499 ( ), ( ) 6.25, 4, p -value 0.3083. ( ). p -value = 0.3083, H0 30.83%. , 5% .
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( ANalysis Of VAriance ANOVA), F‑ , ( ) ().
. () , () . ( ) :
- , - i - ( i - ), - j - ( j - ), - ( ), - , . , , (, , , , ( ), .
, , :
SS | F | |||
() | ||||
- , - i - , - .
R , .
anova(object)
object | lm, glm. |
, 20 ( weight, 10 group), , . ( ).
> ctl <- c(4.17,5.58,5.18,6.11,4.50,4.61,5.17,4.53,5.33,5.14)
> trt <- c(4.81,4.17,4.41,3.59,5.87,3.83,6.03,4.89,4.32,4.69)
> group <- gl(2,10,20, labels=c("Ctl","Trt"))
> weight <- c(ctl, trt)
> boxplot(weight ~ group)
> lm.D <- lm(weight ~ group)
> summary(lm.D)
Residuals:
Min 1Q Median 3Q Max
-1.0710 -0.4938 0.0685 0.2462 1.3690
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 4.8465 0.1557 31.124 <2e-16 ***
group1 -0.1855 0.1557 -1.191 0.249
Residual standard error: 0.6964 on 18 degrees of freedom
Multiple R-Squared: 0.07308, Adjusted R-squared: 0.02158
F-statistic: 1.419 on 1 and 18 DF, p-value: 0.249
> anova(lm.D)
Analysis of Variance Table
Response: weight
Df Sum Sq Mean Sq F value Pr(>F)
group 1 0.6882 0.6882 1.4191 0.249
Residuals 18 8.7293 0.4850
summary(), anova() : F- 1.419 1 18 , H0 , group weight, (p -value) 0.249, , 24.9% . , 5% .
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