r - 计算 R 中的方差和置信区间之内和之间

Question

作为开发新的分析化学方法的一部分，我需要根据某些数据计算运行内和运行之间的差异。我还需要使用 R 语言从这些数据中获得置信区间

我想我需要使用 anova 之类的吗？

我的数据就像

> variance
   Run Rep Value
1    1   1  9.85
2    1   2  9.95
3    1   3 10.00
4    2   1  9.90
5    2   2  8.80
6    2   3  9.50
7    3   1 11.20
8    3   2 11.10
9    3   3  9.80
10   4   1  9.70
11   4   2 10.10
12   4   3 10.00

Answer 1

您有四组三个观察值:

> run1 = c(9.85, 9.95, 10.00)
> run2 = c(9.90, 8.80, 9.50)
> run3 = c(11.20, 11.10, 9.80)
> run4 = c(9.70, 10.10, 10.00)
> runs = c(run1, run2, run3, run4)
> runs
 [1]  9.85  9.95 10.00  9.90  8.80  9.50 11.20 11.10  9.80  9.70 10.10 10.00

做一些标签:

> n = rep(3, 4)
> group = rep(1:4, n)
> group
 [1] 1 1 1 2 2 2 3 3 3 4 4 4

计算运行内统计数据:

> withinRunStats = function(x) c(sum = sum(x), mean = mean(x), var = var(x), n = length(x))
> tapply(runs, group, withinRunStats)
$`1`
         sum         mean          var            n 
29.800000000  9.933333333  0.005833333  3.000000000 

$`2`
  sum  mean   var     n 
28.20  9.40  0.31  3.00 

$`3`
  sum  mean   var     n 
32.10 10.70  0.61  3.00 

$`4`
        sum        mean         var           n 
29.80000000  9.93333333  0.04333333  3.00000000 

你可以在这里做一些方差分析:

> data = data.frame(y = runs, group = factor(group))
> data
       y group
1   9.85     1
2   9.95     1
3  10.00     1
4   9.90     2
5   8.80     2
6   9.50     2
7  11.20     3
8  11.10     3
9   9.80     3
10  9.70     4
11 10.10     4
12 10.00     4

> fit = lm(runs ~ group, data)
> fit

Call:
lm(formula = runs ~ group, data = data)

Coefficients:
(Intercept)       group2       group3       group4  
  9.933e+00   -5.333e-01    7.667e-01   -2.448e-15 

> anova(fit)
Analysis of Variance Table

Response: runs
          Df  Sum Sq Mean Sq F value  Pr(>F)  
group      3 2.57583 0.85861  3.5437 0.06769 .
Residuals  8 1.93833 0.24229                  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

> degreesOfFreedom = anova(fit)[, "Df"]
> names(degreesOfFreedom) = c("treatment", "error")
> degreesOfFreedom
treatment     error 
        3         8

误差或组内差异:

> anova(fit)["Residuals", "Mean Sq"]
[1] 0.2422917

处理或组间差异:

> anova(fit)["group", "Mean Sq"]
[1] 0.8586111

这应该给你足够的信心来做置信区间。