Prueba t-Student

par(mfrow=c(1,2))
set.seed(2020)
MO1= round(rnorm(n = 50,1.8,sd = 0.2),2)
MO1
##  [1] 1.88 1.86 1.58 1.57 1.24 1.94 1.99 1.75 2.15 1.82 1.63 1.98 2.04 1.73 1.78
## [16] 2.16 2.14 1.19 1.34 1.81 2.23 2.02 1.86 1.79 1.97 1.84 2.06 1.99 1.77 1.82
## [31] 1.64 1.65 2.02 2.29 1.88 1.86 1.74 1.82 1.69 1.89 1.98 1.70 1.74 1.65 1.56
## [46] 1.85 1.73 1.80 1.93 1.90
x1=runif(50,0,800)
y1=runif(50,0,800)
plot(x1,y1,cex=MO1, pch=20,col="goldenrod3")
MO2= round(rnorm(50,2.5,0.25),2)
MO2
##  [1] 2.07 2.25 2.35 2.60 2.69 2.27 2.42 2.89 2.57 2.57 2.42 2.86 2.75 2.07 2.57
## [16] 2.29 2.20 2.18 2.47 3.04 2.42 2.59 2.82 1.93 2.18 2.55 2.69 2.95 2.88 2.26
## [31] 2.53 2.35 2.48 2.47 2.24 2.48 2.94 2.14 3.17 2.18 2.50 2.49 3.05 2.01 2.62
## [46] 2.43 2.22 2.55 2.52 1.74
x2=runif(50,0,600)
y2=runif(50,0,600)
plot(x2,y2,cex=MO2, pch=20,col="brown")

## Estadísticas Descriptivas

library(psych)
## Warning: package 'psych' was built under R version 4.5.2
psych::describe(MO1)
##    vars  n mean   sd median trimmed mad  min  max range  skew kurtosis   se
## X1    1 50 1.82 0.22   1.83    1.83 0.2 1.19 2.29   1.1 -0.58     0.83 0.03
hist(MO1)

psych::describe(MO2)
##    vars  n mean   sd median trimmed  mad  min  max range skew kurtosis   se
## X1    1 50 2.48 0.31   2.48    2.47 0.31 1.74 3.17  1.43 0.11    -0.33 0.04

FORMATO ANCHO

length(MO1);length(MO2)
## [1] 50
## [1] 50
MOC=cbind(MO1,MO2)
MOC
##        MO1  MO2
##  [1,] 1.88 2.07
##  [2,] 1.86 2.25
##  [3,] 1.58 2.35
##  [4,] 1.57 2.60
##  [5,] 1.24 2.69
##  [6,] 1.94 2.27
##  [7,] 1.99 2.42
##  [8,] 1.75 2.89
##  [9,] 2.15 2.57
## [10,] 1.82 2.57
## [11,] 1.63 2.42
## [12,] 1.98 2.86
## [13,] 2.04 2.75
## [14,] 1.73 2.07
## [15,] 1.78 2.57
## [16,] 2.16 2.29
## [17,] 2.14 2.20
## [18,] 1.19 2.18
## [19,] 1.34 2.47
## [20,] 1.81 3.04
## [21,] 2.23 2.42
## [22,] 2.02 2.59
## [23,] 1.86 2.82
## [24,] 1.79 1.93
## [25,] 1.97 2.18
## [26,] 1.84 2.55
## [27,] 2.06 2.69
## [28,] 1.99 2.95
## [29,] 1.77 2.88
## [30,] 1.82 2.26
## [31,] 1.64 2.53
## [32,] 1.65 2.35
## [33,] 2.02 2.48
## [34,] 2.29 2.47
## [35,] 1.88 2.24
## [36,] 1.86 2.48
## [37,] 1.74 2.94
## [38,] 1.82 2.14
## [39,] 1.69 3.17
## [40,] 1.89 2.18
## [41,] 1.98 2.50
## [42,] 1.70 2.49
## [43,] 1.74 3.05
## [44,] 1.65 2.01
## [45,] 1.56 2.62
## [46,] 1.85 2.43
## [47,] 1.73 2.22
## [48,] 1.80 2.55
## [49,] 1.93 2.52
## [50,] 1.90 1.74
class(MOC)
## [1] "matrix" "array"
dim(MOC)
## [1] 50  2
MOF=rbind(MO1,MO2)
MOF
##     [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]
## MO1 1.88 1.86 1.58 1.57 1.24 1.94 1.99 1.75 2.15  1.82  1.63  1.98  2.04  1.73
## MO2 2.07 2.25 2.35 2.60 2.69 2.27 2.42 2.89 2.57  2.57  2.42  2.86  2.75  2.07
##     [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25] [,26]
## MO1  1.78  2.16  2.14  1.19  1.34  1.81  2.23  2.02  1.86  1.79  1.97  1.84
## MO2  2.57  2.29  2.20  2.18  2.47  3.04  2.42  2.59  2.82  1.93  2.18  2.55
##     [,27] [,28] [,29] [,30] [,31] [,32] [,33] [,34] [,35] [,36] [,37] [,38]
## MO1  2.06  1.99  1.77  1.82  1.64  1.65  2.02  2.29  1.88  1.86  1.74  1.82
## MO2  2.69  2.95  2.88  2.26  2.53  2.35  2.48  2.47  2.24  2.48  2.94  2.14
##     [,39] [,40] [,41] [,42] [,43] [,44] [,45] [,46] [,47] [,48] [,49] [,50]
## MO1  1.69  1.89  1.98  1.70  1.74  1.65  1.56  1.85  1.73  1.80  1.93  1.90
## MO2  3.17  2.18  2.50  2.49  3.05  2.01  2.62  2.43  2.22  2.55  2.52  1.74
class(MOF)
## [1] "matrix" "array"
dim(MOF)
## [1]  2 50
MOV=c(MO1,MO2)
MOV
##   [1] 1.88 1.86 1.58 1.57 1.24 1.94 1.99 1.75 2.15 1.82 1.63 1.98 2.04 1.73 1.78
##  [16] 2.16 2.14 1.19 1.34 1.81 2.23 2.02 1.86 1.79 1.97 1.84 2.06 1.99 1.77 1.82
##  [31] 1.64 1.65 2.02 2.29 1.88 1.86 1.74 1.82 1.69 1.89 1.98 1.70 1.74 1.65 1.56
##  [46] 1.85 1.73 1.80 1.93 1.90 2.07 2.25 2.35 2.60 2.69 2.27 2.42 2.89 2.57 2.57
##  [61] 2.42 2.86 2.75 2.07 2.57 2.29 2.20 2.18 2.47 3.04 2.42 2.59 2.82 1.93 2.18
##  [76] 2.55 2.69 2.95 2.88 2.26 2.53 2.35 2.48 2.47 2.24 2.48 2.94 2.14 3.17 2.18
##  [91] 2.50 2.49 3.05 2.01 2.62 2.43 2.22 2.55 2.52 1.74
class(MOV)
## [1] "numeric"
dim(MOV)
## NULL
length(MOV)
## [1] 100

CREAR FACTORES

LOTE=gl(2,50,100, labels = c("LOTE1","LOTE2"))
LOTE
##   [1] LOTE1 LOTE1 LOTE1 LOTE1 LOTE1 LOTE1 LOTE1 LOTE1 LOTE1 LOTE1 LOTE1 LOTE1
##  [13] LOTE1 LOTE1 LOTE1 LOTE1 LOTE1 LOTE1 LOTE1 LOTE1 LOTE1 LOTE1 LOTE1 LOTE1
##  [25] LOTE1 LOTE1 LOTE1 LOTE1 LOTE1 LOTE1 LOTE1 LOTE1 LOTE1 LOTE1 LOTE1 LOTE1
##  [37] LOTE1 LOTE1 LOTE1 LOTE1 LOTE1 LOTE1 LOTE1 LOTE1 LOTE1 LOTE1 LOTE1 LOTE1
##  [49] LOTE1 LOTE1 LOTE2 LOTE2 LOTE2 LOTE2 LOTE2 LOTE2 LOTE2 LOTE2 LOTE2 LOTE2
##  [61] LOTE2 LOTE2 LOTE2 LOTE2 LOTE2 LOTE2 LOTE2 LOTE2 LOTE2 LOTE2 LOTE2 LOTE2
##  [73] LOTE2 LOTE2 LOTE2 LOTE2 LOTE2 LOTE2 LOTE2 LOTE2 LOTE2 LOTE2 LOTE2 LOTE2
##  [85] LOTE2 LOTE2 LOTE2 LOTE2 LOTE2 LOTE2 LOTE2 LOTE2 LOTE2 LOTE2 LOTE2 LOTE2
##  [97] LOTE2 LOTE2 LOTE2 LOTE2
## Levels: LOTE1 LOTE2

formato largo

TABLA=data.frame(MOV,LOTE)
View(TABLA)
psych::describe.by(x = MOV,group = LOTE)
## Warning in psych::describe.by(x = MOV, group = LOTE): describe.by is
## deprecated.  Please use the describeBy function
## 
##  Descriptive statistics by group 
## group: LOTE1
##    vars  n mean   sd median trimmed mad  min  max range  skew kurtosis   se
## X1    1 50 1.82 0.22   1.83    1.83 0.2 1.19 2.29   1.1 -0.58     0.83 0.03
## ------------------------------------------------------------ 
## group: LOTE2
##    vars  n mean   sd median trimmed  mad  min  max range skew kurtosis   se
## X1    1 50 2.48 0.31   2.48    2.47 0.31 1.74 3.17  1.43 0.11    -0.33 0.04
psych::describeBy(x = MOV,group = LOTE,data =TABLA )
## 
##  Descriptive statistics by group 
## group: LOTE1
##    vars  n mean   sd median trimmed mad  min  max range  skew kurtosis   se
## X1    1 50 1.82 0.22   1.83    1.83 0.2 1.19 2.29   1.1 -0.58     0.83 0.03
## ------------------------------------------------------------ 
## group: LOTE2
##    vars  n mean   sd median trimmed  mad  min  max range skew kurtosis   se
## X1    1 50 2.48 0.31   2.48    2.47 0.31 1.74 3.17  1.43 0.11    -0.33 0.04

GRÁFICOS

library(lattice)
bwplot(MOV~LOTE)

lattice::dotplot(MOV~LOTE,data=TABLA)

iNFERENCIAL

\[HO: \mu_{L1}=\mu_{L2} \] \[HA: \mu_{L1}\neq\mu_{L2} \]

# prueba de dos colas (t-two-sides)
pruebat=t.test(x = MO1,y = MO2,alternative ="t",mu =0,paired = F,var.equal = F,conf.level = 0.95  )
pruebat
## 
##  Welch Two Sample t-test
## 
## data:  MO1 and MO2
## t = -12.187, df = 89.46, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -0.7596872 -0.5467128
## sample estimates:
## mean of x mean of y 
##    1.8250    2.4782
ifelse(pruebat$p.value<0.05,"rechazo HO","No rechazo Ho")
## [1] "rechazo HO"

verificar varianzas

varianzas=tapply(MOV, LOTE,var)
varianzas
##      LOTE1      LOTE2 
## 0.04962551 0.09400282

prueba de varianzas

\[HO: \sigma^2_{LOTE1}=\sigma^2_{LOTE2}\]

PRUEBA_VAR=var.test(x=MO1,y = MO2,ratio = 1)
ifelse(PRUEBA_VAR$p.value<0.05,"Rechazo Ho", "NO Rechazo Ho")
## [1] "Rechazo Ho"