criolla = rnorm(n = 180, mean = 2.8, sd = 0.2)
pastusa = rnorm(n = 200, mean = 3.0, sd = 0.21)
criolla
##   [1] 2.724950 2.573584 3.075612 2.747270 2.856830 2.717645 2.615700 2.815126
##   [9] 2.452048 2.394581 2.989804 2.660857 2.931842 2.781141 2.470604 2.584716
##  [17] 3.105530 2.853504 2.899372 2.869759 2.909966 2.884403 2.566691 2.752378
##  [25] 2.926657 2.974275 2.598321 2.914728 2.820083 2.821035 2.826352 2.782637
##  [33] 2.925307 2.855061 2.851667 2.907681 2.754391 2.576814 2.352024 2.665210
##  [41] 2.960041 2.932055 3.144620 2.674022 2.827842 2.696974 2.819886 3.078669
##  [49] 2.952031 2.423440 2.681621 2.784913 2.997341 2.908242 2.452285 2.992675
##  [57] 2.642412 2.640403 2.864182 2.823769 2.796922 2.511943 2.638974 2.880353
##  [65] 2.785218 2.839074 2.776576 3.006160 3.171759 2.709905 2.860986 2.605290
##  [73] 2.607612 2.901960 2.989382 2.702520 2.744208 2.917161 2.684907 2.851447
##  [81] 2.780515 3.012128 2.806680 2.693794 2.988819 2.806176 3.038758 2.882350
##  [89] 2.732737 2.841041 2.726706 2.527750 2.984335 2.594816 2.811915 2.771014
##  [97] 2.967545 2.964874 2.834649 2.540232 3.101104 2.939251 2.678626 2.616381
## [105] 2.906330 2.713503 2.990670 2.609170 2.801851 2.712964 2.575624 2.547424
## [113] 2.842200 2.629230 3.036389 2.693613 3.004864 2.429253 2.565981 3.121703
## [121] 2.857145 2.565847 2.689153 2.369629 3.134987 2.701322 2.676243 2.862805
## [129] 2.850434 2.708406 3.245748 3.015932 2.921517 2.886813 2.735964 3.130192
## [137] 2.731206 2.675769 2.674361 2.863281 2.886214 2.734143 2.776381 3.046883
## [145] 2.857812 2.780190 2.574268 2.790956 2.643647 2.638428 2.781098 2.554302
## [153] 2.717056 2.678774 3.013837 2.970285 2.797838 2.789177 2.844484 2.299218
## [161] 2.767291 2.912863 2.694693 2.790662 2.802359 2.722897 3.319915 2.713047
## [169] 2.731112 3.013226 2.790190 2.750277 2.686877 2.829606 2.798225 2.666676
## [177] 2.937322 2.667928 2.622975 2.648598
pastusa
##   [1] 2.866055 3.022910 2.702665 2.861751 2.739016 3.084168 2.729257 3.089304
##   [9] 3.433951 3.173040 3.318877 3.482628 2.995612 3.181178 2.755614 2.914963
##  [17] 3.031949 3.549931 2.461444 2.669696 2.826140 3.446262 2.829084 3.024254
##  [25] 3.238594 3.018165 2.858926 3.105381 3.274514 3.293180 2.882514 3.397638
##  [33] 3.079094 2.899366 3.303744 3.285201 2.895590 3.164784 2.895547 3.261326
##  [41] 2.951820 3.244750 2.821739 3.252633 2.843295 2.992302 2.814213 2.568701
##  [49] 3.206377 3.242570 3.208440 2.922251 2.991174 2.835888 2.958578 3.178927
##  [57] 3.210703 3.127911 3.244978 3.171005 3.042719 2.724126 3.181167 2.930698
##  [65] 3.162255 3.177334 2.907654 2.931986 2.967734 3.164580 2.990597 2.811453
##  [73] 2.893929 3.120140 2.899353 3.336371 2.569233 2.740898 3.175986 3.186579
##  [81] 3.296028 3.210203 3.048602 3.102708 3.008153 3.150027 3.511439 2.641305
##  [89] 2.867217 3.045771 3.423707 3.196090 3.082538 2.917443 3.073769 3.208869
##  [97] 3.066499 3.069477 3.184726 3.062016 2.951745 3.148943 2.666664 3.314750
## [105] 3.303070 2.631016 2.979631 2.774279 3.083697 2.978059 2.936817 3.099207
## [113] 2.639585 3.152711 2.846890 2.756145 2.907317 2.719262 2.748396 3.514788
## [121] 3.124454 3.477122 3.061563 3.477780 2.992476 2.975362 3.023924 3.047634
## [129] 3.174912 3.204104 3.089249 2.856573 2.987900 2.794150 3.091172 2.957653
## [137] 3.096327 3.039165 3.122070 2.827332 2.995516 2.940319 3.029881 3.148379
## [145] 2.913339 2.693601 3.044590 2.882406 2.834900 3.235857 2.663017 2.637169
## [153] 2.743991 2.724440 2.760930 3.084617 2.657930 2.745232 2.690368 3.439809
## [161] 2.784291 3.234061 3.237913 2.777576 2.779665 3.136258 2.899312 3.286570
## [169] 2.738642 3.261198 2.648566 3.038427 2.945621 2.644088 2.949306 2.983735
## [177] 3.199479 3.043858 2.958728 2.868361 2.951924 2.610033 3.023757 3.306288
## [185] 2.787088 3.158631 3.359719 2.763434 3.091458 2.805712 3.009583 2.650910
## [193] 2.734540 3.120715 2.629787 3.231439 3.241266 3.235618 3.344909 3.120058
par(mfrow=c(1,2))
hist(criolla, col='darkblue')
abline(v=mean(criolla,col='red' , lwd=3))
hist(pastusa, col = 'darkgreen')
abline(v=mean(pastusa,col='red' , lwd=3))

par(mfrow=c(1,2))

boxplot(criolla, main='criolla' , ylab='Rto (kg/planta)')
boxplot(pastusa, main='pastusa' , ylab='Rto (kg/planta)')




summary(criolla)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   2.299   2.678   2.790   2.790   2.908   3.320
summary(pastusa)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   2.461   2.846   3.024   3.015   3.178   3.550
library(psych)
## Warning: package 'psych' was built under R version 4.2.2

psych :: describe(criolla)
##    vars   n mean   sd median trimmed  mad min  max range skew kurtosis   se
## X1    1 180 2.79 0.18   2.79    2.79 0.17 2.3 3.32  1.02    0     0.16 0.01
psych :: describe(criolla)
##    vars   n mean   sd median trimmed  mad min  max range skew kurtosis   se
## X1    1 180 2.79 0.18   2.79    2.79 0.17 2.3 3.32  1.02    0     0.16 0.01
### Digresion

medA = 3.5; sdA = 0.35
medB = 3.2; sdB = 0.20
# ¡cual seleccionar? 
#coeficiente de variacion cv = 100 * ad/mean 
cvA = 100 * sdA/medA
cvB = 100 * sdB/medB

cvA; cvB
## [1] 10
## [1] 6.25

conclusion desde el analisis descrptivo

##analisis inferencial a traves de pruebas de hiptesis \[H_0: \mu_{pastusa} = \mu_{criolla} \\ H_a: \mu_{past usa} = \mu_{criolla}\]

Prueba t-Student para comparar dos muestras indepemdientes

Prueba para comparacion de dos varianzas

\[H_0: \sigma^2_{pastuda} = \sigma^2_{criolla} \\ H_a: \sigma^2__{pastuda} \neq \sigma^2_{criolla} \]

var(pastusa)
## [1] 0.05030329
var(criolla)
## [1] 0.03130239
vt = var.test(pastusa, criolla)
vt$p.value
## [1] 0.001277224
ifelse(vt$p.value<0.025 , 'Rechazo Ho' , "No Rechazo Ho")
## [1] "Rechazo Ho"

Prueba t-Student para comparar las dos medias con varianzas iguales

pt = t.test(pastusa, criolla, alternative = 't' , var.equal = TRUE)
            ifelse(pt$p.value < 0.025, 'Rechazo Ho' , 'No Rechazo Ho')
## [1] "Rechazo Ho"

Coclusion final: los datos proporcionan evidencia estadistica en contra de la hipotesis nula, es decir, que estadisticamente se consideran ambas variedades como de diferente rendimiento. Una de las variedades es mejor que la otra.