#Pruebas de hipotesis

#Se desea comparar dos genotipos de papa con base al rendimiento (biomasa de tuberculos). Un ensayo utilizo dos variedades (criolla y pastusa) involucrando 180 plantas de la primera variedad y 200 de la segunda. Los datos de rendimiento de la cossecha se presentan en los siguientes vectores ## R Markdown

criolla= rnorm(n=180,mean=2.8,sd=0.2)
pastusa=rnorm(n=200,mean=3.0,sd=0.21)
criolla
##   [1] 2.913375 2.870653 3.129747 2.785648 2.605708 2.574237 2.732254 2.694811
##   [9] 2.851892 3.132060 2.628765 2.641549 2.821793 2.636654 2.460836 3.102740
##  [17] 2.811541 2.441499 2.570668 2.999222 2.768523 2.985014 3.174712 2.826811
##  [25] 2.518558 2.927474 3.020696 2.573668 2.718388 3.038240 3.099765 2.742730
##  [33] 2.560721 2.998931 2.637802 2.883797 2.369664 2.457596 2.962178 2.898251
##  [41] 3.120034 2.736642 3.024649 2.881339 2.756725 2.624644 2.954305 2.643156
##  [49] 2.699347 2.943338 2.818802 3.221836 2.926373 2.809021 2.825419 2.458253
##  [57] 2.865577 2.750463 3.001125 2.855323 2.850020 3.061303 3.091564 2.733579
##  [65] 2.721115 2.661453 2.636740 2.392114 2.843878 2.911659 2.818455 3.019363
##  [73] 2.411973 2.697118 3.033580 2.436672 2.819290 2.856805 2.953189 2.821354
##  [81] 2.773676 2.828946 2.649766 2.744977 2.584772 2.844097 2.799046 2.525947
##  [89] 2.884797 2.968670 2.413898 2.795540 2.538542 2.595030 2.773497 2.925452
##  [97] 2.545522 3.110959 2.779372 2.840243 2.627704 2.908555 2.781751 2.509834
## [105] 2.738182 2.858015 2.741164 2.721824 2.815049 2.794034 2.758219 2.831968
## [113] 2.779602 2.714433 3.043275 3.002818 2.839337 2.644488 2.584664 2.723437
## [121] 2.955760 2.766764 2.636011 3.222564 2.917862 2.734279 2.699302 2.783899
## [129] 3.103359 2.950874 2.698914 2.859334 2.782696 2.926319 2.741472 3.286880
## [137] 2.629870 3.169406 2.489645 3.195368 3.078139 2.679637 2.892226 2.939556
## [145] 2.730805 3.059433 2.971480 3.033752 2.783386 3.125315 2.820100 3.040320
## [153] 2.917025 3.067235 2.841558 3.167727 2.274510 2.743643 2.572219 3.140877
## [161] 3.078751 2.946427 2.650649 2.537294 2.732037 2.643600 3.378328 2.714872
## [169] 2.574920 2.550563 2.809432 2.760536 2.637704 2.793016 2.747728 2.727343
## [177] 2.477854 2.852973 3.079317 3.052615
pastusa
##   [1] 2.996133 3.024854 3.196638 2.861123 3.115313 3.327136 2.939730 3.131404
##   [9] 2.969798 2.804499 3.015110 3.260922 3.133428 3.391382 3.010960 2.701335
##  [17] 3.351083 2.921275 2.884771 3.132406 2.962842 2.662637 3.004630 3.438440
##  [25] 2.656704 2.926515 2.770183 3.104355 2.910357 2.873635 3.199675 2.896145
##  [33] 2.386417 3.132273 2.834751 3.249978 3.462598 2.454617 3.251668 3.178259
##  [41] 3.387485 2.836965 3.425549 3.009417 3.098059 2.848833 2.864755 3.159708
##  [49] 3.185542 2.774474 3.153046 2.508701 3.003893 2.809852 2.792942 3.135484
##  [57] 2.678393 3.105422 2.942761 2.982307 3.022863 2.836312 3.136359 2.617198
##  [65] 3.430691 3.174482 3.217796 3.116574 3.120396 3.193341 2.975604 2.779223
##  [73] 3.196604 3.086271 2.852736 2.754791 2.877561 3.266598 3.059105 2.943760
##  [81] 2.772552 3.261332 2.993065 3.114377 3.019907 3.137346 3.246730 2.905802
##  [89] 3.162076 2.808427 3.095334 2.962097 3.027287 3.110027 3.153005 3.316836
##  [97] 2.794145 3.060337 3.135547 2.714479 3.028870 2.831808 3.182094 3.442683
## [105] 3.345997 3.369711 2.872410 3.270287 3.306781 3.197472 3.099119 2.981473
## [113] 2.808858 3.276113 3.026459 3.055565 2.741134 2.971619 3.292747 3.088469
## [121] 2.994810 2.928288 3.051035 3.363075 3.225601 3.080064 3.014368 3.101406
## [129] 3.009444 2.675222 3.258621 2.694418 3.350893 3.116437 2.978233 3.017389
## [137] 3.031954 3.106258 2.903162 2.911417 2.923744 3.105026 2.441843 2.774494
## [145] 2.905001 2.927222 2.899925 2.996613 3.067079 3.148883 2.774725 3.600444
## [153] 2.614718 2.925360 3.155062 2.551490 2.893688 3.048881 3.055083 3.133399
## [161] 2.678039 2.869497 2.885989 2.719626 2.771375 3.088198 3.109227 3.385922
## [169] 3.028187 3.107549 2.768839 3.117792 2.655185 2.973533 3.182866 2.826134
## [177] 3.071554 3.153964 3.348548 2.926295 2.780808 2.907716 2.621231 2.949584
## [185] 2.901547 3.144602 2.964058 3.064882 2.713347 2.759660 3.267688 2.987116
## [193] 3.008530 2.937258 3.189573 2.854452 2.688667 2.949973 2.750503 3.042664
criolla=round(criolla,2)
pastusa=round(pastusa,2)

par(mfrow=c(1,2))

hist(criolla)
abline(v=mean(criolla),col="red", lwd=3)

hist(pastusa)
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. 
##   2.270   2.675   2.805   2.810   2.950   3.380
summary(pastusa)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   2.390   2.870   3.015   3.009   3.140   3.600
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 2.81 0.2    2.8    2.81 0.21 2.27 3.38  1.11 0.06    -0.27 0.02
psych::describe(pastusa)
##    vars   n mean   sd median trimmed mad  min max range  skew kurtosis   se
## X1    1 200 3.01 0.22   3.01    3.01 0.2 2.39 3.6  1.21 -0.14    -0.04 0.02

#coeficiente de variacion cv=100*sd/mean

cvcriolla=100*sd(criolla)/mean(criolla)
cvpastusa=100*sd(pastusa)/mean(pastusa)
cvcriolla
## [1] 7.229342
cvpastusa
## [1] 7.157963

####conclusion desde el analisis descriptivo ambos coeficiente de variacion bajos se puede omitir el problema de diferente variabilidad *selecciono la variedad de mayor rendimiento promedio

analisis inferencia a traves de pruebas de hipotesis

\[H_0:\mu_{pastusa}=\mu_{criolla}\\ H_a:\mu_{pastusa}\neq\mu_{criolla}\]

Prueba t-student para comparar dos muestras independientes Modalidad 1: Varianzas iguales Modalidad 2: Varianzas desiguales

Prueba para la comparacion de dos varianzas

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

var(criolla)
## [1] 0.04125627
var(pastusa)
## [1] 0.04638834
vt=var.test(pastusa,criolla)
vt$p.value
## [1] 0.4236514
ifelse(vt$p.value<0.025,"Rechazo Ho","No rechazo Ho")
## [1] "No rechazo Ho"

prueba t-student para comparar las dos medias con varianzas iguales

pt = t.test(pastusa, criolla,alternative ="t",var.equal=TRUE)

Conclusion final: los datos proporcionan evidencia a favor de la hipotesis nula, es decir que estadisticamente se consideran ambas variedades de igual rendimiento Cualquiera de las variedades es igual de buena.