prueba de hipotesis

Problema 1

se desea comprarar dos fenotipos de papa con base al rendimiento (biomasa de tuberculos). Un ensayo utiliso dos variedades (criolla y pastusa) involucrando 180 plantas de laprimera variedad y 200 de la segunda. Los datos de rendimiento en la cosecha se presentan en los siguientes vectores

Criolla = rnorm(n =180, mean =2.8, sd = 0.2)
Pastusa = rnorm(n = 200, mean =3.0, sd = 0.21)
Criolla
##   [1] 2.580853 2.617055 2.868020 2.721155 3.163003 2.518537 2.488911 2.914118
##   [9] 2.544754 2.851284 2.742061 2.692922 2.952359 2.418543 3.110916 2.802651
##  [17] 2.841906 2.690819 2.676216 2.835530 3.164813 2.924380 2.827428 2.873274
##  [25] 2.676918 3.034212 2.896820 2.786029 2.870328 2.886561 2.859599 2.704411
##  [33] 2.723119 2.929346 3.020642 2.714066 3.096483 2.846807 3.115732 2.926561
##  [41] 2.602551 2.879200 3.048648 2.530309 3.128333 2.739245 2.775516 2.352449
##  [49] 2.848975 2.154213 2.978254 2.559446 2.568051 2.691678 2.835015 3.066727
##  [57] 2.692535 3.061117 2.830334 2.657091 2.828613 2.848799 2.362681 2.934019
##  [65] 2.709938 3.185928 2.859815 2.618981 2.617533 2.970388 2.482013 2.885790
##  [73] 3.000922 2.771513 2.898116 3.048194 3.004164 2.748090 3.011069 2.983409
##  [81] 2.677585 2.499693 2.517228 2.835684 2.999839 2.913395 2.841168 3.249698
##  [89] 2.918446 2.518350 2.585950 2.753604 2.822820 2.571080 2.673730 3.149950
##  [97] 2.693334 2.641565 2.656489 2.795999 2.607725 3.038026 2.942631 3.128387
## [105] 2.667101 2.867660 2.881099 2.658772 2.787728 2.846411 3.035498 2.883247
## [113] 2.751942 2.855143 2.728436 2.536993 3.054765 3.206124 2.336153 2.756626
## [121] 2.660450 2.562685 2.456675 2.574766 2.811474 2.900023 2.712248 2.999706
## [129] 2.556834 2.807157 3.001612 2.428078 2.735652 2.711488 2.730649 2.376887
## [137] 2.724092 2.760127 2.842686 3.048809 2.708107 2.695106 2.904924 2.605307
## [145] 3.115676 2.954969 2.670032 3.055928 2.765596 3.041627 3.013040 2.741207
## [153] 2.956895 2.953639 3.105928 2.551554 2.585291 2.350025 2.731804 2.534284
## [161] 2.690433 2.740438 2.506932 2.837230 2.559844 2.763180 2.791930 2.312865
## [169] 2.475863 2.437294 3.000645 2.615133 3.096777 2.482223 2.909160 2.918898
## [177] 2.805551 2.401619 2.397147 2.691849
Pastusa
##   [1] 3.144082 2.865954 2.754418 2.990409 2.829446 2.969339 3.302068 3.198719
##   [9] 3.375208 3.081029 3.137933 2.759455 3.339532 2.462324 2.770231 3.064651
##  [17] 2.825422 3.288662 2.981751 2.774304 2.782896 2.909661 3.227739 3.256303
##  [25] 3.376780 2.964282 2.904955 2.853102 2.799148 3.221739 2.771847 2.857207
##  [33] 2.977258 3.227022 3.133033 2.970350 2.914518 3.256445 2.834586 2.877729
##  [41] 3.224354 3.193454 2.908061 2.760157 3.194036 3.002889 3.136823 2.931449
##  [49] 3.331643 3.082944 3.200788 3.193495 3.127207 3.075424 2.979906 2.675898
##  [57] 3.089880 3.003012 3.598729 2.957520 3.254360 3.015205 2.826774 2.975665
##  [65] 2.750517 3.009984 3.165836 3.118003 3.089968 3.329980 3.125885 2.949230
##  [73] 3.235670 2.802016 2.712467 3.212087 3.470483 2.833591 3.133903 2.737717
##  [81] 2.624119 2.654648 2.877607 2.872931 2.993505 2.992824 3.297749 2.814155
##  [89] 3.464836 2.939771 3.138021 3.280457 2.898992 3.172626 2.898790 2.581460
##  [97] 2.973802 3.100835 2.841957 3.075678 2.837042 3.310467 3.113864 2.829711
## [105] 3.079259 3.008630 3.052463 2.512341 3.331854 2.692880 3.328502 2.962977
## [113] 2.633532 2.861215 3.276557 2.879773 2.918214 3.110217 3.069546 3.181582
## [121] 2.568324 3.039161 3.083176 2.902680 2.975613 2.579443 3.198188 3.450801
## [129] 2.949881 3.114571 2.790696 2.841845 3.085477 3.247718 3.118048 2.940587
## [137] 2.887134 3.061014 3.077938 2.832923 3.142695 3.183183 2.525525 3.169684
## [145] 3.195613 3.412921 2.981996 2.925462 3.349682 3.128798 3.054767 3.120130
## [153] 2.864745 2.678540 2.968553 2.823602 3.298410 3.109846 2.847089 3.067076
## [161] 3.124509 3.078825 2.794728 3.103448 2.965590 3.081926 3.178664 2.917853
## [169] 2.843031 2.718353 3.064904 3.246989 2.852433 2.979738 2.864263 3.260009
## [177] 3.106536 3.025971 3.528297 2.886997 3.331752 3.001722 3.238092 2.900392
## [185] 2.738902 3.434287 2.980845 3.158044 3.305557 3.275479 2.807526 3.342306
## [193] 3.151478 2.959253 2.899040 2.899314 2.678963 2.968915 2.941551 3.067978
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. 
##   2.154   2.653   2.787   2.780   2.925   3.250
summary(Pastusa)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   2.462   2.866   3.006   3.021   3.170   3.599
library(psych)
## Warning: package 'psych' was built under R version 4.2.2
psych::describe(Pastusa)
##    vars   n mean   sd median trimmed  mad  min max range  skew kurtosis   se
## X1    1 200 3.02 0.21   3.01    3.02 0.22 2.46 3.6  1.14 -0.01    -0.27 0.02
psych::describe(Criolla)
##    vars   n mean   sd median trimmed  mad  min  max range  skew kurtosis   se
## X1    1 180 2.78 0.21   2.79    2.78 0.21 2.15 3.25   1.1 -0.19     -0.4 0.02

medA = 3.5;sdA  = 0.35
medB = 3.2;sdB  = 0.20
#¿cual selecccionar?
#coeficiente de variacion cv = 100 * sd/mean
cvA = 100 * sdA/medA
cvB = 100 * sdB/medB


cvA;cvB
## [1] 10
## [1] 6.25
100 * sd(Criolla) / mean(Criolla)
## [1] 7.597707
100 * sd(Pastusa) / mean(Pastusa)
## [1] 7.034546

conclucion desde el analisis descripivo

  • ambos coeficiente de variacion bajos (menotres de 20%)
  • se puede omitir el problema de diferente variabilidad
  • se selecciona la variedad de mayor rendimiento promedio

##Analisis inferencial atravez de pruebas de hipotesis

\[H_0: \mu_{Pastusa} = \mu_{Criolla}\\ H_a: \mu_{Pastusa} \neq \mu_{Criolla}\\\]

  • modalidad 1: varianzas iguales
  • modalidad 2: varianzas desiguales

Prueba para comparaciopn de dos varianzas

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

var (Pastusa)
## [1] 0.04516682
var (Criolla)
## [1] 0.04461996
vt = var.test(Pastusa, Criolla)
vt$p.value
## [1] 0.9355013
ifelse(vt$p.value < 0.025, 'rechazo Ho', 'no rechazo Ho')
## [1] "no rechazo Ho"

Prueba t-student para comarar las dos medias con varianzas iguales

prueva=t.test(Pastusa, Criolla, alternative = 't', var.equal = TRUE)

ifelse(prueva$p.value < 0.025, 'rechazo Ho', 'no rechazo Ho')
## [1] "rechazo Ho"

CONCLUSION FINAL: los datos proporcionados evidencian estadistica en contra de la hipotesis nula, es decir que estadisticamente se consideran ambas variedades como de diferente rendimento