Pruebas de hipótesis

##Problema 1 Se desea comparar dos genótipos 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 y la cosecha se presentan en los siguientes vectores:

criolla = rnorm(n= 180, mean = 0.8, sd = 0.2)
pastusa= rnorm (n=200, mean = 3.0, sd = 2.1)
criolla 
##   [1] 0.7007838 0.8824019 0.9355406 0.8637726 0.7961465 1.1503280 1.0333997
##   [8] 0.7191956 0.8854574 0.5811249 0.8221910 0.7948834 0.7079526 0.7947740
##  [15] 0.9365268 0.6715135 0.7394762 0.9209445 1.0816148 0.7355044 0.8031073
##  [22] 0.8743033 0.9027362 0.4402821 0.8944469 0.5918888 0.8446542 1.1945071
##  [29] 0.8819105 0.9372101 0.8994391 0.7158668 0.7566257 1.1332736 0.7085340
##  [36] 1.2795150 0.5541388 0.6706614 1.0422720 0.9390568 0.2021195 0.8388170
##  [43] 0.9015339 1.0008830 0.7192430 0.8558335 1.0562105 0.6549985 0.4102765
##  [50] 0.7730799 0.5996700 0.3156598 0.7633223 0.6357910 0.5611582 0.7347494
##  [57] 0.9586377 0.8308963 1.2142866 1.0005627 0.6021166 0.6319059 0.7599975
##  [64] 0.4684947 0.8585848 0.5730846 0.4918876 0.7762116 0.6480764 0.8998347
##  [71] 0.8497462 0.7533498 0.8035981 0.8266881 0.9046438 0.7186082 1.0279067
##  [78] 1.1051246 0.7820734 0.5790025 0.6777413 1.0691775 0.8743455 0.8403761
##  [85] 1.0258833 0.4920227 0.5324092 0.7626553 1.2094652 0.8894684 0.6202474
##  [92] 0.7302784 0.5640782 0.5457513 0.3038469 0.7990793 0.7200389 0.9153692
##  [99] 0.8078853 0.8379623 0.6792853 0.4871195 0.6412298 0.6192070 0.8073603
## [106] 0.6150069 0.9787273 0.9056045 1.0971722 1.0711851 0.8538801 0.8364484
## [113] 1.0814288 0.5835257 0.6373133 0.8177192 0.9982199 1.0467269 0.7733983
## [120] 1.0096412 0.7071603 0.8936884 0.6505909 0.7900569 0.3607458 0.5728694
## [127] 0.8662210 0.2364193 0.8331212 0.7666200 1.0314767 0.7581734 1.3423125
## [134] 0.7796674 0.7252453 0.5973699 0.5876947 0.7920655 0.4730024 0.8404395
## [141] 0.8137929 0.3433865 1.0316581 1.0678504 0.6801868 0.7692909 0.7496359
## [148] 0.7623261 0.5841518 0.9022513 0.5936145 0.6723637 1.0412644 0.5320577
## [155] 0.6125958 0.9746167 0.9935632 0.5774735 0.7656493 0.9600277 1.1845003
## [162] 0.6759032 0.7631754 0.7696420 0.6744518 0.9517780 1.0604376 0.6171986
## [169] 1.0812501 1.0898270 0.2248980 0.5138352 0.6352574 0.8404416 0.5516559
## [176] 0.6287134 0.6257261 0.6881653 0.7809765 1.0055818
pastusa
##   [1]  0.4370967630  1.0465577956 -0.5676085266  0.0009881845  4.0472585730
##   [6]  3.1151579890  2.2679167228  4.1349846479 -0.5152438344 -0.7385874507
##  [11]  2.0209734411  0.9261051531  0.6311021175  2.2684987477  4.8163672707
##  [16]  1.9855995380 -3.9924211553  5.1638139195  4.7022500836  2.8009749959
##  [21]  7.0466311184 -0.1601524737  6.9873064502  2.9828692191  2.7642779891
##  [26]  6.3262429270  3.5098841454  0.3020331640  3.7656289891  4.8936347721
##  [31]  7.0418952649  3.5822158038  1.5614286325  4.2239377714  6.8085562734
##  [36]  3.0214505851  1.9600876574  4.2063604967  4.7406541956  1.2601380545
##  [41]  5.7293057369  0.6647628508  2.1926951791  3.5155889731  6.1766353267
##  [46]  3.4451234008  1.8303240545  3.8887445178  1.7821689214  4.0147682128
##  [51]  1.6097355285  3.8326076000  4.8742952205  1.8111573716  2.1746635294
##  [56]  2.6014766375  5.5081822421  0.1160333726  3.6344719747  1.2847601082
##  [61]  2.8325261916 -2.0428499303 -0.2212728408  5.2799306615  3.9299843466
##  [66]  2.1929160465  1.5524680664  2.9510624608  5.1293177616  3.8193793669
##  [71]  5.5257180654  1.5844139568  5.0833246989  5.8624923130 -0.4174615118
##  [76]  1.4757979689  1.3399022991  5.0608235615  6.6362378140  0.4525368970
##  [81]  4.7259314274  3.4241635398  5.8738023728  2.0738518449  2.9454107908
##  [86]  3.4484405817 -0.2887881913  7.4202511294  2.1636300899  2.2770889627
##  [91]  5.6993128674  3.9244562624  2.2458863905  1.8315363612  0.8052238319
##  [96]  4.3121211919  0.3031502839  4.9657766406  7.3481417302  3.9563406209
## [101]  3.2932466353  3.3846836146  5.6941333154  5.1509467530  3.2327503587
## [106]  2.2705987197  4.3303420516  5.0439712020 -2.0009058714 -0.1382802471
## [111]  1.2602029873  3.5616058638  2.4283489870  5.8717948792  2.4327675550
## [116]  2.8308693548 -0.6691763668  2.2887962185  5.3423276279  2.3833506632
## [121]  5.5734656070  4.5419997599  3.5739545557  1.1490998064  1.6530468020
## [126]  1.5724358137  4.0055637422  5.0583582400  6.8062396637  2.9943237617
## [131]  1.6619516957  4.3311375019  4.4872416165  2.6934518246  2.9499109461
## [136]  5.0008182303  2.1590718146  6.3174435997  5.8391936217  5.2496382921
## [141]  2.0733704379  1.7911562531  3.5986200539  5.1377249453  4.7055816097
## [146] -0.8197031186  0.3655074981  5.2981296454  1.8425351921  2.1354637934
## [151]  4.7218346810  1.5226465204  7.1987578494  4.3059237226  0.4149906716
## [156]  1.5173786699  3.4628351035  6.5339105194  2.4337733928  2.6694039633
## [161]  2.9221166820  2.2882637185  2.2043880608  3.3590139814  5.6068999095
## [166]  3.2447367258  1.1508657980  4.5768213448  0.4650370338  7.4886299901
## [171]  2.2591180913  4.1931541167  0.9614860670  1.2008072996  5.3485805971
## [176]  1.7469357968  5.7344699141  1.1556550028  3.1880579200  3.8329172594
## [181] -1.3924428473  1.9948613802  4.6919784803  4.2122472138  5.7322928783
## [186]  4.0610622049  4.7818212537  2.2803369475  3.5240054427  3.2184093006
## [191]  4.2342896741  3.5970445294  1.8239753931  3.7125387707  2.4735168090
## [196]  5.2257144279  3.5328651519  3.1183923992  3.8096204590  0.3694094146
par(mfrow=c(1,2))
hist(criolla, col="darkblue")
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/plata)")
boxplot(pastusa, main="Pastusa", ylab="Rto (kg/plata)")

summary(criolla)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##  0.2021  0.6369  0.7803  0.7837  0.9049  1.3423
summary(pastusa)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##  -3.992   1.789   3.203   3.120   4.710   7.489
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 0.78 0.21   0.78    0.79 0.2 0.2 1.34  1.14 -0.12     0.12 0.02
psych::describe(pastusa)
##    vars   n mean   sd median trimmed  mad   min  max range  skew kurtosis   se
## X1    1 200 3.12 2.08    3.2    3.16 2.21 -3.99 7.49 11.48 -0.23    -0.08 0.15

###Disgresion

medA= 3.5; sdA =0.35
medB= 3.2; sdB=0.20
# ¿Cual seleccionar?
# Coeficiente de variación cv= 100* sd/mean
cvA= 100* sdA/medA
cvB=100* sdB/medB

cvA; cvB
## [1] 10
## [1] 6.25
#Ambos coeficientes tienen el cv menor que 20, así que uso el promedio para seleccionar la variedad, se elige la A porque tiene mayor promedio
100* sd(criolla)/mean(criolla)
## [1] 26.58599
100 * sd(pastusa)/mean(pastusa)
## [1] 66.72364

#Conclusion desde el analisis descriptivo * Ambos coeficientes de variación son altos, mayores de 20% *Selecciono la variedad con el menor cv, en este caso la criolla

#Analisis inferencial a traves de pruebas de hipótesis

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

Pruebat-student para comparar dos muestras independientes

Entonces tengo que comparar las varianzas de las dos variedades

Prueba para comparación de dos varianzas

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

var(pastusa)
## [1] 4.333767
var(criolla)
## [1] 0.0434085
vt=var.test(pastusa, criolla)
vt$p.value
## [1] 0
ifelse(vt$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= FALSE) 
ifelse(pt$p.value <0.025, "Rechazo Ho", "No rechazo Ho")
## [1] "Rechazo Ho"

Conclusión final: los datos proporcionan evidencia estadística que permite afirmar que ulas variedades son iguales