Taller 2

1. Revisar los datos

En la tabla de datos disponible aquí se encuentran datos de las estaturas de un grupo anterior de la especialización en estadística aplicada

1 Femenino
0 Másculino

library(readxl)
library(DT)
library(tigerstats)

2. Estimación de parámetros

Estime la media, desviación estándar de cada género y la proporción de hombres y mujeres del curso.

BaseEstaturaGenero <- read_excel("BaseEstaturaGenero.xlsx")
DT::datatable(BaseEstaturaGenero)

Fem<-BaseEstaturaGenero  %>% filter(Genero == "1")
Fem

## # A tibble: 6 × 2
##   Estatura Genero
##      <dbl>  <dbl>
## 1      157      1
## 2      160      1
## 3      166      1
## 4      155      1
## 5      167      1
## 6      165      1

Mas<-BaseEstaturaGenero  %>% filter(Genero == "0")
Mas

## # A tibble: 16 × 2
##    Estatura Genero
##       <dbl>  <dbl>
##  1      180      0
##  2      180      0
##  3      170      0
##  4      177      0
##  5      176      0
##  6      179      0
##  7      168      0
##  8      172      0
##  9      177      0
## 10      176      0
## 11      167      0
## 12      174      0
## 13      165      0
## 14      178      0
## 15      173      0
## 16      172      0

x_barraF=mean(Fem$Estatura)
x_barraF

## [1] 161.6667

Y_barraM=mean(Mas$Estatura)
Y_barraM

## [1] 174

desvx=sd(Fem$Estatura)
desvx

## [1] 5.046451

desvy=sd(Mas$Estatura)
desvy

## [1] 4.690416

Proporcion_M=length(Fem$Estatura)
Proporcion_M

## [1] 6

Proporcion_H=length(Mas$Estatura)
Proporcion_H

## [1] 16

3. Hipótesis

Escriba la hipótesis nula y alternativa de la estatura de cada género con referencia al artículo del Tiempo.

Para hombres:

\[ H_o: \mu=\\ H_a: \]

library(tigerstats)
ttestGC(~Estatura,data = Mas, mu=172,alternative="t",graph = TRUE)

## 
## 
## Inferential Procedures for One Mean mu:
## 
## 
## Descriptive Results:
## 
## variable  mean     sd       n          
## Estatura  174.000  4.690    16         
## 
## 
## Inferential Results:
## 
## Estimate of mu:   174 
## SE(x.bar):    1.173 
## 
## 95% Confidence Interval for mu:
## 
##           lower.bound         upper.bound          
##           171.500654          176.499346           
## 
## Test of Significance:
## 
##  H_0:  mu = 172 
##  H_a:  mu != 172 
## 
##  Test Statistic:     t = 1.706 
##  Degrees of Freedom:   15 
##  P-value:        P = 0.1087

El valor P es \[P(t > 1.706) = 0.1087\]

\[ 0.1087 > 0.05\]

EXPLICACIÓN: No hay evidencia estadistica suficiente para rechazar \(H_0\)

Para mujeres:

\[ H_o:\\ H_a: \]

ttestGC(~Estatura,data = Fem, mu=160,alternative="t",graph = TRUE)

## 
## 
## Inferential Procedures for One Mean mu:
## 
## 
## Descriptive Results:
## 
## variable  mean     sd       n          
## Estatura  161.667  5.046    6          
## 
## 
## Inferential Results:
## 
## Estimate of mu:   161.7 
## SE(x.bar):    2.06 
## 
## 95% Confidence Interval for mu:
## 
##           lower.bound         upper.bound          
##           156.370741          166.962592           
## 
## Test of Significance:
## 
##  H_0:  mu = 160 
##  H_a:  mu != 160 
## 
##  Test Statistic:     t = 0.809 
##  Degrees of Freedom:   5 
##  P-value:        P = 0.4553

El valor P es \[P(t > 0.809) = 0.4553\]

\[ 0.4553 > 0.05\]

EXPLICACIÓN: No hay evidencia estadistica suficiente para rechazar \(H_0\)

Realizar los respectivos contrastes y concluir

4 .Hipótesis diferencia de estatura entre géneros

Ahora ponga a prueba la hipótesis de diferencia de altura de ambos géneros en el curso. para ver si la altura media de las mujeres es igual a la altura media de los hombres.

Hipótesis para contrastar el estudio:

\[ H_o:μ_1 - μ_2= 12\\ H_a:μ_1 - μ_2> 12 \]

Concluya y escriba las consecuencias de la decisión

\[T_Est= \frac{\overline{X}-\overline{Y}-(μ_1-μ_2)}{Sp\sqrt\frac{1}{n1}+\sqrt\frac{1}{n2}} ~ t_(n_1+n_2-2)\]

Sp= ((Proporcion_H-1)*desvy+(Proporcion_M-1)*desvx)/(Proporcion_H+Proporcion_M-2)
Sp

## [1] 4.779425

Test = (Y_barraM-x_barraF-12)/(Sp*sqrt((1/Proporcion_H)+(1/Proporcion_M)))
Test

## [1] 0.1456892

qt(0.05,20,lower.tail = F)

## [1] 1.724718

t.test(Mas$Estatura, Fem$Estatura, mu=12,var.equal =F, alternative="greater", graph = TRUE)

## 
##  Welch Two Sample t-test
## 
## data:  Mas$Estatura and Fem$Estatura
## t = 0.14062, df = 8.468, p-value = 0.4457
## alternative hypothesis: true difference in means is greater than 12
## 95 percent confidence interval:
##  7.956585      Inf
## sample estimates:
## mean of x mean of y 
##  174.0000  161.6667

El valor P es \[P(t > 0.14062) = 0.4457\]

\[ 0.4457 > 0.05\]

EXPLICACIÓN: No hay evidencia estadistica suficiente para rechazar \(H_0\)

5. Cáncer de mama

Considere el conjunto de datos en Kaggle sobre Datos reales sobre el cáncer de mama aquí

library(readr)

BRCA <- read_csv("BRCA.csv")

## Rows: 341 Columns: 16
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr (11): Patient_ID, Gender, Tumour_Stage, Histology, ER status, PR status,...
## dbl  (5): Age, Protein1, Protein2, Protein3, Protein4
## 
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.

DT::datatable(BRCA)

BRCA

## # A tibble: 341 × 16
##    Patient_ID     Age Gender Protein1 Protein2 Protein3 Protein4 Tumour_Stage
##    <chr>        <dbl> <chr>     <dbl>    <dbl>    <dbl>    <dbl> <chr>       
##  1 TCGA-D8-A1XD    36 FEMALE   0.0804    0.426   0.547    0.274  III         
##  2 TCGA-EW-A1OX    43 FEMALE  -0.420     0.578   0.614   -0.0315 II          
##  3 TCGA-A8-A079    69 FEMALE   0.214     1.31   -0.327   -0.234  III         
##  4 TCGA-D8-A1XR    56 FEMALE   0.345    -0.211  -0.193    0.124  II          
##  5 TCGA-BH-A0BF    56 FEMALE   0.222     1.91    0.520   -0.312  II          
##  6 TCGA-AO-A1KQ    84 MALE    -0.0819    1.72   -0.0573   0.0430 III         
##  7 TCGA-D8-A73X    53 FEMALE  -0.0695    1.42   -0.361    0.392  II          
##  8 TCGA-A7-A426    50 FEMALE   0.672     1.28   -0.321   -0.112  III         
##  9 TCGA-EW-A1P5    77 FEMALE  -0.152    -0.663   1.19     0.217  II          
## 10 TCGA-A8-A09A    40 FEMALE  -0.566     1.27   -0.293    0.194  II          
## # … with 331 more rows, and 8 more variables: Histology <chr>,
## #   `ER status` <chr>, `PR status` <chr>, `HER2 status` <chr>,
## #   Surgery_type <chr>, Date_of_Surgery <chr>, Date_of_Last_Visit <chr>,
## #   Patient_Status <chr>

Realizar un análisis descriptivo (numérico, gráfico,…) de por lo menos dos variables y comente sus resultados

Femenino<- BRCA %>% filter(Gender == "FEMALE")
Femenino

## # A tibble: 330 × 16
##    Patient_ID     Age Gender Protein1 Protein2 Protein3 Protein4 Tumour_Stage
##    <chr>        <dbl> <chr>     <dbl>    <dbl>    <dbl>    <dbl> <chr>       
##  1 TCGA-D8-A1XD    36 FEMALE   0.0804    0.426    0.547   0.274  III         
##  2 TCGA-EW-A1OX    43 FEMALE  -0.420     0.578    0.614  -0.0315 II          
##  3 TCGA-A8-A079    69 FEMALE   0.214     1.31    -0.327  -0.234  III         
##  4 TCGA-D8-A1XR    56 FEMALE   0.345    -0.211   -0.193   0.124  II          
##  5 TCGA-BH-A0BF    56 FEMALE   0.222     1.91     0.520  -0.312  II          
##  6 TCGA-D8-A73X    53 FEMALE  -0.0695    1.42    -0.361   0.392  II          
##  7 TCGA-A7-A426    50 FEMALE   0.672     1.28    -0.321  -0.112  III         
##  8 TCGA-EW-A1P5    77 FEMALE  -0.152    -0.663    1.19    0.217  II          
##  9 TCGA-A8-A09A    40 FEMALE  -0.566     1.27    -0.293   0.194  II          
## 10 TCGA-S3-A6ZG    71 FEMALE  -0.223     0.506   -0.349  -0.835  II          
## # … with 320 more rows, and 8 more variables: Histology <chr>,
## #   `ER status` <chr>, `PR status` <chr>, `HER2 status` <chr>,
## #   Surgery_type <chr>, Date_of_Surgery <chr>, Date_of_Last_Visit <chr>,
## #   Patient_Status <chr>

mean(Femenino$Age)

## [1] 58.85152

median(Femenino$Age)

## [1] 58

length(Femenino$Age)

## [1] 330

sd(Femenino$Age)

## [1] 12.92293

max(Femenino$Age)

## [1] 90

min(Femenino$Age)

## [1] 29

summary(Femenino)

##   Patient_ID             Age           Gender             Protein1        
##  Length:330         Min.   :29.00   Length:330         Min.   :-2.340900  
##  Class :character   1st Qu.:49.00   Class :character   1st Qu.:-0.361740  
##  Mode  :character   Median :58.00   Mode  :character   Median : 0.004813  
##                     Mean   :58.85                      Mean   :-0.039322  
##                     3rd Qu.:67.75                      3rd Qu.: 0.336462  
##                     Max.   :90.00                      Max.   : 1.593600  
##     Protein2          Protein3           Protein4        Tumour_Stage      
##  Min.   :-0.9787   Min.   :-1.62740   Min.   :-2.02550   Length:330        
##  1st Qu.: 0.3518   1st Qu.:-0.51375   1st Qu.:-0.38120   Class :character  
##  Median : 0.9928   Median :-0.17318   Median : 0.04340   Mode  :character  
##  Mean   : 0.9468   Mean   :-0.08907   Mean   : 0.01081                     
##  3rd Qu.: 1.6279   3rd Qu.: 0.28093   3rd Qu.: 0.43440                     
##  Max.   : 3.4022   Max.   : 2.19340   Max.   : 1.62990                     
##   Histology          ER status          PR status         HER2 status       
##  Length:330         Length:330         Length:330         Length:330        
##  Class :character   Class :character   Class :character   Class :character  
##  Mode  :character   Mode  :character   Mode  :character   Mode  :character  
##                                                                             
##                                                                             
##                                                                             
##  Surgery_type       Date_of_Surgery    Date_of_Last_Visit Patient_Status    
##  Length:330         Length:330         Length:330         Length:330        
##  Class :character   Class :character   Class :character   Class :character  
##  Mode  :character   Mode  :character   Mode  :character   Mode  :character  
##                                                                             
##                                                                             
##

library(ggplot2)

ggplot(Femenino, aes(x = Protein2, y = Age, color=Surgery_type, size=Tumour_Stage)) +
  geom_point() + 
  scale_x_log10()

## Warning: Using size for a discrete variable is not advised.

## Warning in self$trans$transform(x): NaNs produced

## Warning: Transformation introduced infinite values in continuous x-axis

## Warning: Removed 60 rows containing missing values (geom_point).

Masculino<- BRCA %>% filter(Gender == "MALE")
Masculino

## # A tibble: 4 × 16
##   Patient_ID     Age Gender Protein1 Protein2 Protein3 Protein4 Tumour_Stage
##   <chr>        <dbl> <chr>     <dbl>    <dbl>    <dbl>    <dbl> <chr>       
## 1 TCGA-AO-A1KQ    84 MALE    -0.0819    1.72   -0.0573   0.0430 III         
## 2 TCGA-AQ-A54O    51 MALE     0.838     0.506  -0.545    0.315  II          
## 3 TCGA-AR-A1AV    68 MALE     1.47      0.469   0.136   -0.290  II          
## 4 TCGA-A8-A085    44 MALE     0.733     1.11   -0.270   -0.355  II          
## # … with 8 more variables: Histology <chr>, `ER status` <chr>,
## #   `PR status` <chr>, `HER2 status` <chr>, Surgery_type <chr>,
## #   Date_of_Surgery <chr>, Date_of_Last_Visit <chr>, Patient_Status <chr>

mean(Masculino$Age)

## [1] 61.75

median(Masculino$Age)

## [1] 59.5

length(Masculino$Age)

## [1] 4

sd(Masculino$Age)

## [1] 17.93274

max(Masculino$Age)

## [1] 84

min(Masculino$Age)

## [1] 44

summary(Masculino)

##   Patient_ID             Age           Gender             Protein1       
##  Length:4           Min.   :44.00   Length:4           Min.   :-0.08187  
##  Class :character   1st Qu.:49.25   Class :character   1st Qu.: 0.52907  
##  Mode  :character   Median :59.50   Mode  :character   Median : 0.78531  
##                     Mean   :61.75                      Mean   : 0.73978  
##                     3rd Qu.:72.00                      3rd Qu.: 0.99602  
##                     Max.   :84.00                      Max.   : 1.47040  
##     Protein2         Protein3            Protein4        Tumour_Stage      
##  Min.   :0.4690   Min.   :-0.545130   Min.   :-0.35492   Length:4          
##  1st Qu.:0.4971   1st Qu.:-0.338423   1st Qu.:-0.30611   Class :character  
##  Median :0.8091   Median :-0.163428   Median :-0.12341   Mode  :character  
##  Mean   :0.9528   Mean   :-0.184111   Mean   :-0.07171                     
##  3rd Qu.:1.2648   3rd Qu.:-0.009116   3rd Qu.: 0.11099                     
##  Max.   :1.7241   Max.   : 0.135540   Max.   : 0.31490                     
##   Histology          ER status          PR status         HER2 status       
##  Length:4           Length:4           Length:4           Length:4          
##  Class :character   Class :character   Class :character   Class :character  
##  Mode  :character   Mode  :character   Mode  :character   Mode  :character  
##                                                                             
##                                                                             
##                                                                             
##  Surgery_type       Date_of_Surgery    Date_of_Last_Visit Patient_Status    
##  Length:4           Length:4           Length:4           Length:4          
##  Class :character   Class :character   Class :character   Class :character  
##  Mode  :character   Mode  :character   Mode  :character   Mode  :character  
##                                                                             
##                                                                             
##

library(ggplot2)

ggplot(Masculino, aes(x = Protein1, y = Age, color=Surgery_type, size=Patient_Status)) +
  geom_point() + 
  scale_x_log10()

## Warning: Using size for a discrete variable is not advised.

## Warning in self$trans$transform(x): NaNs produced

## Warning: Transformation introduced infinite values in continuous x-axis

## Warning: Removed 1 rows containing missing values (geom_point).