---
title: "UAHDataScienceSF"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{Introduction to UAHDataScienceSF}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(
  comment = "#>", 
  collapse = TRUE
)
library(UAHDataScienceSF)
```

The UAHDataScienceSF package provides statistical functions that can be used in three different ways:  
  
As calculation functions that simply return the result.  
As explanatory functions that show the calculation process step by step.  
As interactive functions that allow users to practice calculations with feedback.  
  
These three modes are integrated into each function through the learn and interactive parameters. When both are FALSE (by default), the function performs a simple calculation. When learn = TRUE, the function shows a detailed explanation. When interactive = TRUE, the function enters interactive mode.

## Usage Examples:

To demonstrate the use of the functions, we will work with the following datasets:

```{r}
data <- c(1,1,2,3,4,7,8,8,8,10,10,11,12,15,20,22,25)
plot(data); 
data2 <- c(1,1,4,5,5,5,7,8,10,10,10,11,20,22,22,24,25)
plot(data2);

#Binomial variables
n = 3
x = 2
p = 0.7
    
#Poisson variables
lam = 2
k = 3

#Normal variables
nor = 0.1

#T-Student variables
xt = 290 
ut = 310
st = 50
nt = 16

```

The arithmetic mean calculus function:
```{r}
# Simple calculation
mean_(data)

# Learning mode with step-by-step explanation
mean_(data, learn = TRUE)

# Interactive mode would be called like this (cannot be ran in vignette):
# mean_(interactive = TRUE)
```

The geometric mean calculus function:
```{r}
# Simple calculation
geometric_mean(data)

# Learning mode with step-by-step explanation
geometric_mean(data, learn = TRUE)

# Interactive mode would be called like this (cannot be ran in vignette):
# geometric_mean(interactive = TRUE)
```

The mode calculus function:
```{r}
# Simple calculation
mode_(data)

# Learning mode with step-by-step explanation
mode_(data, learn = TRUE)

# Interactive mode would be called like this (cannot be ran in vignette):
# mode_(interactive = TRUE)
```

The median calculus function:
```{r}
# Simple calculation
median_(data)

# Learning mode with step-by-step explanation
median_(data, learn = TRUE)

# Interactive mode would be called like this (cannot be ran in vignette):
# median_(interactive = TRUE)
```

The standard deviation calculus function:
```{r}
# Simple calculation
standard_deviation(data)

# Learning mode with step-by-step explanation
standard_deviation(data, learn = TRUE)

# Interactive mode would be called like this (cannot be ran in vignette):
# standard_deviation(interactive = TRUE)
```

The average absolute deviation calculus function:
```{r}
# Simple calculation
average_deviation(data)

# Learning mode with step-by-step explanation
average_deviation(data, learn = TRUE)

# Interactive mode would be called like this (cannot be ran in vignette):
# average_deviation(interactive = TRUE)
```

The variance calculus function:
```{r}
# Simple calculation
variance(data)

# Learning mode with step-by-step explanation
variance(data, learn = TRUE)

# Interactive mode would be called like this (cannot be ran in vignette):
# variance(interactive = TRUE)
```

The quartiles calculus function:
```{r}
# Simple calculation
quartile(data)

# Learning mode with step-by-step explanation
quartile(data, learn = TRUE)

# Interactive mode would be called like this (cannot be ran in vignette):
# quartile(interactive = TRUE)

```

The percentile calculus function:
```{r}
# Simple calculation
percentile(data, 0.3)

# Learning mode with step-by-step explanation
percentile(data, 0.3, learn = TRUE)

# Interactive mode would be called like this (cannot be ran in vignette):
# percentile(interactive = TRUE)
```

The absolute frecuency calculus function:
```{r}
# Simple calculation
absolute_frequency(data, 1)

# Learning mode with step-by-step explanation
absolute_frequency(data, 1, learn = TRUE)

# Interactive mode would be called like this (cannot be ran in vignette):
# absolute_frequency(interactive = TRUE)
```

The relative frecuency calculus function:
```{r}
# Simple calculation
relative_frequency(data, 20)

# Learning mode with step-by-step explanation
relative_frequency(data, 20, learn = TRUE)

# Interactive mode would be called like this (cannot be ran in vignette):
# relative_frequency(interactive = TRUE)
```

The absolute acumulated frecuency calculus function:
```{r}
# Simple calculation
absolute_acum_frequency(data, 1)

# Learning mode with step-by-step explanation
absolute_acum_frequency(data, 1, learn = TRUE)

# Interactive mode would be called like this (cannot be ran in vignette):
# absolute_acum_frequency(interactive = TRUE)
```

The relative acumulated frecuency calculus function:
```{r}
# Simple calculation
relative_acum_frequency(data, 20)

# Learning mode with step-by-step explanation
relative_acum_frequency(data, 20, learn = TRUE)

# Interactive mode would be called like this (cannot be ran in vignette):
# relative_acum_frequency(interactive = TRUE)
```


The covariance calculus function:
```{r}
# Simple calculation
covariance(data, data2)

# Learning mode with step-by-step explanation
covariance(data, data2, learn = TRUE)

# Interactive mode would be called like this (cannot be ran in vignette):
# covariance(interactive = TRUE)
```

The harmonic mean calculus funtion:
```{r}
# Simple calculation
harmonic_mean(data)

# Learning mode with step-by-step explanation
harmonic_mean(data, learn = TRUE)

# Interactive mode would be called like this (cannot be ran in vignette):
# harmonic_mean(interactive = TRUE)
```

The pearson correlaction calculus funtion:
```{r}
# Simple calculation
pearson(data, data2)

# Learning mode with step-by-step explanation
pearson(data, data2, learn = TRUE)

# Interactive mode would be called like this (cannot be ran in vignette):
# pearson(interactive = TRUE)
```

The coefficient of variation calculus funtion:
```{r}
# Simple calculation
cv(data)

# Learning mode with step-by-step explanation
cv(data, learn = TRUE)

# Interactive mode would be called like this (cannot be ran in vignette):
# cv(interactive = TRUE)
```

The Laplace rule calculus funtion:
```{r}
# Simple calculation
laplace(data, data2)

# Learning mode with step-by-step explanation
laplace(data, data2, learn = TRUE)

# Interactive mode would be called like this (cannot be ran in vignette):
# laplace(interactive = TRUE)
```

The binomial distribution calculus funtion:
```{r}
# Simple calculation
binomial_(n, x, p)

# Learning mode with step-by-step explanation
binomial_(n, x, p, learn = TRUE)

# Interactive mode would be called like this (cannot be ran in vignette):
# binomial_(interactive = TRUE)
```

The poisson distribution calculus funtion:
```{r}
# Simple calculation
poisson_(k, lam)

# Learning mode with step-by-step explanation
poisson_(k, lam, learn = TRUE)

# Interactive mode would be called like this (cannot be ran in vignette):
# poisson_(interactive = TRUE)
```

The normal distribution calculus funtion:
```{r}
# Simple calculation
normal(nor)

# Learning mode with step-by-step explanation
normal(nor, learn = TRUE)

# Interactive mode would be called like this (cannot be ran in vignette):
# normal(interactive = TRUE)
```

The tstudent distribution calculus function:
```{r}
# Simple calculation
tstudent(xt, ut, st, nt)

# Learning mode with step-by-step explanation
tstudent(xt, ut, st, nt, learn = TRUE)

# Interactive mode would be called like this (cannot be ran in vignette):
# tstudent(interactive = TRUE)
```

The chisquared distribution calculus function:
```{r}
# Simple calculation
chisquared(data, data2)

# Learning mode with step-by-step explanation
chisquared(data, data2, learn = TRUE)

# Interactive mode would be called like this (cannot be ran in vignette):
# chisquared(interactive = TRUE)
```

The fisher distribution calculus function:
```{r}
# Simple calculation
fisher(data, data2)

# Learning mode with step-by-step explanation
fisher(data, data2, learn = TRUE)

# Interactive mode would be called like this (cannot be ran in vignette):
# fisher(interactive = TRUE)
```