Solutions to this workshop can be found here

Review

review_vector <- c(1, 2.6, NA, 4.98, 1.5, NA)

# run a function that will determine which of the values in review_vector is a
# missing value

# run an operation that will determine which of the numbers in review_vector is
# greater than 2 and less than 4

# use the logical vector above to create a subvector of review_vector that only
# includes the elements of review_vector that are greater than 2 and less than 4



leaf_number <- c(5, 8, 5, 11, 4, 5, 8, 13, 10, 4, 7)

# make a logical vector called many_leaves that tells you whether each position
# in leaf_number is greater than 10

# use many_leaves to set each value of leaf_number over 10 to infinity (Inf)

Data Frames: Reading in and manipulating data, writing data

So far, everything we’ve been doing in R has involved vectors. However, we haven’t yet learned about the most useful data structure in R: data frames.

Data frames are essentially just tables. They have rows and columns, and if you set your data up right, they make it incredibly easy to explore your data. R has a ton of operations that are specialized in reading data frames and either plotting them in an easy way, or summarizing the data inside, and we’re going to be spending the next couple of days learning about those.

if (dir.exists('class_figures')){
  library(knitr)
  include_graphics('class_figures/df_illustration.png')
}

Reading in tables from excel

A lot of times, it’s not really convenient to enter your data in R. When collecting data by hand, it can be really convenient to type it into excel (or google sheets). Although there is a special package in R that can read excel format files (.xlsx), this is not commonly used. Instead, we usually save files in .csv format, which throws out all of the special formatting excel does and just keeps the data itself.

csv stands for comma-separated values, and that’s just what they are. These files can be easily opened in excel or google sheets, but if you open them in notepad, you can see that they’re really just rows of numbers and words separated by… you guessed it, commas.

You should have a dataset in csv format called iris.csv. This is a set of information on flower structure collected from plants of 3 iris species. Follow along with this file as we go through the rules. The code below will only work if you have iris.csv saved in the same folder as this file.

First, let’s get R to read in the iris data. You can download it from here; right-click (or, on a Mac, control-click) the ’Raw" button on the upper right, select “save link as…”, and download it into the same folder as this workshop file.

# this is actually a built-in dataset in R, but I saved it as a csv so we can
# practice importing
iris_df <- read.csv('iris.csv')
View(iris_df)

There are some good practices for how to organize and record your data, and following these will make your life MUCH easier when you try to analyze your data. Following these rules means that R will be able to easily read you data, and that the data is immediately set up in such a way that the built-in R functions for processing data can easily work with it.

  • Give each column a short, informative title. Avoid spaces and weird symbols/punctuation. You can use letters, numbers, periods, underscores ( _ ) and hyphens. NEVER use commas in your data entry.

  • You can also name rows, but I suggest avoiding this for now, since you will need to provide a special argument to read.csv if you do this.

  • Keep a single column as one data type (e.g. a column can contain strings, or numbers, or logicals). R will usually know which is which, and treat the data accordingly.

  • Notice that in the iris dataframe, every row holds a single observation. That is, data on each single data point (plant) is one row, and each individual piece of information about it is one column (e.g. how wide were its petals? What species did this plant belong to?)

The last point on this list involves thinking about what constitutes an ‘observation’ in your data. This can seem subjective! Let’s say you’re tracking plant growth over time: is a single observation one plant, or one timepoint? As you program, you’ll start getting an intuitive feeling for better and worse ways to organize data. But remember that data can always be re-organized in R if you don’t like how you originally did it (or if someone else collected the data!) These principles of data organization are called tidy data, and there is hugely useful package, tidyr that contains functions to re-organize and tidy up your data. We won’t cover it in this class, but I want to share a link with some info in case you continue programming in the future and find that you need it.

Selecting data from data frames: row numbers and column numbers and $

Let’s say we wanted to calculate the mean petal width of all the irises measured in the iris dataset. How can we do this? We need to select the petal width column. There are a couple of ways to do this. The easiest and most common one is using $.

# print out all the sepal lengths
print(iris_df$Sepal.Length)

# get the mean of the petal widths

We can also use indexing to get a specific row and column position in the data frame. Remember that when we used indexing for vectors, we put the necessary position (or vector of positions) in square brackets after the name of the vector. In a data frame, we need to specify both the row position(s), and the column position(s).

When using indices to specify position in a data frame, rows first, columns second

# Get the value in the second row and third column in the iris dataset
print(iris_df[2, 3])

# Get the values in the 2nd to 5th rows in the fifth column in iris_df

In addition to using numeric indices, you can also use names of columns (or rows, if they’re named!)

print(iris_df[2, 'Petal.Length'])

Finally, if you want to get every row or every column, just leave that index blank.

# get every element from 2nd column (same as iris_df$Sepal.Width)
print(iris_df[ , 2])

# get every value in the 6th row of iris_df

Creating new columns from operations on other columns

A lot of times, we need to process the data we have in order for it to be interesting to us. You can imagine a scenario in which we’d want to do this in the iris dataset. We have a list of measures petal widths and lengths from various species, and maybe we want to eventually investigate how these vary across species. But the problem is that even within a species, some flowers just happen to be larger, by chance. These would have BOTH higher petal lengths and widths, making our dataset noisier. Maybe what we really care about is the ratio of petal length to width? R makes calculating this easy.

# remember that to specify a column, we can use $. We can also use this to
# create a new column, Petal.Ratio
iris_df$Petal.Ratio <- iris_df$Petal.Length / iris_df$Petal.Width

Creating new data frames from scratch and writing them

Sometimes, you will want to create a brand new data frame from scratch. There are several ways to do this. One way is to create vectors for each column, and then combine them together in a data frame. For example, let’s imagine we have investigated the populations of squirrels and pigeons in 4 parks in NYC.

We can make 3 vectors, one with the names of the parks, one with the population of squirrels, and one with the population of pigeons.

park <- c("WashingtonSq", "CentralPark", "ProspectPark", "BatteryPark")
pigeons <- c(8.62e3, 1.5e4, 1939, 276)
rats <- c(1500, 41320, 20003, 4057)
squirrels<- c("358", "546", "439", "344")

Then, we can use the function data.frame() to turn these into a single data frame. The positions in the vectors will correspond to rows, and the names of the vectors will become the column names.

parks_df <- data.frame(park, squirrels, rats, pigeons)
parks_df

# another common way to do the same thing
parks_df_2 <-
  data.frame(
    park = c("WashingtonSq", "CentralPark", "ProspectPark", "BatteryPark"),
    squirrels = c("358", "546", "439", "344"),
    rats = c(1500, 41320, 20003, 4057),
    pigeons = c(8.62e3, 1.5e4, 1939, 276)
    )
parks_df_2
#try accessing the values rows 1, 2, and 3 of column 1

What if you wanted to share this data with a colleague, so they could do their own calculations? The nicest way would be to send them a csv. We can make csvs from data frames in R using write.csv(). Take a look at the documentation for this function.

# write a csv called 'parks.csv' with the data in parks_df

Watch out for factors!

You may have noticed that accessing the park column gave us something that involved “levels”. These are because they’re actually not characters, but something called factors. Factors are categorical variables. These are very important for some types of statistical models, but they can be a problem if you are expecting characters or numbers.

Let’s look at the data.frame again.

View(parks_df)

Let’s try to access the population of squirrels as a number.

parks_df$squirrels
as.numeric(parks_df$squirrels)

As you can see, the character numbers are being converted not to the numbers they should be, but to their factor levels. I’m sure you can imagine how this could be a huge problem.

When something is a factor and your want it to be a number, do this:

as.numeric(as.character(parks_df$squirrels)) 

By first going through as.character and THEN as.numeric, you preserve your entries as intended.

Finally, if you want to change the values in the data frame, you must remember to reassign that column

as.numeric(as.character(parks_df$squirrels)) 
str(parks_df)
parks_df[,3] <- as.numeric(as.character(parks_df$squirrels)) 
str(parks_df)

Calculate column means, standard deviations, standard errors

Now, maybe we want to use these columns to find out something about parks in NYC. Maybe we want to find the average number of rats and pigeons in NYC parks.

# find the mean number of rats and pigeons for parks in NYC

We also want to know the amount of variation in pigeon and rat populations.

# calculate the standard deviation - use google to help you find functions

If we have many columns with numeric data, finding the mean of each of them individually could take a while. We can use the function colMeans() instead. Take a look at the documentation for colMeans()

# try using colMeans() to find the mean number of rats and pigeons for parks in NYC

# do you run into problems? why? how could we get what we want using this function?
---
title: "Intro R Course, Workshop 5: Dataframes"
subtitle: |
    |   - formatting data for analysis and reading excel data into R dataframes
    |   - selecting rows and columns of interest
    |   - adding columns to dataframes
    |   - exporting data from R
    |   - performing operations on individual columns of data
author:
  - Eugene Plavskin
  - Grace Avecilla
  - Tobi Shraink
output:
  html_notebook:
    code_folding: show
    depth: 3
    tidy: yes
    toc: yes
---
**Solutions to this workshop can be found [here](Solutions_Workshop_5.nb.html)**

# Review

```{r}
review_vector <- c(1, 2.6, NA, 4.98, 1.5, NA)

# run a function that will determine which of the values in review_vector is a
# missing value

# run an operation that will determine which of the numbers in review_vector is
# greater than 2 and less than 4

# use the logical vector above to create a subvector of review_vector that only
# includes the elements of review_vector that are greater than 2 and less than 4



leaf_number <- c(5, 8, 5, 11, 4, 5, 8, 13, 10, 4, 7)

# make a logical vector called many_leaves that tells you whether each position
# in leaf_number is greater than 10

# use many_leaves to set each value of leaf_number over 10 to infinity (Inf)

```

# Data Frames: Reading in and manipulating data, writing data

So far, everything we've been doing in R has involved vectors. However, we haven't yet learned about the most useful data structure in R: data frames.

Data frames are essentially just tables. They have rows and columns, and if you set your data up right, they make it *incredibly* easy to explore your data. R has a ton of operations that are specialized in reading data frames and either plotting them in an easy way, or summarizing the data inside, and we're going to be spending the next couple of days learning about those.

```{r}
if (dir.exists('class_figures')){
  library(knitr)
  include_graphics('class_figures/df_illustration.png')
}
```

## Reading in tables from excel

A lot of times, it's not really convenient to enter your data in R. When collecting data by hand, it can be really convenient to type it into excel (or google sheets). Although there is a special package in R that can read excel format files (**.xlsx**), this is not commonly used. Instead, we usually save files in **.csv** format, which throws out all of the special formatting excel does and just keeps the data itself.

**csv** stands for *comma-separated values*, and that's just what they are. These files can be easily opened in excel or google sheets, but if you open them in notepad, you can see that they're really just rows of numbers and words separated by... you guessed it, commas.

You should have a dataset in csv format called *iris.csv*. This is a set of information on flower structure collected from plants of 3 iris species. Follow along with this file as we go through the rules. The code below will only work if you have iris.csv saved in the same folder as this file.

First, let's get R to read in the iris data. You can download it from [here](https://github.com/plavskin/Intro_R_Course/blob/master/iris.csv); right-click (or, on a Mac, control-click) the 'Raw" button on the upper right, select "save link as...", and download it into the same folder as this workshop file.
```{r}
# this is actually a built-in dataset in R, but I saved it as a csv so we can
# practice importing
iris_df <- read.csv('iris.csv')
View(iris_df)
```

There are some good practices for how to organize and record your data, and following these will make your life *MUCH* easier when you try to analyze your data. Following these rules means that R will be able to easily read you data, and that the data is immediately set up in such a way that the built-in R functions for processing data can easily work with it.

* Give each column a short, informative title. Avoid spaces and weird symbols/punctuation. You can use letters, numbers, periods, underscores ( _ ) and hyphens. *NEVER* use commas in your data entry.

* You can also name rows, but I suggest avoiding this for now, since you will need to provide a special argument to `read.csv` if you do this.

* Keep a single column as one data type (e.g. a column can contain strings, or numbers, or logicals). R will usually know which is which, and treat the data accordingly.

* Notice that in the iris dataframe, every row holds a single observation. That is, data on each single data point (plant) is one row, and each individual piece of information about it is one column (e.g. how wide were its petals? What species did this plant belong to?)

The last point on this list involves thinking about what constitutes an 'observation' in your data. This can seem subjective! Let's say you're tracking plant growth over time: is a single observation one plant, or one timepoint? As you program, you'll start getting an intuitive feeling for better and worse ways to organize data. But remember that data can always be re-organized in R if you don't like how you originally did it (or if someone else collected the data!) These principles of data organization are called *tidy* data, and there is *hugely* useful package, **tidyr** that contains functions to re-organize and tidy up your data. We won't cover it in this class, but I want to share a [link](https://cran.r-project.org/web/packages/tidyr/vignettes/tidy-data.html) with some info in case you continue programming in the future and find that you need it.

## Selecting data from data frames: row numbers and column numbers and $

Let's say we wanted to calculate the mean petal width of all the irises measured in the iris dataset. How can we do this? We need to select the petal width column. There are a couple of ways to do this. The easiest and most common one is using `$`.

```{r}
# print out all the sepal lengths
print(iris_df$Sepal.Length)

# get the mean of the petal widths

```

We can also use indexing to get a specific row and column position in the data frame. Remember that when we used indexing for vectors, we put the necessary position (or vector of positions) in square brackets after the name of the vector. In a data frame, we need to specify both the row position(s), and the column position(s).

When using indices to specify position in a data frame, **rows first, columns second**

```{r}
# Get the value in the second row and third column in the iris dataset
print(iris_df[2, 3])

# Get the values in the 2nd to 5th rows in the fifth column in iris_df

```

In addition to using numeric indices, you can also use names of columns (or rows, if they're named!)
```{r}
print(iris_df[2, 'Petal.Length'])
```

Finally, if you want to get *every* row or *every* column, just leave that index blank.
```{r}
# get every element from 2nd column (same as iris_df$Sepal.Width)
print(iris_df[ , 2])

# get every value in the 6th row of iris_df

```

## Creating new columns from operations on other columns

A lot of times, we need to process the data we have in order for it to be interesting to us. You can imagine a scenario in which we'd want to do this in the iris dataset. We have a list of measures petal widths and lengths from various species, and maybe we want to eventually investigate how these vary across species. But the problem is that even within a species, some flowers just happen to be larger, by chance. These would have BOTH higher petal lengths and widths, making our dataset noisier. Maybe what we really care about is the ratio of petal length to width? R makes calculating this easy.

```{r}
# remember that to specify a column, we can use $. We can also use this to
# create a new column, Petal.Ratio
iris_df$Petal.Ratio <- iris_df$Petal.Length / iris_df$Petal.Width

```

## Creating new data frames from scratch and writing them

Sometimes, you will want to create a brand new data frame from scratch. There are several ways to do this. One way is to create vectors for each column, and then combine them together in a data frame. For example, let's imagine we have investigated the populations of squirrels and pigeons in 4 parks in NYC.

We can make 3 vectors, one with the names of the parks, one with the population of squirrels, and one with the population of pigeons. 
```{r}
park <- c("WashingtonSq", "CentralPark", "ProspectPark", "BatteryPark")
pigeons <- c(8.62e3, 1.5e4, 1939, 276)
rats <- c(1500, 41320, 20003, 4057)
squirrels<- c("358", "546", "439", "344")
```
Then, we can use the function `data.frame()` to turn these into a single data frame. The positions in the vectors will correspond to rows, and the names of the vectors will become the column names.
```{r}
parks_df <- data.frame(park, squirrels, rats, pigeons)
parks_df

# another common way to do the same thing
parks_df_2 <-
  data.frame(
    park = c("WashingtonSq", "CentralPark", "ProspectPark", "BatteryPark"),
    squirrels = c("358", "546", "439", "344"),
    rats = c(1500, 41320, 20003, 4057),
    pigeons = c(8.62e3, 1.5e4, 1939, 276)
    )
parks_df_2
```

```{r}
#try accessing the values rows 1, 2, and 3 of column 1
```

What if you wanted to share this data with a colleague, so they could do their own calculations? The nicest way would be to send them a csv. We can make csvs from data frames in R using `write.csv()`. Take a look at the documentation for this function.

```{r}
# write a csv called 'parks.csv' with the data in parks_df
```

## Watch out for factors!
You may have noticed that accessing the park column gave us something that involved "levels". These are because they're actually not characters, but something called factors. Factors are categorical variables. These are very important for some types of statistical models, but they can be a problem if you are expecting characters or numbers.

Let's look at the `data.frame` again.
```{r}
View(parks_df)
```

Let's try to access the population of squirrels as a number.

```{r}
parks_df$squirrels
as.numeric(parks_df$squirrels)
```

As you can see, the character numbers are being converted not to the numbers they should be, but to their factor levels. I'm sure you can imagine how this could be a huge problem.

When something is a factor and your want it to be a number, do this:

```{r}
as.numeric(as.character(parks_df$squirrels)) 
```

By first going through `as.character` and THEN `as.numeric`, you
preserve your entries as intended.

Finally, if you want to change the values in the data frame, you must remember to reassign that column

```{r}
as.numeric(as.character(parks_df$squirrels)) 
str(parks_df)
parks_df[,3] <- as.numeric(as.character(parks_df$squirrels)) 
str(parks_df)
```

## Calculate column means, standard deviations, standard errors

Now, maybe we want to use these columns to find out something about parks in NYC. Maybe we want to find the average number of rats and pigeons in NYC parks.

```{r}
# find the mean number of rats and pigeons for parks in NYC
```

We also want to know the amount of variation in pigeon and rat populations.

```{r}
# calculate the standard deviation - use google to help you find functions
```

If we have many columns with numeric data, finding the mean of each of them individually could take a while. We can use the function `colMeans()` instead. Take a look at the documentation for `colMeans()`

```{r}
# try using colMeans() to find the mean number of rats and pigeons for parks in NYC

# do you run into problems? why? how could we get what we want using this function?
```

