Lecture 6 - stats

Lecture 6 (Chapter 3 of MSMB)

High Quality Graphics in R

Goals for this Chapter

In this lecture we will:

Learn how to rapidly and flexibly explore datasets through visualization.
Create beautiful and intuitive plots for scientific presentations and publications.
Understand the logic behind the grammar of graphics concept.
Introduce ggplot2.
See how to plot data in one, two, or even three to five dimensions, and explore faceting.
Create "along-genome" plots for molecular biology data (or along other sequences, e.g., peptides).

R Packages We Will Use

Install the following library using the R command:

install.packages("ggplot2")

Base Plotting in R

Introduction to base plotting using the DNase dataset.
The DNase data frame includes:
- 176 rows and 3 columns of data.
- Data obtained during the development of an ELISA assay for the recombinant protein DNase in rat serum.
- Columns in DNase dataset:
- Run: assay run
- conc: concentration of the protein
- density: measured optical density in the assay
The first seven rows of the dataset are presented as follows:

DNase[1:7, ]  
## Run  conc density  
## 1  1  0.04882812  0.017  
## 2  1  0.04882812  0.018  
## 3  1  0.19531250  0.121  
## 4  1  0.19531250  0.124  
## 5  1  0.39062500  0.206  
## 6  1  0.39062500  0.215  
## 7  1  0.78125000  0.377

Base Plotting in R (continued)

Create a basic scatter plot using the plot function.

plot(DNase $conc, DNase$ density)

The x-axis represents DNase $conc</code>, and the y-axis represents <code>DNase$ density. The plot will display concentration versus density for the ELISA assay of DNase.
Example Output:

0  2  4  6  8  12  
DNase$conc  
0.0  1.0  2.0  
DNase$density

Figure 1: Plot of concentration vs. density for an ELISA assay of DNase.

Base Plotting in R (continued)

Change the axis labels:

plot(DNase $conc, DNase$ density, xlab="DNase concentration (ng/ml)", ylab="Optical Density")

Example Output:

0  2  4  6  8  12  
DNase concentration (ng/ml)  
0.0  1.0  2.0  
Optical density

Figure 2: Plot of concentration vs. density for an ELISA assay of DNase.

Base Plotting in R – Plot Symbols

Change the plot symbol using the pch parameter:

plot(DNase $conc, DNase$ density, pch=4, xlab="DNase concentration (ng/ml)", ylab="Optical density")

Example Output:

Base Plotting in R – Color

Change the symbol color using the col parameter:

plot(DNase $conc, DNase$ density, pch=4, col="blue", xlab="DNase concentration (ng/ml)", ylab="Optical density")

Example Output:

Base Plotting in R – Adding Fit Lines

Add a linear fit line using abline():

plot(DNase $conc, DNase$ density, pch=4, col="blue",  xlab="DNase concentration (ng/ml)", ylab="Optical density")  
abline(lm(DNase $density ~ DNase$ conc))

Example Output:

Base Plotting in R – Line Type

Change the color and line type of the fit line:

plot(DNase $conc, DNase$ density, pch=4, col="blue", xlab="DNase concentration (ng/ml)", ylab="Optical density")  
abline(lm(DNase $density ~ DNase$ conc), lty=2, col="red")

Example Output:

Boxplot

A box plot is a representation of the five-number summary including:
- Maximum
- Minimum
- Median
- First quartile (25th quantile)
- Third quartile (75th quantile)
Note that outliers are excluded when R computes the above statistics.

Creating a Boxplot in R

boxplot(density ~ Run, data=DNase)

Boxplot (continued)

For a sample vector x:

x = 0:100  
boxplot(x)

Results:
- Minimum: 0
- Maximum: 100
- Median: 50
- 1st quartile: 25
- 3rd quartile: 75

Creating Boxplot with Outliers

For a vector including an outlier:

boxplot(c(0:100, 200))

Histogram

To create a histogram of DNase $density</code>:</p></li></ul><pre><code>hist(DNase$ density)
- This generates a distribution of DNase $density</code> values showing frequency.</p></li></ul><h3 id="961e76f4-e007-41a6-b50b-5c8f78c0b231" data-toc-id="961e76f4-e007-41a6-b50b-5c8f78c0b231" collapsed="false" seolevelmigrated="true">Histogram (continued)</h3><ul><li><p>Define custom x-axis label and split the x-axis into 25 intervals:</p></li></ul><pre><code>hist(DNase$ density, breaks=25, xlab="DNase concentration (ng/ml)")
  Introduction to ggplot2
  - A package developed by Hadley Wickham that implements the grammar of graphics.
  - The package is popular among statisticians and data practitioners.
  - Notable features include that its syntax differs significantly from base R plot commands.
  - Online tutorials available for learning ggplot2.
  Grammar of Graphics
  - Introduced by Wilkinson (2005), the grammar of graphics describes the deep features underlying all statistical graphics.
  - Key components of any plot:
    - Data: The data to be visualized and a set of aesthetic mappings describing how variables in the data are mapped to aesthetic attributes such as color, size, or shape.
    - Layers: Composed of geometric elements (geoms), representing what you see on the plot (points, lines, polygons, etc.) and statistical transformations (stats) that summarize the data.
    - Scales: Map values in the data space to values in an aesthetic space.
    - Coordinate Systems: Define how data coordinates are mapped to the graphic plane.
    - Faceting: Specification to separate data into subsets and display them as small multiples.
    - Theme: Controls finer aspects of the display, such as font size and background color.
  ggplot for the DNase Dataset
  - Using ggplot to create a scatter plot for the DNase dataset (concentration vs. density).
```
library("ggplot2")  
ggplot(DNase, aes(x = conc, y = density)) + geom_point()  
```
  ggplot for the DNase Dataset – Scatter Plot
  - Understanding the ggplot grammar:
    - ggplot: specifies the dataset and the aesthetic mapping (i.e. aes).
    - geom_point: specifies the layer to be added to the plot; geom_point can be replaced by other geometries like boxplot, histogram, or bar.
  ggplot for the DNase Dataset – Boxplot
  - Creating a boxplot:
```
ggplot(DNase, aes(x = Run, y = density)) + geom_boxplot()  
```
  ggplot for the DNase Dataset – Histogram
  - Creating a histogram:
```
ggplot(DNase, aes(density)) + geom_histogram()  
```
  Faceting
  - To examine the relationship between concentration and density for each assay run separately, faceting divides the dataset into subsets according to Run, creating a plot for each subset.
```
ggplot(DNase, aes(x = conc, y = density)) + geom_point() + facet_wrap(Run ~ ., ncol=3)  
```
  Faceting (continued)
  - Change the points to blue open circles:
```
ggplot(DNase, aes(x = conc, y = density)) + geom_point(shape=1, colour="blue") + facet_wrap(Run ~ .)  
```
  Arguments for ggplot vs plot
  - Key differences in argument names:
    - colour in ggplot vs col in base plot.
    - shape in ggplot vs pch in base plot.
  - Although pch and col can also be used in ggplot, shape and colour cannot be used in base plot.
  ggplot for the chickwts Dataset
  - The chickwts dataset is an in-built R dataset from an experiment measuring the effectiveness of various feed supplements on the growth rates of chickens.
  - Viewing the first six records of chickwts:
```
head(chickwts)  
## weight  feed  
## 1  179 horsebean  
## 2  160 horsebean  
## 3  136 horsebean  
## 4  227 horsebean  
## 5  217 horsebean  
## 6  168 horsebean  
```
  - Levels of the feed variable:
```
levels(chickwts$feed)  
## [1] "casein" "horsebean" "linseed" "meatmeal" "soybean" "sunflower"  
```
  ggplot for the chickwts Dataset – Barplot
  - Creating a barplot for the feed variable:
```
ggplot(chickwts, aes(feed)) + geom_bar()  
```
  ggplot for the chickwts Dataset – Boxplot
  - Creating a boxplot illustrating weight by feed type:
```
ggplot(chickwts, aes(x = feed, y = weight)) + geom_boxplot()  
```
  ggplot for the chickwts Dataset – Boxplot with Fill Color
  - Adding colors to boxplots:
```
ggplot(chickwts, aes(x = feed, y = weight, fill = feed)) + geom_boxplot()  
```
  ggplot for the chickwts Dataset – Dotplot
  - Creating a dotplot is advisable when the number of data points is small:
```
ggplot(chickwts, aes(x = feed, y = weight, fill = feed)) + geom_dotplot(binaxis='y', stackdir="center", dotsize=0.8)  
```
  - Note: Overlapping points can obscure data and may result in a cluttered visualization.
  ggplot for the chickwts Dataset – Violin Plot
  - Generating a violin plot to visualize weight by feed type:
```
ggplot(chickwts, aes(x = feed, y = weight, fill = feed)) + geom_violin()  
```
  ggplot for the chickwts Dataset – Density Plot
  - Creating a density plot:
```
ggplot(chickwts, aes(x = weight, color = feed)) + geom_density()  
```
  Finding the Optimal Dose Level
  - Considering a new drug for lowering blood pressure, different doses are applied to patients with hypertension, recording the reduction in blood pressure:
```
head(highbp)  
## dose  bp.drop  
## 1 0.05 -1.32581524  
## 2 0.10  3.05457330  
## 3 0.15  0.07748555  
## 4 0.20 10.86112321  
## 5 0.25  6.81803109  
## 6 0.30  3.19812646  
```
  Finding the Optimal Dose Level – Scatter Plot
  - First, create a scatter plot:
```
ggplot(highbp, aes(x=dose, y=bp.drop)) + geom_point(shape=1)  
```
  Finding the Optimal Dose Level – Geom Smooth
  - To visualize the trend in data, using geom_smooth:
```
ggplot(highbp, aes(x=dose, y=bp.drop)) + geom_smooth()  
```
  - The blue line indicates the mean and gray band indicates confidence intervals.
  Finding the Optimal Dose Level – Combined Plot
  - Combine the scatter plot and smooth line in a single plot:
```
ggplot(highbp, aes(x=dose, y=bp.drop)) + geom_point(shape=1) + geom_smooth()  
```
  Stepwise ggplot Approach
  - Create a stepwise plot where layers are added incrementally:
```
our.plot = ggplot(highbp, aes(x=dose, y=bp.drop))  
our.plot = our.plot + geom_point(shape=1)  
our.plot = our.plot + geom_smooth()  
your.plot  
```
  Data Transformation
  - If variables x and y are already defined, a scatterplot can be generated:
```
ggplot(data=NULL, aes(x=x, y=y)) + geom_point()  
```
  Data Transformation - Transparency
  - To improve visibility when dealing with numerous data points; make points transparent using alpha:
```
ggplot(NULL, aes(x=x, y=y)) + geom_point(alpha=0.2)  
```
  Data Transformation - Square Root
  - Instead of plotting y versus x, plot sqrt(y) versus x:
```
ggplot(NULL, aes(x=x, y=sqrt(y))) + geom_point(alpha=0.2)  
```
  - The variance of y appears stabilized after transformation.
  Genomic Data Visualization
  - A display of the ideogram of human chromosome 1:
```
library("ggbio")  
data("hg19IdeogramCyto", package = "biovizBase")  
plotIdeogram(hg19IdeogramCyto, subchr="chr1")  
```
  Genomic Data: Editing Sites
  - Visualization of 500 RNA editing sites in the human genome:
```
library("GenomicRanges")  
data("darned_hg19_subset500", package = "biovizBase")  
autoplot(darned_hg19_subset500, layout="karyogram", aes(color=exReg, fill=exReg))  
```
  - This renders a karyogram layout displaying the editing sites mapped against the human chromosome data linked to exReg values.

Lecture 6 - stats

Lecture 6 (Chapter 3 of MSMB)

Goals for this Chapter

R Packages We Will Use

Base Plotting in R

Base Plotting in R (continued)

Base Plotting in R (continued)

Base Plotting in R – Plot Symbols

Base Plotting in R – Color

Base Plotting in R – Adding Fit Lines

Base Plotting in R – Line Type

Boxplot

Creating a Boxplot in R

Boxplot (continued)

Creating Boxplot with Outliers

Histogram

Introduction to ggplot2

Grammar of Graphics

ggplot for the DNase Dataset

ggplot for the DNase Dataset – Scatter Plot

ggplot for the DNase Dataset – Boxplot

ggplot for the DNase Dataset – Histogram

Faceting

Faceting (continued)

Arguments for ggplot vs plot

ggplot for the chickwts Dataset

ggplot for the chickwts Dataset – Barplot

ggplot for the chickwts Dataset – Boxplot

ggplot for the chickwts Dataset – Boxplot with Fill Color

ggplot for the chickwts Dataset – Dotplot

ggplot for the chickwts Dataset – Violin Plot

ggplot for the chickwts Dataset – Density Plot

Finding the Optimal Dose Level

Finding the Optimal Dose Level – Scatter Plot

Finding the Optimal Dose Level – Geom Smooth

Finding the Optimal Dose Level – Combined Plot

Stepwise ggplot Approach

Data Transformation

Data Transformation - Transparency

Data Transformation - Square Root

Genomic Data Visualization

Genomic Data: Editing Sites