In statistics, a P–P plot (probability–probability plot or percent–percent plot or P value plot) is a probability plot for assessing how closely two data sets agree, which plots the two cumulative distribution functions against each other. P-P plots are vastly used to evaluate the skewness of a distribution.

Looking for the definition of PLOT? Find out what is the full meaning of PLOT on Abbreviations.com! 'Porous Layer Open Tubular' is one option - get in to view more @ The Web's largest and most authoritative acronyms and abbreviations resource.

1. I'm using R to plot statistical graphs. I can plot simple graphs. However, I not have idea how to plot complex data. Someone could help me put together a chart with all this information?
2. The definition of a plot is a marked off area that is intended for a specific use. An example of plot is a space designed to be used as a community garden.
3. Noun a secret plan or scheme to accomplish some purpose, especially a hostile, unlawful, or evil purpose: a plot to overthrow the government. Also called storyline. The plan, scheme, or main story of a literary or dramatic work, as a play, novel, or short story. Verb (used with object), plotted, plotting.

The Q–Q plot is more widely used, but they are both referred to as 'the' probability plot, and are potentially confused.

Definition[edit]

A P–P plot plots two cumulative distribution functions (cdfs) against each other:^[1]given two probability distributions, with cdfs 'F' and 'G', it plots ${\displaystyle (F(z),G(z))}$ as z ranges from ${\displaystyle -\mathrm{\infty }}$ to ${\displaystyle \mathrm{\infty }.}$ As a cdf has range [0,1], the domain of this parametric graph is ${\displaystyle (-\mathrm{\infty },\mathrm{\infty })}$ and the range is the unit square ${\displaystyle [0,1]\times [0,1].}$

Thus for input z the output is the pair of numbers giving what percentage of f and what percentage of g fall at or below z.

The comparison line is the 45° line from (0,0) to (1,1) – the distributions are equal if and only if the plot falls on this line – any deviation indicates a difference between the distributions.^[2]

Example Of Plot

Example[edit]

As an example, if the two distributions do not overlap, say F is below G, then the P–P plot will move from left to right along the bottom of the square – as z moves through the support of F, the cdf of F goes from 0 to 1, while the cdf of G stays at 0 – and then moves up the right side of the square – the cdf of F is now 1, as all points of F lie below all points of G, and now the cdf of G moves from 0 to 1 as z moves through the support of G. (need a graph for this paragraph)

Use[edit]

As the above example illustrates, if two distributions are separated in space, the P–P plot will give very little data – it is only useful for comparing probability distributions that have nearby or equal location. Notably, it will pass through the point (1/2, 1/2) if and only if the two distributions have the same median.

P–P plots are sometimes limited to comparisons between two samples, rather than comparison of a sample to a theoretical model distribution.^[3] However, they are of general use, particularly where observations are not all modelled with the same distribution.

However, it has found some use in comparing a sample distribution from a known theoretical distribution: given n samples, plotting the continuous theoretical cdf against the empirical cdf would yield a stairstep (a step as z hits a sample), and would hit the top of the square when the last data point was hit. Instead one only plots points, plotting the observed kth observed points (in order: formally the observed kth order statistic) against the k/(n + 1) quantile of the theoretical distribution.^[3] This choice of 'plotting position' (choice of quantile of the theoretical distribution) has occasioned less controversy than the choice for Q–Q plots. The resulting goodness of fit of the 45° line gives a measure of the difference between a sample set and the theoretical distribution.

A P–P plot can be used as a graphical adjunct to a tests of the fit of probability distributions,^[4][5] with additional lines being included on the plot to indicate either specific acceptance regions or the range of expected departure from the 1:1 line. An improved version of the P–P plot, called the SP or S–P plot, is available,^[4][5] which makes use of a variance-stabilizing transformation to create a plot on which the variations about the 1:1 line should be the same at all locations.

See also[edit]

Examples Of A Story Plot

References[edit]

Citations[edit]

1. ^Nonparametric statistical inference by Jean Dickinson Gibbons, Subhabrata Chakraborti, 4th Edition, CRC Press, 2003, ISBN978-0-8247-4052-8, p. 145
2. ^Derrick, B; Toher, D; White, P (2016). 'Why Welchs test is Type I error robust'. The Quantitative Methods for Psychology. 12 (1): 30–38. doi:10.20982/tqmp.12.1.p030.
3. ^ ^abTesting for Normality, by Henry C. Thode, CRC Press, 2002, ISBN978-0-8247-9613-6, Section 2.2.3, Percent–percent plots, p. 23
4. ^ ^abMichael J.R. (1983) 'The stabilized probability plot'. Biometrika, 70(1), 11–17. JSTOR2335939
5. ^ ^abShorack, G.R., Wellner, J.A (1986) Empirical Processes with Applications to Statistics, Wiley. ISBN0-471-86725-X p248–250

Sources[edit]

• Davidson, Russell; MacKinnon, James (January 1998). 'Graphical Methods for Investigating the Size and Power of Hypothesis Tests'. The Manchester School. 66 (1): 1–26. CiteSeerX10.1.1.57.4335. doi:10.1111/1467-9957.00086.

In this article, we’ll describe how to plot easily means or medians with error bars. We’ll use ggplot2 based helper functions available in the ggpubr R package.

Contents:

• Prerequisites

Prerequisites

Required R package

You need to install the R package ggpubr, to easily create ggplot2-based publication ready plots.

We recommend to install the latest developmental version from GitHub as follow:

If the installation from Github failed, then try to install from CRAN as follow:

Load ggpubr:

Demo data sets

Data: ToothGrowth and mtcars data sets.

Error plots

R function: ggerrorplot() [in ggpubr].

Simplified format:

• data: a data frame
• x, y: x and y variables for plotting
• desc_stat: descriptive statistics to be used for visualizing errors. Default value is “mean_se”. Allowed values are one of , “mean”, “mean_se”, “mean_sd”, “mean_ci”, “mean_range”, “median”, “median_iqr”, “median_mad”, “median_range”

For example, the following R code uses the ToothGrowth data set and plots y = “len” by x = “dose”.

It’s also possible to add jitter points (representing individual points), dot plots and violin plots:

To add p-values comparing means, use this:

Read more at : Add P-values and Significance Levels to ggplots.

Color by a grouping variable:

Line plots

You can create a line plot of mean +/- error using the function ggline()[in ggpubr]. The format is as follow:

Color by groups:

Bar plots

R function ggbarplot()[in ggpubr]. The format is as follow:

Color by groups:

Add labels

In this section we’ll plot group means with individual information.

Data: mtcars.

Create a bar plot with individual labels.

Land Plot Drawing

Application to gene expression data

Plots Means In Bengali

In our previous article - Facilitating Exploratory Data Visualization: Application to TCGA Genomic Data - we described how to visualize gene expression data using box plots, violin plots, dot plots and stripcharts. We also demonstrated how to combine the plot of multiples variables (genes) in the same plot.

Here we provide some R code to visualize the mean expression profile of one or multiple genes. We’ll use the gene expression data set described in our previous tutorial: Facilitating Exploratory Data Visualization: Application to TCGA Genomic Data.

The data set contains the mRNA expression for five genes of interest - GATA3, PTEN, XBP1, ESR1 and MUC1 - from 3 different data sets:

• Breast invasive carcinoma (BRCA),
• Ovarian serous cystadenocarcinoma (OV) and
• Lung squamous cell carcinoma (LUSC)

The R code below displays the mean expression of three genes - “GATA3”, “PTEN” and “XBP1”.

You can also add other geometries on the mean plot such as jitter points, dotplot or violin. To add a violin plot, type this:

To add jitter points, we’ll use a small subset of data for readability:

As previously shown, you can merge the three plots as follow:

Show line labels:

Let’s plot a complex plot with point labels:

Plot Means

Plot a bar plot of means:

Na Plots Means

Error plots: