symoon9/bioinfokit

Bioinformatics data analysis and visualization toolkit

The bioinfokit toolkit aimed to provide various easy-to-use functionalities to analyze,
visualize, and interpret the biological data generated from genome-scale omics experiments.

How to install:

bioinfokit requires

• Python 3
• NumPy
• scikit-learn
• seaborn
• pandas
• matplotlib
• SciPy
• matplotlib_venn

bioinfokit can be installed using pip, easy_install and git.

latest bioinfokit version:

Install using pip for Python 3 (easiest way)

# install
pip install bioinfokit

# upgrade to latest version
pip install bioinfokit --upgrade

# uninstall 
pip uninstall bioinfokit

Install using easy_install for Python 3 (easiest way)

# install latest version
easy_install bioinfokit

# specific version
easy_install bioinfokit==0.3

# uninstall 
pip uninstall bioinfokit

Install using conda

conda install -c bioconda bioinfokit

Install using git

# download and install bioinfokit (Tested on Linux, Mac, Windows) 
git clone https://github.com/reneshbedre/bioinfokit.git
cd bioinfokit
python setup.py install

Check the version of bioinfokit

>>> import bioinfokit
>>> bioinfokit.__version__
'0.4'

Gene expression analysis

Volcano plot

latest update v2.0.1

bioinfokit.visuz.gene_exp.volcano(df, lfc, pv, lfc_thr, pv_thr, color, valpha, geneid, genenames, gfont, dim, r, ar, dotsize, markerdot, sign_line, gstyle, show, figtype, axtickfontsize, axtickfontname, axlabelfontsize, axlabelfontname, axxlabel, axylabel, xlm, ylm, plotlegend, legendpos, figname, legendanchor, legendlabels, theme)

Parameters	Description
df	Pandas dataframe table having atleast gene IDs, log fold change, P-values or adjusted P-values columns
lfc	Name of a column having log or absolute fold change values [string][default:logFC]
pv	Name of a column having P-values or adjusted P-values [string][default:p_values]
lfc_thr	Log fold change cutoff for up and downregulated genes [Tuple or list][default:(1.0, 1.0)]
pv_thr	p value or adjusted p value cutoff for up and downregulated genes [Tuple or list][default:(0.05, 0.05)]
color	Tuple of three colors [Tuple or list][default: color=("green", "grey", "red")]
valpha	Transparency of points on volcano plot [float (between 0 and 1)][default: 1.0]
geneid	Name of a column having gene Ids. This is necessary for plotting gene label on the points [string][default: None]
genenames	Tuple of gene Ids to label the points. The gene Ids must be present in the geneid column. If this option set to "deg" it will label all genes defined by lfc_thr and pv_thr [string, tuple, dict][default: None]
gfont	Font size for genenames [float][default: 10.0]. gfont not compatible with gstyle=2.
dim	Figure size [Tuple of two floats (width, height) in inches][default: (5, 5)]
r	Figure resolution in dpi [int][default: 300]. Not compatible with show= True
ar	Rotation of X and Y-axis ticks labels [float][default: 90]
dotsize	The size of the dots in the plot [float][default: 8]
markerdot	Shape of the dot marker. See more options at https://matplotlib.org/3.1.1/api/markers_api.html [string][default: "o"]
sign_line	Show grid lines on plot with defined log fold change (lfc_thr) and P-value (pv_thr) threshold value [True or False][default:False]
gstyle	Style of the text for genenames. 1 for default text and 2 for box text [int][default: 1]
show	Show the figure on console instead of saving in current folder [True or False][default:False]
figtype	Format of figure to save. Supported format are eps, pdf, pgf, png, ps, raw, rgba, svg, svgz [string][default:'png']
axtickfontsize	Font size for axis ticks [float][default: 9]
axtickfontname	Font name for axis ticks [string][default: 'Arial']
axlabelfontsize	Font size for axis labels [float][default: 9]
axlabelfontname	Font name for axis labels [string][default: 'Arial']
axxlabel	Label for X-axis. If you provide this option, default label will be replaced [string][default: None]
axylabel	Label for Y-axis. If you provide this option, default label will be replaced [string][default: None]
xlm	Range of ticks to plot on X-axis [float (left, right, interval)][default: None]
ylm	Range of ticks to plot on Y-axis [float (bottom, top, interval)][default: None]
plotlegend	plot legend on volcano plot [True or False][default:False]
legendpos	position of the legend on plot. For more options see loc parameter at https://matplotlib.org/3.1.1/api/_as_gen/matplotlib.pyplot.legend.html [string ][default:"best"]
figname	name of figure [string ][default:"volcano"]
legendanchor	position of the legend outside of the plot. For more options see bbox_to_anchor parameter at https://matplotlib.org/3.1.1/api/_as_gen/matplotlib.pyplot.legend.html [list][default:None]
legendlabels	legend label names. If you provide custom label names keep the same order of label names as default [list][default:['significant up', 'not significant', 'significant down']]
theme	Change background theme. If theme set to dark, the dark background will be produced instead of white [string][default:'None']

Returns:

Volcano plot image in same directory (volcano.png) Working example

Inverted Volcano plot

latest update v2.0.1

bioinfokit.visuz.gene_exp.involcano(table, lfc, pv, lfc_thr, pv_thr, color, valpha, geneid, genenames, gfont, gstyle, dotsize, markerdot, r, dim, show, figtype, axxlabel, axylabel, axlabelfontsize, axtickfontsize, axtickfontname, plotlegend, legendpos, legendanchor, figname, legendlabels, ar, theme)

Parameters	Description
table	Pandas dataframe table having atleast gene IDs, log fold change, P-values or adjusted P-values
lfc	Name of a column having log fold change values [default:logFC]
pv	Name of a column having P-values or adjusted P-values [default:p_values]
lfc_thr	Log fold change cutoff for up and downregulated genes [Tuple or list] [default:(1.0, 1.0)]
pv_thr	p value or adjusted p value cutoff for up and downregulated genes [Tuple or list] [default:(0.05, 0.05)]
color	Tuple of three colors [Tuple or list][default: color=("green", "grey", "red")]
valpha	Transparency of points on volcano plot [float (between 0 and 1)][default: 1.0]
geneid	Name of a column having gene Ids. This is necessary for plotting gene label on the points [string][default: None]
genenames	Tuple of gene Ids to label the points. The gene Ids must be present in the geneid column. If this option set to "deg" it will label all genes defined by lfc_thr and pv_thr [string, Tuple, dict][default: None]
gfont	Font size for genenames [float][default: 10.0]
gstyle	Style of the text for genenames. 1 for default text and 2 for box text [int][default: 1]
dotsize	The size of the dots in the plot [float][default: 8]
markerdot	Shape of the dot marker. See more options at https://matplotlib.org/3.1.1/api/markers_api.html [string][default: "o"]
dim	Figure size [Tuple of two floats (width, height) in inches][default: (5, 5)]
r	Figure resolution in dpi [int][default: 300]. Not compatible with show= True
figtype	Format of figure to save. Supported format are eps, pdf, pgf, png, ps, raw, rgba, svg, svgz [string][default:'png']
show	Show the figure on console instead of saving in current folder [True or False][default:False]
axxlabel	Label for X-axis. If you provide this option, default label will be replaced [string][default: None]
axylabel	Label for Y-axis. If you provide this option, default label will be replaced [string][default: None]
axlabelfontsize	Font size for axis labels [float][default: 9]
axtickfontsize	Font size for axis ticks [float][default: 9]
axtickfontname	Font name for axis ticks [string][default: 'Arial']
plotlegend	plot legend on inverted volcano plot [True or False][default:False]
legendpos	position of the legend on plot. For more options see loc parameter at https://matplotlib.org/3.1.1/api/_as_gen/matplotlib.pyplot.legend.html [string ][default:"best"]
legendanchor	position of the legend outside of the plot. For more options see bbox_to_anchor parameter at https://matplotlib.org/3.1.1/api/_as_gen/matplotlib.pyplot.legend.html [list][default:None]
figname	name of figure [string ][default:"involcano"]
legendlabels	legend label names. If you provide custom label names keep the same order of label names as default [list][default:['significant up', 'not significant', 'significant down']]
ar	Rotation of X and Y-axis ticks labels [float][default: 90]
theme	Change background theme. If theme set to dark, the dark background will be produced instead of white [string][default:'None']

Returns:

Inverted volcano plot image in same directory (involcano.png) Working example

MA plot

latest update v2.0.3

bioinfokit.visuz.GeneExpression.ma(df, lfc, ct_count, st_count, lfc_thr, color, dim, dotsize, show, r, valpha, figtype, axxlabel, axylabel, axlabelfontsize, axtickfontsize, axtickfontname, xlm, ylm, fclines, fclinescolor, legendpos, legendanchor, figname, legendlabels, plotlegend, ar, theme, geneid, genenames, gfont, gstyle, title)

Parameters	Description
df	Pandas dataframe table having atleast gene IDs, log fold change, and normalized counts (control and treatment) columns
lfc	Name of a column having log fold change values [default:logFC]
ct_count	Name of a column having count values for control sample [default:value1]
st_count	Name of a column having count values for treatment sample [default:value2]
lfc_thr	Log fold change cutoff for up and downregulated genes [Tuple or list][default:(1.0, 1.0)]
color	Tuple of three colors [Tuple or list][default: ("green", "grey", "red")]
dotsize	The size of the dots in the plot [float][default: 8]
markerdot	Shape of the dot marker. See more options at https://matplotlib.org/3.1.1/api/markers_api.html [string][default: "o"]
valpha	Transparency of points on plot [float (between 0 and 1)][default: 1.0]
dim	Figure size [Tuple of two floats (width, height) in inches][default: (5, 5)]
r	Figure resolution in dpi [int][default: 300]. Not compatible with show= True
figtype	Format of figure to save. Supported format are eps, pdf, pgf, png, ps, raw, rgba, svg, svgz [string][default:'png']
show	Show the figure on console instead of saving in current folder [True or False][default:False]
axxlabel	Label for X-axis. If you provide this option, default label will be replaced [string][default: None]
axylabel	Label for Y-axis. If you provide this option, default label will be replaced [string][default: None]
axlabelfontsize	Font size for axis labels [float][default: 9]
axtickfontsize	Font size for axis ticks [float][default: 9]
axtickfontname	Font name for axis ticks [string][default: 'Arial']
xlm	Range of ticks to plot on X-axis [float (left, right, interval)][default: None]
ylm	Range of ticks to plot on Y-axis [float (bottom, top, interval)][default: None]
fclines	draw log fold change threshold lines as defines by lfc [True or False][default:False]
fclinescolor	color of fclines [string][default: '#2660a4']
plotlegend	plot legend on MA plot [True or False][default:False]
legendpos	position of the legend on plot. For more options see loc parameter at https://matplotlib.org/3.1.1/api/_as_gen/matplotlib.pyplot.legend.html [string ][default:"best"]
legendanchor	position of the legend outside of the plot. For more options see bbox_to_anchor parameter at https://matplotlib.org/3.1.1/api/_as_gen/matplotlib.pyplot.legend.html [list][default:None]
figname	name of figure [string ][default:"ma"]
legendlabels	legend label names. If you provide custom label names keep the same order of label names as default [list][default:['significant up', 'not significant', 'significant down']]
ar	Rotation of X and Y-axis ticks labels [float][default: 90]
theme	Change background theme. If theme set to dark_background, the dark background will be produced instead of default white. See more themes here [string][default:'None']
geneid	Name of a column having gene Ids. This is necessary for plotting gene label on the points [string][default: None]
genenames	Tuple of gene Ids to label the points. The gene Ids must be present in the geneid column. If this option set to "deg" it will label all genes defined by lfc_thr and pv_thr [string, Tuple, dict][default: None]
gfont	Font size for genenames [float][default: 10.0]
gstyle	Style of the text for genenames. 1 for default text and 2 for box text [int][default: 1]
title	Add main title to the plot [string][default: None]

Returns:

MA plot image in same directory (ma.png)

Working example

Heatmap

latest update v2.0.1

bioinfokit.visuz.gene_exp.hmap(table, cmap='seismic', scale=True, dim=(6, 8), rowclus=True, colclus=True, zscore=None, xlabel=True, ylabel=True, tickfont=(12, 12), show, r, figtype, figname, theme)

Parameters	Description
file	CSV delimited data file. It should not have NA or missing values
cmap	Color Palette for heatmap [string][default: 'seismic']
scale	Draw a color key with heatmap [boolean (True or False)][default: True]
dim	heatmap figure size [Tuple of two floats (width, height) in inches][default: (6, 8)]
rowclus	Draw hierarchical clustering for rows [boolean (True or False)][default: True]
colclus	Draw hierarchical clustering for columns [boolean (True or False)][default: True]
zscore	Z-score standardization of row (0) or column (1). It works when clus is True. [None, 0, 1][default: None]
xlabel	Plot X-label [boolean (True or False)][default: True]
ylabel	Plot Y-label [boolean (True or False)][default: True]
tickfont	Fontsize for X and Y-axis tick labels [Tuple of two floats][default: (14, 14)]
show	Show the figure on console instead of saving in current folder [True or False][default:False]
r	Figure resolution in dpi [int][default: 300]. Not compatible with show= True
figtype	Format of figure to save. Supported format are eps, pdf, pgf, png, ps, raw, rgba, svg, svgz [string][default:'png']
figname	name of figure [string ][default:"heatmap"]
theme	Change background theme. If theme set to dark, the dark background will be produced instead of white [string][default:'None']

Returns:

heatmap plot (heatmap.png, heatmap_clus.png)

Working example

Clustering analysis

Scree plot

latest update v2.0.1

bioinfokit.visuz.cluster.screeplot(obj, axlabelfontsize, axlabelfontname, axxlabel, axylabel, figtype, r, show, dim, theme)

Parameters	Description
obj	list of component name and component variance
axlabelfontsize	Font size for axis labels [float][default: 9]
axlabelfontname	Font name for axis labels [string][default: 'Arial']
axxlabel	Label for X-axis. If you provide this option, default label will be replaced [string][default: None]
axylabel	Label for Y-axis. If you provide this option, default label will be replaced [string][default: None]
figtype	Format of figure to save. Supported format are eps, pdf, pgf, png, ps, raw, rgba, svg, svgz [string][default:'png']
r	Figure resolution in dpi [int][default: 300]
show	Show the figure on console instead of saving in current folder [True or False][default:False]
dim	Figure size [Tuple of two floats (width, height) in inches][default: (6, 4)]
theme	Change background theme. If theme set to dark, the dark background will be produced instead of white [string][default:'None']

Returns:

Scree plot image (screeplot.png will be saved in same directory)

Working Example

Principal component analysis (PCA) loadings plots

latest update v2.0.1

bioinfokit.visuz.cluster.pcaplot(x, y, z, labels, var1, var2, var3, axlabelfontsize, axlabelfontname, figtype, r, show, plotlabels, dim, theme)

Parameters	Description
x	loadings (correlation coefficient) for principal component 1 (PC1)
y	loadings (correlation coefficient) for principal component 2 (PC2)
z	loadings (correlation coefficient) for principal component 3 (PC2)
labels	original variables labels from dataframe used for PCA
var1	Proportion of PC1 variance [float (0 to 1)]
var2	Proportion of PC2 variance [float (0 to 1)]
var3	Proportion of PC3 variance [float (0 to 1)]
axlabelfontsize	Font size for axis labels [float][default: 9]
axlabelfontname	Font name for axis labels [string][default: 'Arial']
figtype	Format of figure to save. Supported format are eps, pdf, pgf, png, ps, raw, rgba, svg, svgz [string][default:'png']
r	Figure resolution in dpi [int][default: 300]
show	Show the figure on console instead of saving in current folder [True or False][default:False]
plotlabels	Plot labels as defined by labels parameter [True or False][default:True]
dim	Figure size [Tuple of two floats (width, height) in inches][default: (6, 4)]
theme	Change background theme. If theme set to dark, the dark background will be produced instead of white [string][default:'None']

Returns:

PCA loadings plot 2D and 3D image (pcaplot_2d.png and pcaplot_3d.png will be saved in same directory)

Working Example

Principal component analysis (PCA) biplots

latest update v2.0.2

bioinfokit.visuz.cluster.biplot(cscore, loadings, labels, var1, var2, var3, axlabelfontsize, axlabelfontname, figtype, r, show, markerdot, dotsize, valphadot, colordot, arrowcolor, valphaarrow, arrowlinestyle, arrowlinewidth, centerlines, colorlist, legendpos, datapoints, dim, theme)

Parameters	Description
cscore	principal component scores (obtained from PCA().fit_transfrom() function in sklearn.decomposition)
loadings	loadings (correlation coefficient) for principal components
labels	original variables labels from dataframe used for PCA
var1	Proportion of PC1 variance [float (0 to 1)]
var2	Proportion of PC2 variance [float (0 to 1)]
var3	Proportion of PC3 variance [float (0 to 1)]
axlabelfontsize	Font size for axis labels [float][default: 9]
axlabelfontname	Font name for axis labels [string][default: 'Arial']
figtype	Format of figure to save. Supported format are eps, pdf, pgf, png, ps, raw, rgba, svg, svgz [string][default:'png']
r	Figure resolution in dpi [int][default: 300]
show	Show the figure on console instead of saving in current folder [True or False][default:False]
markerdot	Shape of the dot on plot. See more options at https://matplotlib.org/3.1.1/api/markers_api.html [string][default: "o"]
dotsize	The size of the dots in the plot [float][default: 6]
valphadot	Transparency of dots on plot [float (between 0 and 1)][default: 1]
colordot	Color of dots on plot [string or list ][default:"#4a4e4d"]
arrowcolor	Color of the arrow [string ][default:"#fe8a71"]
valphaarrow	Transparency of the arrow [float (between 0 and 1)][default: 1]
arrowlinestyle	line style of the arrow. check more styles at https://matplotlib.org/3.1.0/gallery/lines_bars_and_markers/linestyles.html [string][default: '-']
arrowlinewidth	line width of the arrow [float][default: 1.0]
centerlines	draw center lines at x=0 and y=0 for 2D plot [bool (True or False)][default: True]
colorlist	list of the categories to assign the color [list][default:None]
legendpos	position of the legend on plot. For more options see loc parameter at https://matplotlib.org/3.1.1/api/_as_gen/matplotlib.pyplot.legend.html [string ][default:"best"]
datapoints	plot data points on graph [bool (True or False)][default: True]
dim	Figure size [Tuple of two floats (width, height) in inches][default: (6, 4)]
theme	Change background theme. If theme set to dark, the dark background will be produced instead of white [string][default:'None']

Returns:

PCA biplot 2D and 3D image (biplot_2d.png and biplot_3d.png will be saved in same directory)

Working Example

t-SNE plot

latest update v2.0.1

bioinfokit.visuz.cluster.tsneplot(score, colorlist, axlabelfontsize, axlabelfontname, figtype, r, show, markerdot, dotsize, valphadot, colordot, dim, figname, legendpos, legendanchor, theme)

Parameters	Description
score	t-SNE component embeddings (obtained from TSNE().fit_transfrom() function in sklearn.manifold)
colorlist	list of the categories to assign the color [list][default:None]
axlabelfontsize	Font size for axis labels [float][default: 9]
axlabelfontname	Font name for axis labels [string][default: 'Arial']
figtype	Format of figure to save. Supported format are eps, pdf, pgf, png, ps, raw, rgba, svg, svgz [string][default:'png']
r	Figure resolution in dpi [int][default: 300]
show	Show the figure on console instead of saving in current folder [True or False][default:False]
markerdot	Shape of the dot on plot. See more options at https://matplotlib.org/3.1.1/api/markers_api.html [string][default: "o"]
dotsize	The size of the dots in the plot [float][default: 6]
valphadot	Transparency of dots on plot [float (between 0 and 1)][default: 1]
colordot	Color of dots on plot [string or list ][default:"#4a4e4d"]
legendpos	position of the legend on plot. For more options see loc parameter at https://matplotlib.org/3.1.1/api/_as_gen/matplotlib.pyplot.legend.html [string ][default:"best"]
legendanchor	position of the legend outside of the plot. For more options see bbox_to_anchor parameter at https://matplotlib.org/3.1.1/api/_as_gen/matplotlib.pyplot.legend.html [list][default:None]
dim	Figure size [Tuple of two floats (width, height) in inches][default: (6, 4)]
figname	name of figure [string ][default:"tsne_2d"]
theme	Change background theme. If theme set to dark, the dark background will be produced instead of white [string][default:'None']

Returns:

t-SNE 2D image (tsne_2d.png will be saved in same directory)

Working Example

Normalization

RPM or CPM normalization

latest update v0.8.9

Normalize raw gene expression counts into Reads per million mapped reads (RPM) or Counts per million mapped reads (CPM)

bioinfokit.analys.norm.cpm(df)

Parameters	Description
df	Pandas dataframe containing raw gene expression values. Genes with missing expression values (NA) will be dropped.

Returns:

RPM or CPM normalized Pandas dataframe as class attributes (cpm_norm)

Working Example

RPKM or FPKM normalization

latest update v0.9

Normalize raw gene expression counts into Reads per kilo base per million mapped reads (RPKM) or Fragments per kilo base per million mapped reads (FPKM)

bioinfokit.analys.norm.rpkm(df, gl)

Parameters	Description
df	Pandas dataframe containing raw gene expression values. Genes with missing expression or gene length values (NA) will be dropped.
gl	Name of a column having gene length in bp [string][default: None]

Returns:

RPKM or FPKM normalized Pandas dataframe as class attributes (rpkm_norm)

Working Example

TPM normalization

latest update v0.9.1

Normalize raw gene expression counts into Transcript per million (TPM)

bioinfokit.analys.norm.tpm(df, gl)

Parameters	Description
df	Pandas dataframe containing raw gene expression values. Genes with missing expression or gene length values (NA) will be dropped.
gl	Name of a column having gene length in bp [string][default: None]

Returns:

TPM normalized Pandas dataframe as class attributes (tpm_norm)

Working Example

Variant analysis

Manhattan plot

latest update v2.0.1

bioinfokit.visuz.marker.mhat(df, chr, pv, log_scale, color, dim, r, ar, gwas_sign_line, gwasp, dotsize, markeridcol, markernames, gfont, valpha, show, figtype, axxlabel, axylabel, axlabelfontsize, ylm, gstyle, figname, theme)

Parameters	Description
df	Pandas dataframe object with atleast SNP, chromosome, and P-values columns
chr	Name of a column having chromosome numbers [string][default:None]
pv	Name of a column having P-values. Must be numeric column [string][default:None]
log_scale	Change the values provided in pv column to minus log10 scale. If set to False, the original values in pv will be used. This is useful in case of Fst values. [Boolean (True or False)][default:True]
color	List the name of the colors to be plotted. It can accept two alternate colors or the number colors equal to chromosome number. If nothing (None) provided, it will randomly assign the color to each chromosome [list][default:None]
gwas_sign_line	Plot statistical significant threshold line defined by option gwasp [Boolean (True or False)][default: False]
gwasp	Statistical significant threshold to identify significant SNPs [float][default: 5E-08]
dotsize	The size of the dots in the plot [float][default: 8]
markeridcol	Name of a column having SNPs. This is necessary for plotting SNP names on the plot [string][default: None]
markernames	The list of the SNPs to display on the plot. These SNP should be present in SNP column. Additionally, it also accepts the dict of SNPs and its associated gene name. If this option set to True, it will label all SNPs with P-value significant score defined by gwasp [string, list, Tuple, dict][default: True]
gfont	Font size for SNP names to display on the plot [float][default: 8]. gfont not compatible with gstyle=2.
valpha	Transparency of points on plot [float (between 0 and 1)][default: 1.0]
dim	Figure size [Tuple of two floats (width, height) in inches][default: (6, 4)]
r	Figure resolution in dpi [int][default: 300]
ar	Rotation of X-axis labels [float][default: 90]
figtype	Format of figure to save. Supported format are eps, pdf, pgf, png, ps, raw, rgba, svg, svgz [string][default:'png']
show	Show the figure on console instead of saving in current folder [Boolean (True or False)][default:False]
axxlabel	Label for X-axis. If you provide this option, default label will be replaced [string][default: None]
axylabel	Label for Y-axis. If you provide this option, default label will be replaced [string][default: None]
axlabelfontsize	Font size for axis labels [float][default: 9]
ylm	Range of ticks to plot on Y-axis [float Tuple (bottom, top, interval)][default: None]
gstyle	Style of the text for markernames. 1 for default text and 2 for box text [int][default: 1]
figname	name of figure [string][default:"manhattan"]
theme	Change background theme. If theme set to dark, the dark background will be produced instead of white [string][default:'None']

Returns:

Manhattan plot image in same directory (Manhattan.png)

Working example

Variant annotation

latest update v0.9.3

Assign genetic features and function to the variants in VCF file

bioinfokit.analys.marker.vcf_anot(file, id, gff_file, anot_attr)

Parameters	Description
file	VCF file
id	chromosome id column in VCF file [string][default='#CHROM']
gff_file	GFF3 genome annotation file
anot_attr	Gene function tag in attributes field of GFF3 file

Returns:

Tab-delimited text file with annotation (annotated text file will be saved in same directory)

Working Example

Concatenate VCF files

latest update v0.9.4

Concatenate multiple VCF files into single VCF file (for example, VCF files for each chromosome)

bioinfokit.analys.marker.concatvcf(file)

Parameters	Description
file	Multiple vcf files separated by comma

Returns:

Concatenated VCF file (concat_vcf.vcf)

Working example

Split VCF file

bioinfokit.analys.marker.splitvcf(file)

Split single VCF file containing variants for all chromosomes into individual file containing variants for each chromosome

Parameters	Description
file	VCF file to split
id	chromosome id column in VCF file [string][default='#CHROM']

Returns:

VCF files for each chromosome

Working example

High-throughput sequence analysis

FASTQ batch downloads from SRA database

latest update v0.9.7

bioinfokit.analys.fastq.sra_bd(file, t, other_opts)

FASTQ files will be downloaded using fasterq-dump. Make sure you have the latest version of the NCBI SRA toolkit (version 2.10.8) is installed and binaries are added to the system path

Parameters	Description
file	List of SRA accessions for batch download. All accession must be separated by a newline in the file.
t	Number of threads for parallel run [int][default=4]
other_opts	Provide other relevant options for fasterq-dump [str][default=None] Provide the options as a space-separated string. You can get a detailed option for fasterq-dump using the -help option.

Returns:

FASTQ files for each SRA accession in the current directory unless specified by other_opts

Description and working example

FASTQ quality format detection

bioinfokit.analys.format.fq_qual_var(file)

Parameters	Description
file	FASTQ file to detect quality format [deafult: None]

Returns:

Quality format encoding name for FASTQ file (Supports only Sanger, Illumina 1.8+ and Illumina 1.3/1.4)

Working Example

Sequencing coverage

latest update v0.9.7

bioinfokit.analys.fastq.seqcov(file, gs)

Parameters	Description
file	FASTQ file
gs	Genome size in Mbp

Returns:

Sequencing coverage of the given FASTQ file

Description and Working example

Split the sequence into smaller subsequences

latest update v2.0.6

bioinfokit.analys.Fasta.split_seq(seq, seq_size, seq_overlap, any_cond, outfmt)

Parameters	Description
seq	Input sequence [string]
seq_size	subsequence size [int][default: 3]
seq_overlap	Split the sequence in overlap mode [bool][default: True]
any_cond	Split sequence based on a condition. Note yet defined.
outfmt	Output format for the subsequences. If parameter set to 'fasta', the file will be saved in same folder with name output_chunks.fasta ['list' or 'fasta'][default: 'list']

Returns:

Subsequences in list or fasta file (output_chunks.fasta) format

Description and Working example

Reverse complement of DNA sequence

latest update v2.0.4

bioinfokit.analys.Fasta.rev_com(sequence)

Parameters	Description
seq	DNA sequence to perform reverse complement
file	DNA sequence in a fasta file

Returns:

Reverse complement of original DNA sequence

Working example

File format conversions

bioinfokit.analys.format

Function	Parameters	Description
bioinfokit.analys.format.fqtofa(file)	FASTQ file	Convert FASTQ file into FASTA format
bioinfokit.analys.format.hmmtocsv(file)	HMM file	Convert HMM text output (from HMMER tool) to CSV format
bioinfokit.analys.format.tabtocsv(file)	TAB file	Convert TAB file to CSV format
bioinfokit.analys.format.csvtotab(file)	CSV file	Convert CSV file to TAB format

Returns:

Output will be saved in same directory

Working example

GFF3 to GTF file format conversion

latest update v1.0.1

bioinfokit.analys.gff.gff_to_gtf(file, trn_feature_name)

Parameters	Description
file	GFF3 genome annotation file
trn_feature_name	Name of the feature (column 3 of GFF3 file) of RNA transcripts if other than 'mRNA' or 'transcript'

Returns:

GTF format genome annotation file (file.gtf will be saved in same directory)

Working Example

Bioinformatics file readers and processing (FASTA, FASTQ, and VCF)

latest update v2.0.4

Function	Parameters	Description
bioinfokit.analys.Fasta.fasta_reader(file)	FASTA file	FASTA file reader
bioinfokit.analys.fastq.fastq_reader(file)	FASTQ file	FASTQ file reader
bioinfokit.analys.marker.vcfreader(file)	VCF file	VCF file reader

Returns:

File generator object (can be iterated only once) that can be parsed for the record

Description and working example

Extract subsequence from FASTA files

latest update v2.0.4

bioinfokit.analys.Fasta.ext_subseq(file, id, st, end, strand)

Extract the subsequence of specified region from FASTA file. If the target subsequence region is on minus strand. the reverse complementary of subsequence will be printed.

Parameters	Description
file	FASTA file [file]
id	The ID of sequence from FASTA file to extract the subsequence [string]
st	Start integer coordinate of subsequnece [int]
end	End integer coordinate of subsequnece [int]
strand	Strand of the subsequence ['plus' or 'minus'][default: 'plus']

Returns:

Subsequence to stdout

Extract sequences from FASTA file

latest update v2.0.4

bioinfokit.analys.Fasta.extract_seq(file, id)

Extract the sequences from FASTA file based on the list of sequence IDs provided from other file

Parameters	Description
file	FASTA file [file]
id	List of sequence IDs separated by new line [file] or Pandas series

Returns:

Sequences extracted from FASTA file based on the given IDs provided in id file. Output FASTA file will be saved as output.fasta in current working directory.

Split FASTA file into multiple FASTA files

latest update v2.0.4

bioinfokit.analys.Fasta.split_fasta(file, n, bases_per_line)

Split one big FASTA file into multiple smaller FASTA files

Parameters	Description
file	FASTA file [file]
n	Number of FASTA files to split the big FASTA file [int][default: 2]
bases_per_line	Number of bases per line for ouput FASTA files [int][default: 60]

Returns:

Number of smaller FASTA files with prefix output (output_0.fasta, output_1.fasta and so on)

Merge counts files from featureCounts

latest update v2.0.5

bioinfokit.analys.HtsAna.merge_featureCount(pattern, gene_column_name)

Merge counts files generated from featureCounts when it runs individually on large samples. The count files must be in same folder and should end with .txt file extension.

Parameters	Description
pattern	file name pattern for each count file [default: '*.txt']
gene_column_name	gene id column name for feature and meta-features [default: 'Geneid']

Returns:

Merge count file (gene_matrix_count.csv) in same folder

Functional enrichment analysis

Gene family enrichment analysis (GenFam)

latest update v1.0.0

bioinfokit.analys.genfam.fam_enrich(id_file, species, id_type, stat_sign_test, multi_test_corr, min_map_ids, alpha)

GenFam is a comprehensive classification and enrichment analysis tool for plant genomes. It provides a unique way to characterize the large-scale gene datasets such as those from transcriptome analysis (read GenFam paper for more details)

Parameters	Description
id_file	Text file containing the list of gene IDs to analyze using GenFam. IDs must be separated by newline.
species	Plant species ID for GenFam analysis. All plant species ID provided here
id_type	Plant species ID type 1: Phytozome locus ID 2: Phytozome transcript ID 3: Phytozome PAC ID
stat_sign_test	Statistical significance test for enrichment analysis [default=1]. 1: Fisher exact test 2: Hypergeometric distribution 3: Binomial distribution 4: Chi-squared distribution
multi_test_corr	Multiple testing correction test [default=3]. 1: Bonferroni 2: Bonferroni-Holm 3: Benjamini-Hochberg
min_map_ids	Minimum number of gene IDs from the user list (id_file) must be mapped to the background database for performing GenFam analysis [default=5]
alpha	Significance level [float][default: 0.05]

Returns:

Attribute	Description
df_enrich	Enriched gene families with p < 0.05
genfam_info	GenFam run information
Output files	Output figures and files from GenFam analysis genfam_enrich.png: GenFam figure for enriched gene families fam_enrich_out.txt: List of enriched gene families with mapped gene IDs, GO annotation, and detailed statistics fam_all_out.txt: List of all gene families with mapped gene IDs, GO annotation, and detailed statistics

Description and working example

Check allowed ID types for plant species for GenFam

latest update v1.0.0

bioinfokit.analys.genfam.check_allowed_ids(species)

Parameters	Description
species	Plant species ID to check for allowed ID type. All plant species ID provided here

Returns:

Allowed ID types for GenFam

Description and working example

Biostatistical analysis

Correlation matrix plot

latest update v2.0.1

bioinfokit.visuz.stat.corr_mat(table, corm, cmap, r, dim, show, figtype, axtickfontsize, axtickfontname, theme)

Parameters	Description
table	Dataframe object with numerical variables (columns) to find correlation. Ideally, you should have three or more variables. Dataframe should not have identifier column.
corm	Correlation method [pearson,kendall,spearman] [default:pearson]
cmap	Color Palette for heatmap [string][default: 'seismic']. More colormaps are available at https://matplotlib.org/3.1.0/tutorials/colors/colormaps.html
r	Figure resolution in dpi [int][default: 300]. Not compatible with show= True
dim	Figure size [Tuple of two floats (width, height) in inches][default: (6, 5)]
show	Show the figure on console instead of saving in current folder [True or False][default:False]
figtype	Format of figure to save. Supported format are eps, pdf, pgf, png, ps, raw, rgba, svg, svgz [string][default:'png']
axtickfontsize	Font size for axis ticks [float][default: 7]
axtickfontname	Font name for axis ticks [string][default: 'Arial']
theme	Change background theme. If theme set to dark, the dark background will be produced instead of white [string][default:'None']

Returns:

Correlation matrix plot image in same directory (corr_mat.png)

Working example

Bar-dot plot

latest update v0.8.5

bioinfokit.visuz.stat.bardot(df, colorbar, colordot, bw, dim, r, ar, hbsize, errorbar, dotsize, markerdot, valphabar, valphadot, show, figtype, axxlabel, axylabel, axlabelfontsize, axlabelfontname, ylm, axtickfontsize, axtickfontname, yerrlw, yerrcw)

Parameters	Description
df	Pandas dataframe object
colorbar	Color of bar graph [string or list][default:"#bbcfff"]
colordot	Color of dots on bar [string or list][default:"#ee8972"]
bw	Width of bar [float][default: 0.4]
dim	Figure size [Tuple of two floats (width, height) in inches][default: (6, 4)]
r	Figure resolution in dpi [int][default: 300]
ar	Rotation of X-axis labels [float][default: 0]
hbsize	Horizontal bar size for standard error bars [float][default: 4]
errorbar	Draw standard error bars [bool (True or False)][default: True]
dotsize	The size of the dots in the plot [float][default: 6]
markerdot	Shape of the dot marker. See more options at https://matplotlib.org/3.1.1/api/markers_api.html [string][default: "o"]
valphabar	Transparency of bars on plot [float (between 0 and 1)][default: 1]
valphadot	Transparency of dots on plot [float (between 0 and 1)][default: 1]
figtype	Format of figure to save. Supported format are eps, pdf, pgf, png, ps, raw, rgba, svg, svgz [string][default:'png']
show	Show the figure on console instead of saving in current folder [True or False][default:False]
axxlabel	Label for X-axis. If you provide this option, default label will be replaced [string][default: None]
axylabel	Label for Y-axis. If you provide this option, default label will be replaced [string][default: None]
axlabelfontsize	Font size for axis labels [float][default: 9]
axlabelfontname	Font name for axis labels [string][default: 'Arial']
ylm	Range of ticks to plot on Y-axis [float Tuple (bottom, top, interval)][default: None]
axtickfontsize	Font size for axis ticks [float][default: 9]
axtickfontname	Font name for axis ticks [string][default: 'Arial']
yerrlw	Error bar line width [float][default: None]
yerrcw	Error bar cap width [float][default: None]

Returns:

Bar-dot plot image in same directory (bardot.png)

Working Example

One sample and two sample (independent and paired) t-tests

latest update v0.9.6

bioinfokit.analys.stat.ttest(df, xfac, res, evar, alpha, test_type, mu)

Parameters	Description
df	Pandas dataframe for appropriate t-test. One sample: It should have atleast dependent (res) variable Two sample independent: It should have independent (xfac) and dependent (res) variables Two sample paired: It should have two dependent (res) variables
xfac	Independent group column name with two levels [string][default: None]
res	Dependent variable column name [string or list or Tuple][default: None]
evar	t-test with equal variance [bool (True or False)][default: True]
alpha	Significance level for confidence interval (CI). If alpha=0.05, then 95% CI will be calculated [float][default: 0.05]
test_type	Type of t-test [int (1,2,3)][default: None]. 1: One sample t-test 2: Two sample independent t-test 3: Two sample paired t-test
mu	Population or known mean for the one sample t-test [float][default: None]

Returns:

Summary output as class attribute (summary)

Description and Working example

Chi-square test

latest update v0.9.5

bioinfokit.analys.stat.chisq(df, p)

Parameters	Description
df	Pandas dataframe. It should be one or two-dimensional contingency table.
p	Theoretical expected probabilities for each group. It must be non-negative and sum to 1. If p is provide Goodness of Fit test will be performed [list or Tuple][default: None]

Returns:

Summary and expected counts as class attributes (summary and expected_df)

Working example

Linear regression analysis

bioinfokit.visuz.stat.lin_reg(df, x, y)

Parameters	Description
df	Pandas dataframe object
x	Name of column having independent X variables [list][default:None]
y	Name of column having dependent Y variables [list][default:None]

Returns:

Regression analysis summary

Working Example

Regression plot

latest update v2.0.1

bioinfokit.visuz.stat.regplot(df, x, y, yhat, dim, colordot, colorline, r, ar, dotsize, markerdot, linewidth, valphaline, valphadot, show, figtype, axxlabel, axylabel, axlabelfontsize, axlabelfontname, xlm, ylm, axtickfontsize, axtickfontname, theme)

Parameters	Description
df	Pandas dataframe object
x	Name of column having independent X variables [string][default:None]
y	Name of column having dependent Y variables [string][default:None]
yhat	Name of column having predicted response of Y variable (y_hat) from regression [string][default:None]
dim	Figure size [Tuple of two floats (width, height) in inches][default: (6, 4)]
r	Figure resolution in dpi [int][default: 300]
ar	Rotation of X-axis labels [float][default: 0]
dotsize	The size of the dots in the plot [float][default: 6]
markerdot	Shape of the dot marker. See more options at https://matplotlib.org/3.1.1/api/markers_api.html [string][default: "o"]
valphaline	Transparency of regression line on plot [float (between 0 and 1)][default: 1]
valphadot	Transparency of dots on plot [float (between 0 and 1)][default: 1]
linewidth	Width of regression line [float][default: 1]
figtype	Format of figure to save. Supported format are eps, pdf, pgf, png, ps, raw, rgba, svg, svgz [string][default:'png']
show	Show the figure on console instead of saving in current folder [True or False][default:False]
axxlabel	Label for X-axis. If you provide this option, default label will be replaced [string][default: None]
axylabel	Label for Y-axis. If you provide this option, default label will be replaced [string][default: None]
axlabelfontsize	Font size for axis labels [float][default: 9]
axlabelfontname	Font name for axis labels [string][default: 'Arial']
xlm	Range of ticks to plot on X-axis [float Tuple (bottom, top, interval)][default: None]
ylm	Range of ticks to plot on Y-axis [float Tuple (bottom, top, interval)][default: None]
axtickfontsize	Font size for axis ticks [float][default: 9]
axtickfontname	Font name for axis ticks [string][default: 'Arial']
theme	Change background theme. If theme set to dark, the dark background will be produced instead of white [string][default:'None']

Returns:

Regression plot image in same directory (reg_plot.png)

Working Example

Tukey HSD test

latest update v1.0.3

bioinfokit.analys.stat.tukey_hsd(df, res_var, xfac_var, anova_model, phalpha, ss_typ)

It performs multiple pairwise comparisons of treatment groups using Tukey's HSD (Honestly Significant Difference) test to check if group means are significantly different from each other. It uses the Tukey-Kramer approach if the sample sizes are unequal among the groups.

Parameters	Description
df	Pandas dataframe with the variables mentioned in the res_var, xfac_var and anova_model options. It should not have missing data. The missing data will be omitted.
res_var	Name of a column having response variable [string][default: None]
xfac_var	Name of a column having factor or group for pairwise comparison [string][default: None]
anova_model	ANOVA model (calculated using statsmodels ols function) [string][default: None]
phalpha	Significance level [float][default: 0.05]
ss_typ	Type of sum of square to perform ANOVA [int][default: 2]

Returns:

Attribute	Description
tukey_summary	Pairwise comparisons for main and interaction effects by Tukey HSD test

Description and Working example

Bartlett's test

latest update v1.0.3

bioinfokit.analys.stat.bartlett(df, xfac_var, res_var)

It performs Bartlett's test to check the homogeneity of variances among the treatment groups. It accepts the input table in a stacked format. More details https://docs.scipy.org/doc/scipy-0.14.0/reference/generated/scipy.stats.bartlett.html

Parameters	Description
df	Pandas dataframe containing response (res_var) and independent variables (xfac_var) in a stacked format. It should not have missing data. The missing data will be omitted.
res_var	Name of a column having response variable [string][default: None]
xfac_var	Name of a column having treatment groups (independent variables) [string or list][default: None]

Returns:

Attribute	Description
bartlett_summary	Pandas dataframe containing Bartlett's test statistics, degree of freedom, and p value

Description and Working example

Levene's test

latest update v1.0.3

bioinfokit.analys.stat.levene(df, xfac_var, res_var)

It performs Levene's test to check the homogeneity of variances among the treatment groups. It accepts the input table in a stacked format. More details https://docs.scipy.org/doc/scipy-0.14.0/reference/generated/scipy.stats.levene.html

Parameters	Description
df	Pandas dataframe containing response (res_var) and independent variables (xfac_var) in a stacked format. It should not have missing data. The missing data will be omitted.
res_var	Name of a column having response variable [string][default: None]
xfac_var	Name of a column having treatment groups (independent variables) [string or list][default: None]
center	Choice for the Levene's test [string (median, mean, trimmed)] [default: median] median: Brown-Forsythe Levene-type test mean: original Levene's test trimmed: Brown-Forsythe Levene-type test

Returns:

Attribute	Description
levene_summary	Pandas dataframe containing Levene's test statistics, degree of freedom, and p value

Description and Working example

ROC plot

latest update v2.0.1

bioinfokit.visuz.stat.roc(fpr, tpr, c_line_style, c_line_color, c_line_width, diag_line, diag_line_style, diag_line_width, diag_line_color, auc, shade_auc, shade_auc_color, axxlabel, axylabel, axtickfontsize, axtickfontname, axlabelfontsize, axlabelfontname, plotlegend, legendpos, legendanchor, legendcols, legendfontsize, legendlabelframe, legend_columnspacing, dim, show, figtype, figname, r, ylm, theme)

Receiver operating characteristic (ROC) curve for visualizing classification performance

Parameters	Description
fpr	Increasing false positive rates obtained from sklearn.metrics.roc_curve [list][default:None]
tpr	Increasing true positive rates obtained from sklearn.metrics.roc_curve [list][default:None]
c_line_style	Line style for ROC curve [string][default:'-']
c_line_color	Line color for ROC curve [string][default:'#f05f21']
c_line_width	Line width for ROC curve [float][default:1]
diag_line	Plot reference line [True or False][default: True]
diag_line_style	Line style for reference line [string][default:'--']
diag_line_width	Line width for reference line [float][default:1]
diag_line_color	Line color for reference line [string][default:'b']
auc	Area under ROC. It can be obtained from sklearn.metrics.roc_auc_score [float][default: None]
shade_auc	Shade are for AUC [True or False][default: False]
shade_auc_color	Shade color for AUC [string][default: '#f48d60']
axxlabel	Label for X-axis [string][default: 'False Positive Rate (1 - Specificity)']
axylabel	Label for Y-axis [string][default: 'True Positive Rate (Sensitivity)']
axtickfontsize	Font size for axis ticks [float][default: 9]
axtickfontname	Font name for axis ticks [string][default: 'Arial']
axlabelfontsize	Font size for axis labels [float][default: 9]
axlabelfontname	Font name for axis labels [string][default: 'Arial']
plotlegend	plot legend [True or False][default:True]
legendpos	position of the legend on plot. For more options see loc parameter at https://matplotlib.org/3.1.1/api/_as_gen/matplotlib.pyplot.legend.html [string ][default:'lower right']
legendanchor	position of the legend outside of the plot. For more options see bbox_to_anchor parameter at https://matplotlib.org/3.1.1/api/_as_gen/matplotlib.pyplot.legend.html [list][default:None]
legendcols	Number of columns for legends [int][default: 1]
legendfontsize	Font size for the legends [float][default:8]
legendlabelframe	Box frame for the legend [True or False][default: False]
legend_columnspacing	Spacing between the legends [float][default: None]
dim	Figure size [Tuple of two floats (width, height) in inches][default: (5, 4)]
show	Show the figure on console instead of saving in current folder [True or False][default:False]
figtype	Format of figure to save. Supported format are eps, pdf, pgf, png, ps, raw, rgba, svg, svgz [string][default:'png']
figname	name of figure [string ][default:'roc']
r	Figure resolution in dpi [int][default: 300]. Not compatible with show= True
ylm	Range of ticks to plot on Y-axis [float (bottom, top, interval)][default: None]
theme	Change background theme. If theme set to dark, the dark background will be produced instead of white [string][default:'None']

Returns:

ROC plot image in same directory (roc.png) Working example

Regression metrics

Calculate Root Mean Square Error (RMSE), Mean squared error (MSE), Mean absolute error (MAE), and Mean absolute percent error (MAPE) from regression fit

latest update v1.0.8

bioinfokit.analys.stat.reg_metric(y, yhat, resid)

Parameters	Description
y	Original values for dependent variable [numpy array] [default: None]
yhat	Predicted values from regression [numpy array] [default: None]
resid	Regression residuals [numpy array][default: None]

Returns:

Pandas dataframe with values for RMSE, MSE, MAE, and MAPE

Working example

Venn Diagram

bioinfokit.visuz.venn(vennset, venncolor, vennalpha, vennlabel)

Parameters	Description
vennset	Venn dataset for 3 and 2-way venn. Data should be in the format of (100,010,110,001,101,011,111) for 3-way venn and 2-way venn (10, 01, 11) [default: (1,1,1,1,1,1,1)]
venncolor	Color Palette for Venn [color code][default: ('#00909e', '#f67280', '#ff971d')]
vennalpha	Transparency of Venn [float (0 to 1)][default: 0.5]
vennlabel	Labels to Venn [string][default: ('A', 'B', 'C')]

Returns:

Venn plot (venn3.png, venn2.png)

Working example

How to cite bioinfokit?

• Renesh Bedre. (2020, March 5). reneshbedre/bioinfokit: Bioinformatics data analysis and visualization toolkit. Zenodo. http://doi.org/10.5281/zenodo.3698145.
• Additionally check Zenodo to cite specific version of bioinfokit

References:

• Travis E. Oliphant. A guide to NumPy, USA: Trelgol Publishing, (2006).
• John D. Hunter. Matplotlib: A 2D Graphics Environment, Computing in Science & Engineering, 9, 90-95 (2007), DOI:10.1109/MCSE.2007.55 (publisher link)
• Fernando Pérez and Brian E. Granger. IPython: A System for Interactive Scientific Computing, Computing in Science & Engineering, 9, 21-29 (2007), DOI:10.1109/MCSE.2007.53 (publisher link)
• Michael Waskom, Olga Botvinnik, Joel Ostblom, Saulius Lukauskas, Paul Hobson, MaozGelbart, … Constantine Evans. (2020, January 24). mwaskom/seaborn: v0.10.0 (January 2020) (Version v0.10.0). Zenodo. http://doi.org/10.5281/zenodo.3629446
• Fabian Pedregosa, Gaël Varoquaux, Alexandre Gramfort, Vincent Michel, Bertrand Thirion, Olivier Grisel, Mathieu Blondel, Peter Prettenhofer, Ron Weiss, Vincent Dubourg, Jake Vanderplas, Alexandre Passos, David Cournapeau, Matthieu Brucher, Matthieu Perrot, Édouard Duchesnay. Scikit-learn: Machine Learning in Python, Journal of Machine Learning Research, 12, 2825-2830 (2011)
• Wes McKinney. Data Structures for Statistical Computing in Python, Proceedings of the 9th Python in Science Conference, 51-56 (2010)
• Pauli Virtanen, Ralf Gommers, Travis E. Oliphant, Matt Haberland, Tyler Reddy, David Cournapeau, Evgeni Burovski, Pearu Peterson, Warren Weckesser, Jonathan Bright, Stéfan J. van der Walt, Matthew Brett, Joshua Wilson, K. Jarrod Millman, Nikolay Mayorov, Andrew R. J. Nelson, Eric Jones, Robert Kern, Eric Larson, CJ Carey, İlhan Polat, Yu Feng, Eric W. Moore, Jake VanderPlas, Denis Laxalde, Josef Perktold, Robert Cimrman, Ian Henriksen, E.A. Quintero, Charles R Harris, Anne M. Archibald, Antônio H. Ribeiro, Fabian Pedregosa, Paul van Mulbregt, and SciPy 1.0 Contributors. (2020) SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods, 17(3), 261-272.
• David C. Howell. Multiple Comparisons With Unequal Sample Sizes. https://www.uvm.edu/~statdhtx/StatPages/MultipleComparisons/unequal_ns_and_mult_comp.html

Last updated: August 16, 2021