T Plot Method

• T Plot Method Definition
• Barrett Joyner Halenda Method
• Wilson Plot Method
• T Plot Method Crossword
• T-plot Method Microporous

A visualization of a correlation matrix.

• . Photo Plot Method. 3 INTRODUCTION C. Guidelines The techniques described here are guides for establishing and sampling vegetation attributes. They are not standards.
• The t-plot method is a well-known technique which allows determining the micro- and/or mesoporous volumes and the specific surface area of a sample by comparison with a reference adsorption.

A graphical display of a correlation matrix, confidence interval. The detailsare paid great attention to. It can also visualize a general matrix bysetting is.corr = FALSE.

We can plot multiple bar charts by playing with the thickness and the positions of the bars. The data variable contains three series of four values. The following script will show three bar charts of four bars. The bars will have a thickness of 0.25 units. Each bar chart will be shifted 0.25 units from the previous one. The time series plot method does not attempt to update labels and titles when hold is on because the descriptors for the series can be different. Plot intersection1 and intersection2 in the same figure. Prevent overwriting the plot, but remove axis labels and title. Add a legend and set the DisplayName property of the line series to label each.

Arguments

The correlation matrix to visualize, must be square iforder is not 'original'. For general matrix, please usingis.corr = FALSE to convert.

Character, the visualization method of correlation matrix to be used. Currently, it supports seven methods, named 'circle' (default), 'square', 'ellipse', 'number', 'pie', 'shade' and 'color'. See examples for details.

The areas of circles or squares show the absolute value of corresponding correlation coefficients. Method 'pie' and 'shade' came from Michael Friendly's job (with some adjustment about the shade added on), and 'ellipse' came from D.J. Murdoch and E.D. Chow's job, see in section References.

Character, 'full' (default), 'upper' or'lower', display full matrix, lower triangular or upper triangularmatrix.

Logical, if TRUE, the graph is added to an existing plot,otherwise a new plot is created.

Vector, the color of glyphs. It is distributed uniformly incl.lim. If NULL, col will becolorRampPalette(col2)(200), see example about col2.

The background color.

Character, title of the graph.

Logical, whether the input matrix is a correlation matrix ornot. We can visualize the non-correlation matrix by settingis.corr = FALSE.

Logical, whether display the correlation coefficients on theprincipal diagonal.

Logical or character, whether plot outline of circles, squareand ellipse, or the color of these glyphs. For pie, this represents thecolor of the circle outlining the pie. If outline is TRUE,the default value is 'black'.

See par.

The color of the grid. If NA, don't add grid. IfNULL the default value is chosen. The default value depends onmethod, if method is color or shade, the colorof the grid is NA, that is, not draw grid; otherwise 'grey'.

Color of coefficients added on the graph. If NULL(default), add no coefficients.

Logic, whether translate coefficients into percentagestyle for spacesaving.

Character, the ordering method of the correlation matrix.

• 'original' for original order (default).

• 'AOE' for the angular order of the eigenvectors.

• 'FPC' for the first principal component order.

• 'hclust' for the hierarchical clustering order.

• 'alphabet' for alphabetical order.

See function corrMatOrder for details.

Character, the agglomeration method to be used whenorder is hclust. This should be one of 'ward','ward.D', 'ward.D2', 'single', 'complete','average', 'mcquitty', 'median' or 'centroid'.

Integer, the number of rectangles draws on the graph accordingto the hierarchical cluster, only valid when order is hclust.If NULL (default), then add no rectangles.

Color for rectangle border(s), only valid when addrectis equal or greater than 1.

Numeric, line width for borders for rectangle border(s), onlyvalid when addrect is equal or greater than 1.

Character or logical, position of text labels. If character, itmust be one of 'lt', 'ld', 'td', 'd' or'n'. 'lt'(default if type'full') means left and top,'ld'(default if type'lower') means left and diagonal,'td'(default if type'upper') means top and diagonal(near),'d' means diagonal, 'n' means don't add textlabel.

Numeric, for the size of text label (variable names).

The color of text label.

Numeric, for text label, see text.

Numeric, for text label string rotation in degrees, seetext.

Character or logical, position of color labels; If character,it must be one of 'r' (default if type'upper' or'full'), 'b' (default if type'lower') or 'n','n' means don't draw colorlabel.

The limits (x1, x2) in the colorlabel.

Integer, the number of number-text in colorlabel, passed tocolorlegend. If NULL, cl.length islength(col) + 1 when length(col) <=20; cl.length is 11when length(col) > 20

Numeric, cex of number-label in colorlabel, passed tocolorlegend.

Numeric, to justify the width of colorlabel, 0.1~0.2 issuggested.

Character, 'l', 'c' (default) or'r', for number-label in colorlabel, 'l' means left,'c' means center, and 'r' means right.

Numeric, for number-label in colorlabel, seetext.

The cex parameter to send to the call to textwhen writing the correlation coefficients into the plot.

the font parameter to send to the call totext when writing the correlation coefficients into the plot.

indicating the number of decimal digits to beadded into the plot. Non-negative integer or NULL, default NULL.

Character for shade style, 'negative','positive' or 'all', only valid when method is'shade'. If 'all', all correlation coefficients' glyph willbe shaded; if 'positive', only the positive will be shaded; if'negative', only the negative will be shaded. Note: the angle ofshade line is different, 45 degrees for positive and 135 degrees fornegative.

Numeric, the line width of shade.

T Plot Method Definition

The color of shade line.

Matrix of p-value, if NULL, arguments sig.level,insig, pch, pch.col, pch.cex is invalid.

Significant level, if the p-value in p-mat is biggerthan sig.level, then the corresponding correlation coefficient isregarded as insignificant. If insig is 'label_sig', this maybe an increasing vector of significance levels, in which case pchwill be used once for the highest p-value interval and multiple times(e.g. '*', '**', '***') for each lower p-value interval.

Character, specialized insignificant correlation coefficients,'pch' (default), 'p-value', 'blank', 'n', or'label_sig'. If 'blank', wipe away the corresponding glyphs;if 'p-value', add p-values the corresponding glyphs;if 'pch', add characters (see pch for details) oncorresponding glyphs; if 'n', don't take any measures; if'label_sig', mark significant correlations with pch(see sig.level).

Add character on the glyphs of insignificant correlationcoefficients(only valid when insig is 'pch'). Seepar.

The color of pch (only valid when insig is'pch').

The cex of pch (only valid when insig is 'pch').

Character, method of ploting confidence interval. If'n', don't plot confidence interval. If 'rect', plot rectangleswhose upper side means upper bound and lower side means lower bound,respectively, and meanwhile correlation coefficients are also added on therectangles. If 'circle', first plot a circle with the bigger absolutebound, and then plot the smaller. Warning: if the two bounds are the samesign, the smaller circle will be wiped away, thus forming a ring. Method'square' is similar to 'circle'.

Matrix of the lower bound of confidence interval.

Matrix of the upper bound of confidence interval.

Label to be used for rendering NA cells. Default is'?'. If 'square', then the cell is rendered as a square with thena.label.col color.

Color used for rendering NA cells. Default is'black'.

Aspect ration for the whole plot. Value other than 1 iscurrently compatible only with methods 'circle' and 'square'.

Additional arguments passing to function text for drawingtext lable.

Details

corrplot function offers flexible ways to visualize correlation matrix, lower and upper bound of confidence interval matrix.

Value

(Invisibly) returns a reordered correlation matrix.

Note

Cairo and cairoDevice packages is strongly recommended to produce high-quality PNG, JPEG, TIFF bitmap files, especially for that methodcircle, ellipse.

Row- and column names of the input matrix are used as labels rendered in the corrplot. Plothmath expressions will be used if the name is prefixed by one of the following characters: :, = or $. For example ':alpha + beta'.

References

Michael Friendly (2002).Corrgrams: Exploratory displays for correlation matrices.The American Statistician, 56, 316--324.

D.J. Murdoch, E.D. Chow (1996).A graphical display of large correlation matrices.The American Statistician, 50, 178--180.

See Also

Function plotcorr in the ellipse package and corrgram in the corrgram package have some similarities.

Package seriation offered more methods to reorder matrices, such as ARSA, BBURCG, BBWRCG, MDS, TSP, Chen and so forth.

Aliases

• corrplot

Barrett Joyner Halenda Method

Wilson Plot Method

T Plot Method Crossword

© A.W.Marczewski 2002

A Practical Guide to Isotherms of ADSORPTION on Heterogeneous Surfaces

t-plot and t/F-plot

(see an example in a surface area / pore volume analysis report)
(see a short summary of t-plot, t/F-plot and α_s methods)
(see a comparison of t-plot and α_s-plot)

t-plot

This method of isotherm data analysis was introduced by de Boer. It assumes, that in a certain isotherm region, the micropres are already filled-up, whereas the adsorption in larger pores occurs according to some simple equation, characteristic for a large class of solids. This equation should approximate adsorption in mesopores, macropores and on a flat surface in a narrow pressure range just above complete filling of micropores, but below vapour condensation in mesopores. Such assumption may be valid, if micropores are small and super-micropores are not present. Then the adsorption within this pressure region may be described by a simple linear dependence :
a(x) = a_micro,max + k S_ext t_layer(x)
where:
x = p/p_s
a_micro,max - adsorption in saturated micropores,
S_ext - 'external' surface area; here it is the surface area of pores larger than micropores,
t_layer(x) - estimated statistical thickness of adsorbed layer (in meso- and macropores) - usually by Harkins-Jura (HJ) and Halsey / Frenkel-Halsey-Hill (FHH) equations - often used are their experimental versions HJ and Halsey; in the t-plot calculated thickness values are within 0.354 nm (i.e. t_mono) and 0.5 nm (it corresponds roughly to the range of relative pressures 0.1 - 0.2); for solids with small amounts of micropores, the Halsey isotherm may give negative value as an estimate of micropore volume/area, thus it sould be used with caution.
k - coefficient which depends on units used for the values of adsorption a(x), layer thickness t(x) and surface area S_ext. E.g. for t [nm] , S [m²/g] and a [cm³/g STP] we obtain: k = 1 / (4.3532 t_mono), where t_mono = 0.354 nm is monolayer thickness for N₂ adsorbed layers and 4.3532 is a coefficient for calculation of occupied area [m²/g] from adsorbed amount [cm³/g STP] (N₂ adsorption at 78K).

T-plot Method Microporous

t/F-plot

Introduced by Kadlec in order to increase precision of t-plot analysis. In this method the Dubinin-Radushkevich isotherm is fitted in the micropore range (low pressures / adsorption range). This method may help to compensate for t-plots non-linearity in the case of solids containing some super-micropores. However much wider data range is required and t-plot method looses its great simplicity.

A preferred method (see comparison) should be α_s-method. This method requires some standard isotherm data for comparisons, however it gives information largely free of adsorption model influences and additionally provides description of mesopore and - to some extent - macropore system.

Send a message to Adam.Marczewski AT@AT umcs.lublin.pl