Graphical Anova

Description

Dots plot displaying the deviations of factor levels from the mean showing the residuals as reference distribution.

Usage

    anovaPlot(obj, stacked = TRUE, base = TRUE, axes = TRUE,
    faclab = TRUE, labels = FALSE, cex = par("cex"),
    cex.lab = par("cex.lab"), ...)

Arguments

Details

Dots plot are displayed for the scaled deviations of factor levels from the grand mean and the distribution of the residuals is shown at the bottom of the plot for graphical comparison. The scaled factor for the factor deviations is \sqrt{n/k}, where k and n are the factor and residuals degrees of freedom reported by anova(obj). If labels=TRUE then the factor levels are used for as points instead of dots. This option is useful to post labelling the dot plots. See dots function. The Anova plot is built in a (0,1)\times(0,1) plot area. The area plot is divided to accommodate each of the factors and the residual at the bottom of the plotting area. The function returns a list with the coordinates of all the dots displayed.

Value

The function is called for graphical display of factor levels mean and residuals as reference distribution. An invisible list with the actual (x,y) coordinates used for each of the factors and residuals.

warning

The function identifies as an interaction factor any factor with the colon character ":" in its name. Factors like "I(A:B)" will give you problems.

Note

The anova plot presented here is thought for graphical comparison of factor effects in one-layer balanced designed experiments. The function is not prepared for general situations. However, representation of some simple split-plot experiments is possible.

Author(s)

Ernesto Barrios

References

Box G. E. P. (2000). Box on Quality. Edited by G. C. Tiao et al. New York: Wiley.

Box G. E. P, Hunter, J. S. and Hunter, W. C. (2005). Statistics for Experimenters II. New York: Wiley.

See Also

dots, dotPlot

Examples

library(BHH2)
data(heads.data)
heads.data$periods <- factor(heads.data$periods)
heads.data$heads <- factor(heads.data$heads)

heads.aov <- aov(resp~periods+heads,data=heads.data)
anovaPlot(heads.aov)

anovaPlot(heads.aov,labels=TRUE,faclab=TRUE)

Corrosion data

Description

Corrosion resistance study data set.

Usage

data(corrosion.data)

Format

A data frame with 24 observations on the following 4 variables.

run

factor with 6 levels. The casting order.

heats

factor with 3 levels. The casting temperature.

coating

factor with 4 levels. The coating treatment.

resistance

numeric vector. Corrosion resistance response.

References

Box G. E. P, Hunter, J. S. and Hunter, W. C. (2005). Statistics for Experimenters II. New York: Wiley.

Examples

data(corrosion.data)
str(corrosion.data)
plot(corrosion.data)

Dot plot: scatter plot with stacked dots similar to the stem-and-leaf plot

Description

Displays an one-dimensional scatter plot with stacking similar to stem-and-leaf plot or histograms.

Usage

dotPlot(x, y = 0, xlim = range(x,na.rm=TRUE), xlab = NULL, 
    scatter = FALSE, hmax = 1, base = TRUE, axes = TRUE, frame = FALSE, 
    pch = 21, pch.size = "x", labels = NULL, hcex = 1, cex =par("cex"), 
    cex.axis = par("cex.axis"),...)

Arguments

Details

Basically function dotPlot calls function dots to display a stacked one-dimensional scatter plot within vertical limits 0 and 1. See dots for more details.

Value

The function is called for its side effect which is to produce one-dimensional scatter plot with stacking as described, for example, in Chambers et al. (1983) It returns invisible a data frame with the actual coordinates (in users units).

Note

Since the dots are stacked vertically, their alignment is subject to rounding errors. Dots may be slightly moved in either side from their actual value.

Author(s)

Ernesto Barrios

References

Chambers, J. M., Cleveland, W. S., Kleiner, B. and Tukey, P. A. (1983) Graphical Methods for Data Analysis. New York: Chapman \& Hall

See Also

dots, stem,hist,dotchart

Examples

library(BHH2)
data(tab03B1)
attach(tab03B1)
stem(yield) #stem-leaf plot
plt <- dotPlot(yield) # equivalent dotPlot

# same dot plot with max and min observations labelled
plt <- dotPlot(yield,xlim=c(75,95),xlab="yield",pch.size="x",hcex=1)
text(c(min(yield),max(yield),80),rep(0.05,3),c("min","max",80))
segments(80,min(plt$y),80,max(plt$y),lty=2)
detach()

Dots display

Description

The function adds to the current plot an one-dimensional scatter plot with stacking similar to a stem-leaf plot or histograms but using characters. .

Usage

    dots(x = , y = 0.1, xlim = range(x,na.rm=TRUE), stacked = FALSE, hmax= 0.5,
    base = TRUE, axes = FALSE, pch = 21, pch.size = "x", labels = NULL,
    hcex = 1, cex = par("cex"), cex.axis = par("cex.axis"))

Arguments

Details

Function dots adds to the current plot a dot plot similar to a stem-and-leaf plot using characters specified by pch and labels=NULL. If labels is not NULL then it is expected to be a character vector and will will be used to display each of the points. Its use is repeated or cut short if necessary. The function computes the width and height size using character pch.size calling strwidth and strheight, but displays pch instead. Mainly this is used when pch is not given by a quoted character, for example, pch=21. Also, currently the par("mkh") is ignored so hcex is used to compute the "working" height of the characters: hcex*strheight(pch.size,units="user"). If stacked=TRUE, the base line is divided in subintervals of size strwidth(pch.size) and computed the number of points in each subinterval. If maximum number of stacked characters exceed hmax then the characters are overlapped to adjust their total height to hmax.

Value

Invisible data frame with columns (x,y,labels). ‘x’ and ‘y’ are the coordinates in user units of each point and ‘labels’ the corresponding character displayed.

Author(s)

Ernesto Barrios

See Also

dotPlot, anovaPlot

Examples

library(BHH2)
set.seed(4)
# Defines the height of the plot area between c(0,1)
dotPlot(rnorm(100),xlab="x")

x <- rnorm(100)

# plots (possibly) overlapping points at y=0.3
dots(x,y=0.3)
# plots (possibly) overlapping points at y=0.4
dots(x,y=0.4,stacked=TRUE,base=FALSE)
# plots (hopefully) stacked points at y=0.5 allowing the dots to as high as 0.9
dots(x,y=0.5,stacked=TRUE,base=FALSE,hmax=.9)

Full or fractional factorial design matrix generation

Description

The function generates the design matrix provided the number of 2-levels design factors and defining relations.

Usage

ffDesMatrix(k, gen = NULL)

Arguments

Details

A defining relation is declared by a vector where the first entry corresponds to the left hand side (LHS) of the defining equation. For example, if k=5, and gen=list(c(-5,1,2,3,4)), then the defining equation is -5=1*2*3*4. A full 2-levels (-1,1) factorial design is generated. For each defining relation the LHS column is replaced by the corresponding columns product. At the end repeated runs are removed from the matrix.

Value

The function returns a 2-levels design matrix with k columns.

Author(s)

Ernesto Barrios

See Also

conf.design of the conf.design package, FrF2 from the FrF2 package.

Examples

ffDesMatrix(5) # Full 2^5 factorial design
ffDesMatrix(5,gen=list(c(5,1,2,3,4))) # 2^(5-1) factorial design
ffDesMatrix(5,gen=list(c(4,1,2),c(-5,1,3))) # 2^(5-2) factorial design

Full model matrix from a design matrix

Description

The function builds the full matrix with the constant term, main effects and interactions from a design matrix.

Usage

    ffFullMatrix(X, x, maxInt, blk = NULL)

Arguments

Details

Columns x of matrix X are used for main effects. All the 2, ... , maxInt order interaction are constructed. The first columns of the final matrix correspond to the constant term (1's) and block factors.

Value

The function returns list with the following components:

. Augmented matrix with columns for the constant terms, blocking factors, main effects, second order interactions, ..., etc.

Author(s)

Ernesto Barrios

See Also

ffDesMatrix

Examples

print(X <- ffDesMatrix(5,gen=list(c(5,1,2,3,4))))
ffFullMatrix(X[,1:4],x=c(1,2,3,4),maxInt=2,blk=X[,5])
ffFullMatrix(X[,1:5],x=c(1,3,5),maxInt=3)

Machine heads data

Description

Data set of the variability of machine heads in a quality improvement experiment.

Usage

data(heads.data)

Format

A data frame with 30 observations on the following 6 variables.

obs

numeric. Observation number.

periods

factor. Periods factor (P1, ..., P6).

heads

factor. Type of head factor (H1, ..., H5).

days

factor. Day factor (D1 and D2).

shifts

factor. Shift factor (S1, S2, and S3).

resp

numeric. Response.

Source

Box, G. E. P. (1993). "How to Get Lucky". Quality Engineering, Vol. 5, No. 3, pp 517-524.

References

Box G. E. P, Hunter, J. S. and Hunter, W. C. (2005). Statistics for Experimenters II. New York: Wiley.

Examples

data(heads.data)
str(heads.data)
plot(heads.data)

Lambda plot: traces the t and F statistics in Box-Cox transformation of the response

Description

Trace regression coefficients' t-values or F-ratios for different values of \lambda in the Box-Cox transformation.

Usage

lambdaPlot(mod, lambda = seq(-1, 1, by = 0.1), stat = "F", global = TRUE,
    cex = par("cex"), ...)

Arguments

Details

The response is transformed as Y=(y^{\lambda}-1)/\lambda for each value of \lambda (lambda) and the model refitted. The t-values or F-ratios of the coefficients are saved for the display. If global=TRUE, then the F-ratio of the whole model is plotted instead.

Value

The function returns an invisible list with components:

Note

For each value of \lambda the model is refitted. Computations can be done more efficiently and will be incorporated in future versions.

Author(s)

Ernesto Barrios

References

Box, G. E. P. and C. Fung (1995) "The Importance of Data Transformation in Designed Experiments for Life Testing". Quality Engineering, Vol. 7, No. 3, pp. 625-68.

Box G. E. P, Hunter, J. S. and Hunter, W. C. (2005). Statistics for Experimenters II. New York: Wiley.

Examples

library(BHH2)
# Lambda Plot tracing t values.
data(woolen.data)
woolen.lm <- lm(y~x1+x2+x3+I(x1^2)+I(x2^2)+I(x3^2)+
                    I(x1*x2)+I(x1*x3)+I(x2*x3)+I(x1*x2*x3),data=woolen.data)
lambdaPlot(woolen.lm,cex=.8,stat="t")

# Lambda Plot tracing F values.
woolen2.lm <- lm(y~x1+x2+x3,data=woolen.data)
lambdaPlot(woolen2.lm,lambda=seq(-1,1,length=41),stat="F",global=TRUE)

# Lambda Plot tracing F values.
data(poison.data)
poison.lm <- lm(y~treat*poison,data=poison.data)
lambdaPlot(poison.lm,lambda=seq(-3,1,by=.1),stat="F",global=FALSE)

Penicillin data

Description

Penicillin yield example data set.

Usage

data(penicillin.data)

Format

A data frame with 20 observations on the following 4 variables.

blend

factor with 5 levels: B1 B2 B3 B4 B5. Blend factor used to block the experiment.

run

numeric vector. Run order within the blocking (Blend) factor.

treat

factor with levels: A B C D. The process variants called treatment.

yield

numeric vector. Experiment yield response.

Source

Box G. E. P, Hunter, W. C. and Hunter, J. S. (1978). Statistics for Experimenters. New York: Wiley.

References

Box G. E. P, Hunter, J. S. and Hunter, W. C. (2005). Statistics for Experimenters II. New York: Wiley.

Examples

data(penicillin.data)
str(penicillin.data)
plot(penicillin.data)

Permutation test: randomization test for small size samples

Description

Permutation test for means and variance comparisons.

Usage

       permtest(x, y = NULL)

Arguments

Details

In the one–sample problem, the function builds all 2^n possible \pm x_i combinations. For the two–sample problem, all possible B(n+m,n) samples size n (=length(x)) and m (=length(y)) are generated and the permutation distributions for the t-statistics and F-ratios. p-values are computed based on these distributions.

Value

The function returns the number N of different samples generated for the permutation distribution, the observed t-statistic, its p-value, based on both, the parametric and permutation distributions as well as the observed F-ratio and its corresponding p-values. The test may take a long time to generate all the possible combinations. It has been tested for n + m = 22 and n < 12.

WARNING

The test may take a long time to generate all the possible combinations.

Author(s)

Ernesto Barrios

References

Box G. E. P, Hunter, J. S. and Hunter, W. C. (2005). Statistics for Experimenters II. New York: Wiley.

See Also

onet.permutation and towt.permutation of DAAG package, and perm.test of the exactRankTests.

Examples

library(BHH2)

# Permutation test for Tomato Data
data(tomato.data)
cat("Tomato Data (not paired):\n")
attach(tomato.data)
a <- pounds[fertilizer=="A"]
b <- pounds[fertilizer=="B"]
print(round(test <- permtest(b,a),3))
detach()

# Permutation test for Boy's Shoes Example
data(shoes.data)
cat("Shoes Data (paired):\n")
attach(shoes.data)
x <- matB-matA
print(round(test <- permtest(x),3))
detach()

Poison example data set

Description

Poison data from Biological Experiment

Usage

data(poison.data)

Format

This data frame contains the following columns:

poison

factor with 3 levels: P1, P2 and P3.

treat

factor with 4 levels: trA, trB, trC and trD.

y

numeric. Survival time as response.

Source

Box, G. E. P. and D. R. Cox, An Analysis of Transformations (with discussion), Journal of the Royal Statistical Society, Series B, Vol. 26, No. 2, pp. 211–254.

References

Box G. E. P, Hunter, J. S. and Hunter, W. C. (2005). Statistics for Experimenters II. New York: Wiley.

Examples

data(poison.data)
str(poison.data)
plot(poison.data)

Boys' shoes data set

Description

Data for the Boys' Shoes Example.

Usage

data(shoes.data)

Format

A data frame with 10 observations on the following 5 variables.

boy

numeric. Boy number.

matA

numeric. Amount of wear of shoe made from material A.

sideA

factor. Foot side which shoe of material A is used.

matB

numeric. Amount of wear of shoe made from material B.

sideB

factor. Foot side which shoe of material B is used.

Source

Box G. E. P, Hunter, W. C. and Hunter, J. S. (1978). Statistics for Experimenters. New York: Wiley.

References

Box G. E. P, Hunter, J. S. and Hunter, W. C. (2005). Statistics for Experimenters II. New York: Wiley.

Examples

data(shoes.data)
str(shoes.data)
plot(shoes.data)

Generation of all the combinations of k elements from n possible

Description

Generates all different subsets of size r chosen from n different elements.

Usage

subsets(n, r, v = 1:n)

Arguments

Value

A matrix of dimension (N \times r), where N is the total number of different combinations of r elements chosen from n possible.

Note

This particular version of the function was taken from a message from Bill Venables to ‘r-help’ list on Sun, 17 Dec 2000.

Author(s)

Bill Venables Bill.Venables@cmis.csiro.au

References

Venables, Bill. "Programmers Note", R-News, Vol 1/1, Jan. 2001. http://cran.r-project.org/doc/Rnews

See Also

combinations of the gtools package.

Examples

library(BHH2)
subsets(5,3)
subsets(5,3,letters)
subsets(5,3,c(10,20,30,50,80))

Table 3.2

Description

Production record of 210 consecutive batch yield values

Usage

data(tab03B1)

Format

This data frame contains the following columns:

yield

a numeric vector

ave10

a numeric vector. Moving average of last 10 observations. First 9 entries NA

Details

The tab03B1 data frame has 210 rows and 2 columns.

Source

Box G. E. P, Hunter, W. C. and Hunter, J. S. (1978). Statistics for Experimenters. New York: Wiley.

References

Box G. E. P, Hunter, J. S. and Hunter, W. C. (2005). Statistics for Experimenters II. New York: Wiley.

Examples

library(BHH2)
data(tab03B1)
attach(tab03B1)
stem(yield)
stem(ave10)
plot(yield,xlab="time order",ylab="yield")
detach()

Table 3.3

Description

Reference set of differences between averages of two adjacent sets of 10 successive batches.

Usage

data(tab03B2)

Format

This data frame contains the following columns:

diff10

a numeric vector

Details

The tab03B2 data frame has 200 rows and 1 column. First 9 entries are NA.

Source

Box G. E. P, Hunter, W. C. and Hunter, J. S. (1978). Statistics for Experimenters. New York: Wiley.

References

Box G. E. P, Hunter, J. S. and Hunter, W. C. (2005). Statistics for Experimenters II. New York: Wiley.

Examples

library(BHH2)
data(tab03B2)
attach(tab03B2)
# displays the differences as dot plot (similar to histograms)
plt <- dotPlot(diff10,xlim=2.55*c(-1,+1),xlab="differences")
segments(1.3,0,1.3,max(plt$y))  #vertical line at x=1.3
detach()

Tomato plants data set

Description

Yield of tomato plants under two different fertilizers.

Usage

data(tomato.data)

Format

This data frame contains the following columns:

pos

numeric. Row position

pounds

numeric. Plant's yield in pounds.

fertilizer

factor. Type of fertilizer (A or B).

Source

Box G. E. P, Hunter, W. C. and Hunter, J. S. (1978). Statistics for Experimenters. New York: Wiley.

References

Box G. E. P, Hunter, J. S. and Hunter, W. C. (2005). Statistics for Experimenters II. New York: Wiley.

Examples

data(tomato.data)
str(tomato.data)
plot(tomato.data)

Textile experiment data set

Description

Woolen thread experiment data set.

Usage

data(woolen.data)

Format

This data frame with 27 observations contains the following columns:

x1

numeric. Length of test specimens factor.

x2

numeric. Amplitude of loading cycle factor.

x3

numeric. Load factor.

y

numeric. Cycles to failure response.

Source

Box, G. E. P. and D. R. Cox (1964). "An Analysis of Transformations (with discussion)", Journal of the Royal Statistical Society, Series B, Vol. 26, No. 2, pp. 211–254.

References

Box G. E. P, Hunter, J. S. and Hunter, W. C. (2005). Statistics for Experimenters II. New York: Wiley.

Examples

data(woolen.data)
str(woolen.data)
plot(woolen.data)