Plotting Composite Material Data
Ally Fraser
2-May-2020
This vignette demonstrates how to create some of the graphs commonly
used when analyzing composite material data. Here, we rely on the ggplot2 package
for graphing. This package can be loaded either on its own, or through
the tidyverse meta-package, which also includes packages
such as dplyr that we will also use.
We’ll need to load a few packages in order to proceed.
library(dplyr)
library(ggplot2)
library(tidyr)
library(cmstatr)
Throughout this vignette, we’ll use one of the example data sets that
comes with cmstatr and we’ll focus on the warp-tension data
as an example. We’ll load the example data in a variable as follows. By
default the condition will be in an arbitrary order, but throughout the
visualization, we’ll want the conditions shown in a particular order
(from coldest and driest to hottest and wettest). We can define the
order of the conditions using the ordered function. For
brevity, only the first few rows of the data set are displayed
below.
dat <- carbon.fabric.2 %>%
filter(test == "WT") %>%
mutate(condition = ordered(condition, c("CTD", "RTD", "ETW", "ETW2")))
dat %>%
head(10)
#> test condition batch panel thickness nplies strength modulus failure_mode
#> 1 WT CTD A 1 0.112 14 142.817 9.285 LAT
#> 2 WT CTD A 1 0.113 14 135.901 9.133 LAT
#> 3 WT CTD A 1 0.113 14 132.511 9.253 LAT
#> 4 WT CTD A 2 0.112 14 135.586 9.150 LAB
#> 5 WT CTD A 2 0.113 14 125.145 9.270 LAB
#> 6 WT CTD A 2 0.113 14 135.203 9.189 LGM
#> 7 WT CTD A 2 0.113 14 128.547 9.088 LAB
#> 8 WT CTD B 1 0.113 14 127.709 9.199 LGM
#> 9 WT CTD B 1 0.113 14 127.074 9.058 LGM
#> 10 WT CTD B 1 0.114 14 126.879 9.306 LGM
We’ll then calculate the B-Basis value using the pooling by standard
deviation method. This data set happens to fail some of the diagnostic
tests, but for the purpose of this example, we’ll ignore those failures
using the override argument.
b_basis_pooled <- dat %>%
basis_pooled_cv(strength, condition, batch,
override = c("between_group_variability",
"normalized_variance_equal"))
b_basis_pooled
#>
#> Call:
#> basis_pooled_cv(data = ., x = strength, groups = condition, batch = batch,
#> override = c("between_group_variability", "normalized_variance_equal"))
#>
#> Distribution: Normal - Pooled CV ( n = 86, r = 4 )
#> The following diagnostic tests were overridden:
#> `between_group_variability`,
#> `normalized_variance_equal`
#> B-Basis: ( p = 0.9 , conf = 0.95 )
#> CTD 125.1325
#> RTD 129.3447
#> ETW 123.809
#> ETW2 120.3191
The object returned from basis_pooled_cv contains a
number of values. One value is a data.frame containing the
groups (i.e. conditions) and the corresponding basis values. This looks
like the following. We’ll use this in the visualizations.
b_basis_pooled$basis
#> group value
#> CTD CTD 125.1325
#> RTD RTD 129.3447
#> ETW ETW 123.8090
#> ETW2 ETW2 120.3191
Batch Plots
Batch plots are used to identify differences between batches. Simple
batch plots can be created using box plots and adding horizontal lines
for the basis values as follows. Note that the heavy line in the box of
the box plot is the median, not the mean. The two hinges
correspond with the first and third quantiles and the whiskers extend to
the most extreme data point, or 1.5 times the inner quantile range.
In the code below, we use the function rename to rename
the column group to condition. The
data.frame produced by basis_pooled_cv uses
the columns value and group, but to match the
data, we need the column with the conditions to be named
condition.
dat %>%
ggplot(aes(x = batch, y = strength)) +
geom_boxplot() +
geom_jitter(width = 0.25) +
geom_hline(aes(yintercept = value),
data = b_basis_pooled$basis %>% rename(condition = group),
color = "blue") +
facet_grid(. ~ condition) +
theme_bw() +
ggtitle("Batch Plot")
It’s sometimes useful add failure modes to the plot so that you can
easily identify whether failure modes differ between conditions or
batches. This can be done with the
geom_jitter_failure_mode() function. This behaves very
similarly to geom_jitter(), except that color
or shape must be specified, and if there are multiple
failure modes (e.g. “LAB/LAT”), both failure modes are plotted as
separate points.
dat %>%
ggplot(aes(x = batch, y = strength)) +
geom_boxplot() +
geom_jitter_failure_mode(aes(color = failure_mode, shape = failure_mode), width = 0.25) +
geom_hline(aes(yintercept = value),
data = b_basis_pooled$basis %>% rename(condition = group),
color = "blue") +
facet_grid(. ~ condition) +
theme_bw() +
ggtitle("Batch Plot with Failure Modes")
Quantile Plots
A quantile plot provides a graphical summary of sample values. This
plot displays the sample values and the corresponding quantile. A
quantile plot can be used to examine the symmetry and tail sizes of the
underlying distribution. Sharp rises may indicate the presence of
outliers.
dat %>%
ggplot(aes(x = strength, color = condition)) +
stat_ecdf(geom = "point") +
coord_flip() +
theme_bw() +
ggtitle("Quantile Plot")
Normal Survival Function Plots
An empirical survival function, and the corresponding normal survival
function can be plotted using two ggplot “stat” functions
provided by cmstatr. In the example below, the empirical
survival function is plotted for each condition, and the survival
function for a normal distribution with the mean and variance from the
data is also plotted (the survival function is 1 minus the cumulative
distribution function). This type of plot can be used to identify how
closely the data follows a normal distribution, and also to compare the
distributions of the various conditions.
dat %>%
ggplot(aes(x = strength, color = condition)) +
stat_normal_surv_func() +
stat_esf() +
theme_bw() +
ggtitle("Normal Survival Function Plot")
Normal Score Plots
The normal scores plot calculates the normal score and plots it
against the normal score. Normal plots are useful to investigate
distributions of the data.
dat %>%
group_by(condition) %>%
mutate(norm.score = scale(strength)) %>%
ggplot(aes(x = norm.score, y = strength, colour = condition)) +
geom_point() +
ggtitle("Normal Scores Plot") +
theme_bw()