Checks for change in the mean value between a qualification data set and a sample. This is normally used to check for properties such as modulus. This function is a wrapper for a two-sample t–test.
equiv_change_mean(
df_qual = NULL,
data_qual = NULL,
n_qual = NULL,
mean_qual = NULL,
sd_qual = NULL,
data_sample = NULL,
n_sample = NULL,
mean_sample = NULL,
sd_sample = NULL,
alpha,
modcv = FALSE
)(optional) a data.frame containing the qualification data. Defaults to NULL.
(optional) a vector of observations from the
"qualification" data to which equivalency is being tested. Or the column of
df_qual that contains this data. Defaults to NULL
the number of observations in the qualification data to which the sample is being compared for equivalency
the mean from the qualification data to which the sample is being compared for equivalency
the standard deviation from the qualification data to which the sample is being compared for equivalency
a vector of observations from the sample being compared for equivalency
the number of observations in the sample being compared for equivalency
the mean of the sample being compared for equivalency
the standard deviation of the sample being compared for equivalency
the acceptable probability of a Type I error
a logical value indicating whether the modified CV approach
should be used. Defaults to FALSE
call the expression used to call this function
alpha the value of alpha passed to this function
n_sample the number of observations in the sample for which
equivalency is being checked. This is either the value n_sample
passed to this function or the length of the vector data_sample.
mean_sample the mean of the observations in the sample for
which equivalency is being checked. This is either the value
mean_sample passed to this function or the mean of the vector
data-sample.
sd_sample the standard deviation of the observations in the
sample for which equivalency is being checked. This is either the value
mean_sample passed to this function or the standard deviation of
the vector data-sample.
n_qual the number of observations in the qualification data
to which the sample is being compared for equivalency. This is either
the value n_qual passed to this function or the length of the
vector data_qual.
mean_qual the mean of the qualification data to which the
sample is being compared for equivalency. This is either the value
mean_qual passed to this function or the mean of the vector
data_qual.
sd_qual the standard deviation of the qualification data to
which the sample is being compared for equivalency. This is either the
value mean_qual passed to this function or the standard deviation
of the vector data_qual.
modcv logical value indicating whether the equivalency
calculations were performed using the modified CV approach
sp the value of the pooled standard deviation. If
modecv = TRUE, this pooled standard deviation includes the
modification to the qualification CV.
t0 the test statistic
t_req the t-value for \(\alpha / 2\) and
\(df = n1 + n2 -2\)
threshold a vector with two elements corresponding to the
minimum and maximum values of the sample mean that would result in a
pass
result a character vector of either "PASS" or "FAIL"
indicating the result of the test for change in mean
There are several optional arguments to this function. Either (but not both)
data_sample or all of n_sample, mean_sample and
sd_sample must be supplied. And, either (but not both)
data_qual
(and also df_qual if data_qual is a column name and not a
vector) or all of n_qual, mean_qual and sd_qual must
be supplied. If these requirements are violated, warning(s) or error(s) will
be issued.
This function uses a two-sample t-test to determine if there is a difference in the mean value of the qualification data and the sample. A pooled standard deviation is used in the t-test. The procedure is per CMH-17-1G.
If modcv is TRUE, the standard deviation used to calculate the
thresholds will be replaced with a standard deviation calculated
using the Modified Coefficient of Variation (CV) approach.
The Modified CV approach is a way of adding extra variance to the
qualification data in the case that the qualification data has less
variance than expected, which sometimes occurs when qualification testing
is performed in a short period of time.
Using the Modified CV approach, the standard deviation is calculated by
multiplying CV_star * mean_qual where mean_qual is either the
value supplied or the value calculated by mean(data_qual) and
\(CV*\) is determined using calc_cv_star().
Note that the modified CV option should only be used if that data passes the Anderson–Darling test.
“Composite Materials Handbook, Volume 1. Polymer Matrix Composites Guideline for Characterization of Structural Materials,” SAE International, CMH-17-1G, Mar. 2012.
equiv_change_mean(alpha = 0.05, n_sample = 9, mean_sample = 9.02,
sd_sample = 0.15785, n_qual = 28, mean_qual = 9.24,
sd_qual = 0.162, modcv = TRUE)
#>
#> Call:
#> equiv_change_mean(n_qual = 28, mean_qual = 9.24, sd_qual = 0.162,
#> n_sample = 9, mean_sample = 9.02, sd_sample = 0.15785, alpha = 0.05,
#> modcv = TRUE)
#>
#> For alpha = 0.05
#> Modified CV used
#> Qualification Sample
#> Number 28 9
#> Mean 9.24 9.02
#> SD 0.162 0.15785
#> Pooled SD 0.4927484
#> t0 -1.16519
#> Result PASS
#> Passing Range 8.856695 to 9.623305
## Call:
## equiv_change_mean(n_qual = 28, mean_qual = 9.24, sd_qual = 0.162,
## n_sample = 9, mean_sample = 9.02, sd_sample = 0.15785,
## alpha = 0.05,modcv = TRUE)
##
## For alpha = 0.05
## Modified CV used
## Qualification Sample
## Number 28 9
## Mean 9.24 9.02
## SD 0.162 0.15785
## Result PASS
## Passing Range 8.856695 to 9.623305