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 )
| df_qual | (optional) a data.frame containing the qualification data. Defaults to NULL. |
|---|---|
| data_qual | (optional) a vector of observations from the
"qualification" data to which equivalency is being tested. Or the column of
|
| n_qual | the number of observations in the qualification data to which the sample is being compared for equivalency |
| mean_qual | the mean from the qualification data to which the sample is being compared for equivalency |
| sd_qual | the standard deviation from the qualification data to which the sample is being compared for equivalency |
| data_sample | a vector of observations from the sample being compared for equivalency |
| n_sample | the number of observations in the sample being compared for equivalency |
| mean_sample | the mean of the sample being compared for equivalency |
| sd_sample | the standard deviation of the sample being compared for equivalency |
| alpha | the acceptable probability of a Type I error |
| modcv | a logical value indicating whether the modified CV approach
should be used. Defaults to |
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 #> 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