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
)

## Arguments

df_qual (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

## Value

• 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

## Details

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.

## References

“Composite Materials Handbook, Volume 1. Polymer Matrix Composites Guideline for Characterization of Structural Materials,” SAE International, CMH-17-1G, Mar. 2012.

calc_cv_star()

stats::t.test()

## Examples

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