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

`df_qual`

that contains this data. Defaults to NULL- 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

`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
```