cmstatr (version 0.9.3)

equiv_change_mean: Equivalency based on change in mean value

Description

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.

Usage

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
)

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

Arguments

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

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.

See Also

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