Replicate responses, matrix of mean

Before discussing the sum of squares due to lack of fit and, later, the sum of squares due to purely experimental uncertainty, it is computationally useful to define a matrix of mean replicate responses, J, which is structured the same as the Y matrix, but contains mean values of response from replicates. For those experiments that were not replicated, the mean response is simply the single value of response. The J matrix is of the form... 

Matrix of mean replicate responses and sum of squares due to lack of fit. Calculate the J matrix for Problem 9.6. Calculate the corresponding L matrix and... 

A third feature is the use of the J matrix (a matrix of mean replicate response) in the least squares treatment. We have found it to be a useful tool for teaching the effects (and usefulness) of replication. 

Matrix of mean replicate responses and sum of squares due to lack of... 

In a sense, calculating the mean replicate response removes the effect of purely experimental uncertainty from the data. It is not unreasonable, then, to expect that the deviation of these mean replicate responses from the estimated responses is due to a lack of fit of the model to the data. The matrix of lack-of-fit deviations, L, is obtained by subtracting f from J... 

Note that in the J matrix, the first two elements are the mean of replicate responses one and two the third and fifth elements are the mean of replicate responses three and five. The fourth element in the Y and J matrices are the same because the experiment was not replicated. 

The matrix of responses as the mean values for the threefold replicate experiments is illustrated in Tab. 8-12. 

Experiment. Prepare test whole blood QC pools at medium QC level. Store at room temperature and 5 °C for 0 (control), 1 and 2 h. Centrifuge the whole blood sample and collect the plasma (test matrix) for extraction and analysis following the validation method. Analyze six (6) replicates for each group. Compare the mean instrument response of stability test samples to that of the control group. 

The recovery of analyte in matrix should be evaluated at a minimum of two concentrations using a sufficient number of replicates (minimum of three). In practice the extraction efficiency is often determined by comparing the mean area response from processed QC samples that are used to determine intra-assay accuracy and precision to the mean area response from recovery samples at each QC concentration. 

The design matrix with operational matrix and outcomes of design points-trials is given in Table 2.104. Note that design points-trials have been replicated so that the table gives response means. 

The limit of detection should be determined using a definition given in Chapter 3. Typically, replicate blanks of the sample matrix are analyzed to determine the mean blank value and its standard deviation. Then a matrix is spiked with analyte near the detection limit (e.g., to give a signal 10 times the standard deviation above the blank mean signal). The limit of detection is the concentration calculated to give a response equal to the blank signal plus three standard deviations. 

For any analytical procedure, it is important to establish the smallest amount of an analyte that can be detected and/or measured quantitatively. In statistical terms, and for instrumental data, this is defined as the smallest amount of an analyte giving a detector response significantly different from a blank or background response (i.e. the response from standards containing the same reagents and having the same overall composition (matrix) as the samples, where this is known, but containing no analyte). Detection limits are usually based on estimates of the standard deviation of replicate measurements of prepared blanks. A detection hmit of two or three times the estimated standard deviation of the blanks above their mean, Xg, is often quoted, where as many blanks as possible (at least 5 to 10) have been prepared and measured. 

---