Term | Description |
---|---|
X | the design matrix, including the constant |
X' | the transpose of X |
Y | the response data |
the inverse of | |
the identity matrix with n rows and columns | |
the variance ratio for the i^{th} random effect in the model | |
the n x m_{i} matrix of known codings for the i^{th} random effect in the model | |
m_{i} | the number of levels for the i^{th} random effect |
c | the number of random effects in the model c = 2 for the model with time, batch, and the time*batch interaction c = 1 for the model with time and batch |
The standard errors of the coefficients depend on the test method for the fixed effects. For further details on the notation, go to the Methods section and the Tests of Fixed Effects section.
The standard errors of the estimated coefficients are the square roots of the dialgonal elements of the matrix .
where
where
For further details on the notation, go to the Methods section and the Tests of Fixed Effects section.
Term | Description |
---|---|
the estimated coefficient | |
the 1 − α/2 percentile from the t distribution with df degrees of freedom | |
the standard error of the estimated coefficient |
Term | Description |
---|---|
test statistic for the coefficient | |
estimated coefficient | |
standard error of the estimated coefficient |
The following equation gives the two-sided p-value for the null hypothesis that a coefficient equals 0:
Term | Description |
---|---|
The probability that under the null hypothesis T is less than the absolute value of the calculated . Here, T follows a t-distribution with df degrees of freedom. | |
The t value for the coefficient. |