Hypothesis Tests
We explore the following hypothesis tests:
Test 1: To test whether the Deming regression slope b1 = 1, we use the following hypotheses: H0: b1 = 1 and H1: b1 ≠ 1.
The test statistic is
Test 2: To test whether the population x and y means are equal, we use the test statistic
Test 3: To test whether the population x and y are identical, we use both Test 1 and Test 2. Since there are two tests, we need to use an expermentwise correction. Thus, we would typically use a Bonferroni correction and set α = .025.
Examples
Example 1: Test whether y = x based on the data from Example 1 of Deming Regression Basic Concepts.
Once again, the hard part of this problem is to calculate the standard errors for the parameters in the two tests. We have already calculated se(b1) for test 1 in Example 1 of Jackknifing. We now calculate se(x̄–ȳ) using the jackknifing method, as shown in Figure 1.
Figure 1 – Hypothesis Testing
The approach is the same as in Example 1. For example, cell G16 contains the formula =DEVSQ(G4:G13)*(A13-1). We see from the right side of Figure 1 that neither null hypothesis is rejected, and so we don’t have sufficient evidence to reject the null hypothesis that y = x.
Worksheet Functions
Real Statistics Functions: For array or range R1 containing X values and R2 containing Y values, we have two forms of the following array function. The first corresponds to data as in Example 1 of Deming Regression Basic Concepts where lambda is known and the second where lambda is calculated from the data as in Example 2 of Deming Regression Basic Concepts.
DRegIdentity(R1, R2, λ, lab) = 2 × 1 array consisting of x̄–ȳ and se(x̄–ȳ) for Deming regression on the data in R1 and R2 where lambda = λ.
DRegIdentity(R1, R2,, lab) = DRegIdentity(R3, R4, λ) where R3 consists of the averages of the X data measurements in R1, R4 consists of the averages of the Y data measurements in R2 and the λ is calculated as in Example 2 of Deming Regression Basic Concepts.
If lab = TRUE (default FALSE), then an extra column is appended to the output from DRegIdentity with the labels “stat” and “s.e”.
Examples Workbook
Click here to download the Excel workbook with the examples described on this webpage.
Reference
NCSS (2016) Deming regression
https://www.ncss.com/wp-content/themes/ncss/pdf/Procedures/NCSS/Deming_Regression.pdf