This tool is based on the ISO-13528 standard. The method consists of identifying, then removing or ignoring outliers and producing robust estimates of both location and scale estimators. Proficiency testing can be performed to assess the performance of laboratories making measurements, to detect problems in one or more laboratories when they arise, or to establish effectiveness and comparability of different methods. Proficiency testing, also called interlaboratory comparison, involves using statistical methods to compare the performance of several participants (which may be laboratories, inspection bodies, or individuals), referred to as “items” in XLSTAT, for specific measurements (referred to as “tests” in XLSTAT). Data is taken from the Economic Survey of Pakistan 1991-1992.What is inter-laboratory proficiency testing? The data file link is at the end of this numerical example of the Goldfeld-Quandt Test.įor an illustration of the Goldfeld-Quandt test, data given in the file should be divided into two sub-samples after dropping (removing/deleting) the middle five observations. Sub-sample 1 consists of data from 1959-60 to 1970-71. The Step by Step procedure to conduct the Goldfeld-Quandt test is: The sub-sample 1 is highlighted in green colour, and sub-sample 2 is highlighted in blue color, while the middle observation that has to be deleted is highlighted in red. (Note that observations are already ranked.) Step 1: Order or Rank the observations according to the value of $X_i$. We selected 1/6 observations to be removed from the middle of the observations. The Estimated regression for the two sub-samples are: Step 3: Fit OLS regression on both samples separately and obtain the Residual Sum of Squares (RSS) for each sub-sample. The critical value of $F(n_1=10, n_2=10$ at 5% level of significance is 2.98. The covariate is independent of the treatment effects (i.e.The lines expressing these linear relationships are all parallel (homogeneity of regression slopes).For each level of the independent variable, there is a linear relationship between the dependent variable and the covariate.In addition, ANCOVA requires the following additional assumptions: Since the computed F value is greater than the critical value, heteroscedasticity exists in this case, that is, the variance of the error term is not consistent, rather it depends on the independent variable, GNP.The same assumptions as for ANOVA (normality, homogeneity of variance and random independent samples) are required for ANCOVA. there is no interaction between the covariant and the independent variable). When this last assumption is not met, we can still perform an ANCOVA-like analysis as explained at ANCOVA when the homogeneity of slopes assumption is not met.Įxample 1: Show that the assumptions hold for the data in Example 1 of Basic Concepts of ANCOVA. We start by creating a box plot of the reading scores for each of the four methods (using the data from Figure 1 of Basic Concepts of ANCOVA). See Figure 1.įigure 1 – Box plot for data in Example 1Įach plot looks relatively symmetric and the variances don’t appear to be wildly different. As we can see from the data in Figure 1 of Basic Concepts of ANCOVA, the variances for the reading scores vary from 44.8 to 164.8, which is likely to be an acceptable range to meet the homogeneity of variances assumption. We now turn our attention to the ANCOVA-specific assumptions. We create a scatter diagram of the y data values against the x data values for each of the four methods. This is done by creating a scatter diagram for Method 1 in the usual way and then choosing Design > Data|Select Data and clicking on the Add button on the left side. Enter the name Method 2 and specify the range for the x and y values in the dialog box that appears. After repeating this procedure for Method 3 and Method 4 and adding linear trend lines for each method, the resulting chart is as in Figure 2.įigure 2 – Checking whether regression lines are parallelĪlthough the four lines are not parallel, their slopes are quite similar, indicating that the homogeneity of slopes assumption is met.
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