After clicking on the OK button, the output shown on the right side of Figure 1 is displayed. When the dialog box shown in Figure 1 of One-Factor ANOVA Analysis Tool appears, fill in the Input Range with A3:D11, make sure that the Column headings included with data is checked and choose the Hsu MCB (Max) option. Real Statistics Data Analysis Tool: We use the Single Factor ANOVA tool to perform Hsu’s MCB post-hoc test.
Minitab express general linear model how to#
Figure 4 summarizes how to interpret the results. The analysis is similar when “best” means “the smallest mean”. In this case, Method 3 is significantly better than the other methods (since Method 3 is the only one with a positive upper-bound). Observation: If all the values in Method 3 are increased by 15, we would get the results shown in Figure 3. =MAX(0,G11-INDEX(G$11:G$14,H11)+ I$8*K$8*SQRT(1/H4+1/INDEX(H$4:H$7,H11))) Analysis of Experiments The analysis of variance (ANOVA) based on a general linear model (GLM) for the collected experimental data was performed by MINITAB.
We see from the analysis shown in Figure 1, that Method 1 is significantly worse than the best (since upper = 0) and there is no significant difference between the other methods and the best method (since zero is contained in these confidence intervals).
Here “best” means has the highest mean value. If interp = TRUE (default) the recommended interpolation is used otherwise linear interpolation is used.Įxample 1: Use Hsu’s MCB to determine, based on the data in Example 2 of ANOVA Basic Concepts, which groups are the best and which are significantly worse than the best. Real Statistics Functions: The following function is provided in the Real Statistics Resource Pack:ĭCRIT1( k, df, alpha, interp) = the critical value d crit for k groups, the given degrees of freedom df and the value of alpha. Since the values of d crit are based on equal group sizes, the above formula is only accurate if the group sizes are not too different. Note that when the group sizes are different, we can define the D-statistic as follows. Here, the first equation is used when best = highest mean and the second equation is used when best = lowest mean. We can also define a center value C i where If, instead, best means lowest mean, then we use dfE).įor each group i, we define an interval as follows in the case where best means highest mean. Where d crit is the critical value in the one-tailed Dunnett’s table at the given values of α, k (# of groups) and df (i.e. Whether to use the highest mean or lowest mean needs to be decided in advance, before the analyses are started and ideally before any data is collected. Note that the highest or lowest sample group mean isn’t necessarily the highest or lowest population group mean. Hsu’s Multiple Comparisons with the Best (MCB) also limits the number of comparisons made, this time instead of only considering comparisons with the Control, all comparisons are made to the group with either the highest mean or lowest mean (“the best”). Dunnett’s Test has the advantage that since fewer comparisons are made, there is less need to reduce the significance level to take experiment-wise error into account.
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