![minitab probability plot minitab probability plot](https://support.minitab.com/en-us/minitab/18/residual_plots_4_in_1_particle_board_strength.png)
Dropping entire factors from the model and other methods.Normal probability plotting of effects (Cuthbert and Daniels, 1959), and/or.Pooling high-order interactions to estimate error, (something we have done already in randomized block design),.Potential solutions to this problem might be:
#MINITAB PROBABILITY PLOT FULL#
With no replication, fitting the full model results in zero degrees of freedom for error.Replication provides an estimate of "pure error" (a better phrase is an internal estimate of error), and.How do we analyze our experiment when we have this type of situation? We must realize that the lack of replication causes potential problems in statistical testing: This is a matter of knowing something about the context for your experiment. In the end, you want to make sure that you choose levels in the region of that factor where you are actually interested and are somewhat aware of a functional relationship between the factor and the response. You need to have some understanding of what your factor is to make a good judgment about where the levels should be.
![minitab probability plot minitab probability plot](https://support.minitab.com/en-us/minitab/18/acc_life_ai_plot.png)
Your conclusion would probably be that there is no effect of that factor. and you picked your low and high level as illustrated above, then you would have missed capturing the true relationship. However, consider the case where the true underlying relationship is curved, i.e., more like this: L H A Y You can reduce this variance by choosing your high and low levels far apart. The variance of the slope of a regression line is inversely related the distance between the extreme points. As most of you know from regression the further apart your two points are the less variance there is in the estimate of the slope. You can pick your two levels low and high close together or you can pick them far apart. When choosing the levels of your factors, we only have two options - low and high. This is where we are headed, a steady progression to designs with more and more factors, but fewer observations and less direct replication. Where are we going with this? We have first discussed factorial designs with replications, then factorial designs with one replication, now factorial designs with one observation per cell and no replications, which will lead us eventually to fractional factorial designs. We will look at an example with one observation per cell, no replications, and what we can do in this case. This would be a minimum in order to get an estimate of variation - but when we are in a tight situation, we might not be able to afford this due to time or expense. As a matter of fact, the general rule of thumb is that you would have at least two replicates. When we introduced this topic we wouldn't have dreamed of running an experiment with only one observation.
![minitab probability plot minitab probability plot](https://support.minitab.com/en-us/minitab/19/media/generated-content/images/normal_display_probabilty_example.png)
In these cases, for the purpose of saving time or money, we want to run a screening experiment with as few observations as possible. You would find these types of designs used where k is very large or the process, for instance, is very expensive or takes a long time to run. An unreplicated \(2^k\) factorial design is also sometimes called a "single replicate" of the \(2^k\) experiment. These are \(2^k\) factorial designs with one observation at each corner of the "cube".