Use the signal-to-noise ratio (S/N ratio) to identify the control factor settings that minimize the variability caused by the noise factors. Minitab calculates the S/N ratio for each combination of control factors and then calculates the average S/N ratio for each level of each control factor. Choose from four S/N ratios, based on the experimental goal and an understanding of the desired outcome of the process. For more information, go to What is the signal-to-noise ratio in a Taguchi design?.
Delta is the difference between the highest and lowest average response values for each factor. Minitab assigns ranks based on Delta values; Rank 1 to the highest Delta value, Rank 2 to the second highest, and so on, to indicate the relative effect of each factor on the response.
Level | Variety | Light | Fertilizer | Water | Spraying |
---|---|---|---|---|---|
1 | -1.9266 | -0.6911 | -4.1399 | -0.9870 | 0.2274 |
2 | 2.8068 | 1.5712 | 5.0201 | 1.8672 | 0.6527 |
Delta | 4.7333 | 2.2623 | 9.1600 | 2.8542 | 0.4253 |
Rank | 2 | 4 | 1 | 3 | 5 |
Level | Variety | Light | Fertilizer | Water | Spraying |
---|---|---|---|---|---|
1 | 0.6867 | 0.6043 | 0.5264 | 0.5437 | 0.7067 |
2 | 0.7440 | 0.8264 | 0.9043 | 0.8870 | 0.7240 |
Delta | 0.0572 | 0.2220 | 0.3778 | 0.3433 | 0.0174 |
Rank | 4 | 3 | 1 | 2 | 5 |
Level | Variety | Light | Fertilizer | Water | Spraying |
---|---|---|---|---|---|
1 | 0.7794 | 0.5450 | 0.7677 | 0.5222 | 0.6207 |
2 | 0.5042 | 0.7387 | 0.5159 | 0.7614 | 0.6629 |
Delta | 0.2752 | 0.1937 | 0.2518 | 0.2392 | 0.0422 |
Rank | 1 | 4 | 2 | 3 | 5 |
If you have a static design and do not have a signal factor, you will have a response table for means instead of slopes.
If a model term is not statistically significant, you can remove it and refit the model. Frequently, a significance level of 0.10 is used for evaluating terms in a model.
The coefficient describes the size and direction of the relationship between a term in the model and the response variable. The absolute value of the coefficient indicates the relative strength of each factor. The number of coefficients Minitab calculates for a factor is the number of levels minus one. If a factor has 3 levels, Minitab provides 2 coefficients, which correspond to factor levels 1 and 2. If a factor has 2 levels, Minitab provides 1 coefficient, which corresponds to factor level 1. Minitab includes the values or text that correspond to the level.
The response tables show the average of each response characteristic for each level of each factor. The tables include ranks based on Delta statistics, which compare the relative magnitude of effects. The Delta statistic is the highest minus the lowest average for each factor. Minitab assigns ranks based on Delta values; rank 1 to the highest Delta value, rank 2 to the second highest, and so on. Use the level averages in the response tables to determine which level of each factor provides the best result.
Term | Coef | SE Coef | T | P |
---|---|---|---|---|
Constant | 0.4401 | 0.2384 | 1.846 | 0.316 |
Variety 1 | -2.3667 | 0.2384 | -9.926 | 0.064 |
Light 1 | -1.1312 | 0.2384 | -4.744 | 0.132 |
Fertiliz 1 | -4.5800 | 0.2384 | -19.209 | 0.033 |
Water 1 | -1.4271 | 0.2384 | -5.985 | 0.105 |
Spraying 1 | -0.2127 | 0.2384 | -0.892 | 0.536 |
Variety*Fertiliz 1 1 | -0.6041 | 0.2384 | -2.534 | 0.239 |
S | R-Sq | R-Sq(adj) |
---|---|---|
0.6744 | 99.81% | 98.69% |
Source | DF | Seq SS | Adj SS | Adj MS | F | P |
---|---|---|---|---|---|---|
Variety | 1 | 44.809 | 44.809 | 44.809 | 98.52 | 0.064 |
Light | 1 | 10.236 | 10.236 | 10.236 | 22.51 | 0.132 |
Fertilizer | 1 | 167.811 | 167.811 | 167.811 | 368.97 | 0.033 |
Water | 1 | 16.293 | 16.293 | 16.293 | 35.82 | 0.105 |
Spraying | 1 | 0.362 | 0.362 | 0.362 | 0.80 | 0.536 |
Variety*Fertilizer | 1 | 2.920 | 2.920 | 2.920 | 6.42 | 0.239 |
Residual Error | 1 | 0.455 | 0.455 | 0.455 | ||
Total | 7 | 242.886 |
In this example, for the signal-to-noise ratio, Fertilizer has a p-value that is less than 0.05, thus, Fertilizer is statistically significant at a significance level of 0.05.
Although you can use these plots to display the effects, be sure to evaluate the statistical significance of the effects in the analysis that fit the model. If the interaction effects are statistically significant in that analysis, you cannot interpret the main effects without considering the interaction effects.
Main effects plots show how each factor affects the response characteristic (S/N ratio, means, slopes, standard deviations). A main effect exists when different levels of a factor affect the characteristic differently. For a factor with two levels, you may discover that one level increases the mean compared to the other level. This difference is a main effect.
In addition to the interaction plots, examine the linear model analysis to determine whether the interaction is significant.
The graphs are arranged in decreasing order of the signal-to-noise ratio, so that the experimental runs with the highest ratios are plotted first. If the experiment has more than nine combinations of factor settings, Minitab displays more than one graph of scatterplots.
Use the residual plots to help you determine whether the model is adequate and meets the assumptions of the analysis. If the assumptions are not met, the model may not fit the data well and you should use caution when you interpret the results.
Use the normal probability plot of the residuals to verify the assumption that the residuals are normally distributed. The normal probability plot of the residuals should approximately follow a straight line.
The patterns in the following table may indicate that the model does not meet the model assumptions.
Pattern | What the pattern may indicate |
---|---|
Not a straight line | Nonnormality |
A point that is far away from the line | An outlier |
Changing slope | An unidentified variable |
Pattern | What the pattern may indicate |
---|---|
Fanning or uneven spreading of residuals across fitted values | Nonconstant variance |
Curvilinear | A missing higher-order term |
A point that is far away from zero | An outlier |
A point that is far away from the other points in the x-direction | An influential point |
Use the residuals versus fits plot to verify the assumption that the residuals are randomly distributed and have constant variance. Ideally, the points should fall randomly on both sides of 0, with no recognizable patterns in the points.
Pattern | What the pattern may indicate |
---|---|
A long tail in one direction | Skewness |
A bar that is far away from the other bars | An outlier |
Because the appearance of a histogram depends on the number of intervals used to group the data, don't use a histogram to assess the normality of the residuals.
A histogram is most effective when you have approximately 20 or more observations. If the sample is too small, then each bar on the histogram does not contain enough observations to reliably show skewness or outliers.