# Coefficients table for Analyze Taguchi Design

Find definitions and interpretation guidance for every statistic in the Estimated Model Coefficients table.

## Coef

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. To minimize multicollinearity among the terms, the coefficients are all in coded units.

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.

### Interpretation

In Taguchi designs, the magnitude of the factor coefficient usually mirrors the factor rank in the response table. Depending on your analysis, the response can be a signal-to-noise ratio, the mean for a static design, the slope for a dynamic design, or a standard deviation.

The size of the effect is usually a good way to assess the practical significance of the effect that a term has on the response variable. The size of the effect does not indicate whether a term is statistically significant because the calculations for significance also consider the variation in the response data. To determine statistical significance, examine the p-value for the term.

## SE Coef

The standard error of the coefficient estimates the variability between coefficient estimates that you would obtain if you repeated the same experiment again and again. The calculation assumes that the experimental design and the coefficients to estimate would remain the same if you sampled again and again.

### Interpretation

Use the standard error of the coefficient to measure the precision of the estimate of the coefficient. The smaller the standard error, the more precise the estimate. Dividing the coefficient by its standard error calculates a t-value. If the p-value associated with this t-statistic is less than your significance level, you conclude that the coefficient is statistically significant.

## T-value

The t-value measures the ratio between the coefficient and its standard error.

### Interpretation

Minitab uses the t-value to calculate the p-value, which you use to test whether the coefficient is significantly different from 0.

You can use the t-value to determine whether to reject the null hypothesis. However, the p-value is used more often because the threshold for the rejection of the null hypothesis does not depend on the degrees of freedom. For more information on using the t-value, go to Using the t-value to determine whether to reject the null hypothesis.

## P-Value

The p-value is a probability that measures the evidence against the null hypothesis. Lower probabilities provide stronger evidence against the null hypothesis.

### Interpretation

To determine whether a coefficient is statistically different from 0, compare the p-value for the term to your significance level to assess the null hypothesis. The null hypothesis is that the coefficient equals 0, which implies that there is no association between the term and the response characteristic that you select. In Taguchi designs, response characteristics refer to functions of the response, such as means, standard deviations, slopes, and signal-to-noise ratios.

Usually, a significance level (denoted as α or alpha) of 0.05 works well. A significance level of 0.05 indicates a 5% risk of concluding that the coefficient is not 0 when it is. Frequently, a significance level of 0.10 is used for evaluating terms in a model.
P-value ≤ α: The association is statistically significant
If the p-value is less than or equal to the significance level, you can conclude that there is a statistically significant association between the response characteristic and the term.
P-value > α: The association is not statistically significant
If the p-value is greater than the significance level, you cannot conclude that there is a statistically significant association between the response characteristic and the term. You may want to refit the model without the term.
If there are multiple predictors without a statistically significant association with the response, you can reduce the model by removing terms one at a time. For more information on removing terms from the model, go to Model reduction.
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