Find definitions and interpretation guidance for the variance components.

Variance components assess the amount of variation in the response because of random factors.

Use to assess how much of the variation in the study can be attributed to each random term. Higher values indicate that the term contributes more variability to the response. For example, batch has a variance component of 0.527403 and accounts for 72.91% of the variance in the model.

Variance Components
Source Var % of Total SE Var Z-Value P-Value
Batch 0.527409 72.91% 0.303853 1.735739 0.041
Month*Batch 0.000174 0.02% 0.000142 1.224102 0.110
Error 0.195739 27.06% 0.036752 5.325932 0.000
Total 0.723322

The standard error of the variance component estimates the uncertainty from estimating the variance component from sample data.

Use the standard error of the variance component to measure the precision of the estimate of the variance component. The smaller the standard error, the more precise the estimate. Dividing the variance component by its standard error calculates a Z-value. If the p-value associated with this Z-statistic is less than your significance level (denoted as alpha or α), you conclude that the variance component is greater than zero.

Confidence Intervals (CI) are ranges of values that are likely to contain the true value of the variance component.

Because samples are random, two samples from a population are unlikely to yield identical confidence intervals. However, if you take many random samples, a certain percentage of the resulting confidence intervals contain the unknown population parameter. The percentage of these confidence intervals that contain the parameter is the confidence level of the interval.

The confidence interval is composed of the following two parts:

- Point estimate
- This single value estimates a population parameter by using your sample data. The confidence interval is centered around the point estimate.
- Margin of error
- The margin of error defines the width of the confidence interval and is determined by the observed variability in the sample, the sample size, and the confidence level. To calculate the upper limit of the confidence interval, the margin of error is added to the point estimate. To calculate the lower limit of the confidence interval, the margin of error is subtracted from the point estimate.

If the confidence level is 95%, you can be 95% confident that the confidence interval contains the true value of the variance component for the corresponding random term. The confidence interval helps you assess the practical significance of your results. Use your specialized knowledge to determine whether the confidence interval includes values that have practical significance for your situation. If the interval is too wide to be useful, consider increasing your sample size.

The Z-value is a test statistic that measures the ratio between the estimated variance component and its standard error.

Minitab uses the Z-value to calculate the p-value, which you use to test whether the variance component is significantly larger than zero.

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

To determine whether the variance component is greater than 0, compare the p-value for the variance component to the significance level. The null hypothesis is that the variance component is 0, which implies that the term does not add variation to the shelf life.

- 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 the variance component is greater than 0.
- P-value > α: The association is not statistically significant
- If the p-value is greater than the significance level, you cannot conclude that the variance component is greater than 0.