# Variance components table for Fit Mixed Effects Model

Find definitions and interpretation guidance for every statistic in the Variance components table.

## Variance components

Variance components represent the variances of the random terms and the random error term in a mixed effects model. Minitab displays the value of the variance component (Var) and how much of the total variation is accounted for by the variance component (% of Total).

### Interpretation

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, field has a variance component of approximately 0.078 and accounts for approximately 73% of the variance in the model.

### Mixed Effects Model: Yield versus Field, Variety

Variance Components Source Var % of Total SE Var 95% CI Z-Value Field 0.077919 72.93% 0.067580 (0.0142361, 0.426476) 1.152996 Error 0.028924 27.07% 0.010562 (0.0141399, 0.059166) 2.738613 Total 0.106843 Source P-Value Field 0.124 Error 0.003 Total -2 Log likelihood = 7.736012

## SE Var

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

### Interpretation

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 interval for variance component (95% CI)

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.

### Interpretation

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.

## Z-value

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

### Interpretation

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

## P-Value for variance components

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 random term significantly affects the response, compare the p-value for the term in the Variance Components table to your significance level. 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 an effect exists when there is no actual effect.
P-value ≤ α: The random term significantly affects the response
If the p-value is less than or equal to the significance level, you can conclude that the random term does significantly affect the response. This means that the variance of the random term is significantly different from zero.
P-value > α: The random term does not significantly affect the response
If the p-value is greater than the significance level, you cannot conclude that the random term significantly affects the response. You may want to refit the model without the non-significant term to assess the effect of the term on other results.
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