# Conditional means table and means for covariates table for Fit Mixed Effects Model

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

## Fitted Mean

The fitted mean uses the coefficients from the corresponding conditional or marginal fitted equation to calculate the mean response for each factor level, or for each level combination of multiple factors.

### Interpretation

Use the Means table to understand the effects of factor levels on mean response values. Each level mean provides an estimate of the mean response for the level. Look for differences between group means for terms that are statistically significant.

For a main effect term made by a single factor, the table displays the factor levels and their level means. For an interaction term, the table displays all possible combinations of the associated factor levels. If an interaction term is statistically significant, do not interpret the main effects without considering the interaction effects.

## SE Mean

The standard error of the mean (SE Mean) estimates the variability between fitted means that you would obtain if you took samples from the same population again and again.

### Interpretation

Use the standard error of the mean to determine how precisely the fitted mean estimates the corresponding mean response.

A smaller value of the standard error of the mean indicates a more precise estimate of the mean response. Usually, a larger standard deviation results in a larger standard error of the mean and a less precise estimate of the mean response. A larger sample size results in a smaller standard error of the mean and a more precise estimate of the mean response.

## DF (conditional means)

The degrees of freedom (DF) are the amount of information in your data to estimate the confidence interval for the mean response. Minitab also uses the degrees of freedom to construct the t-test for the mean response.

## Confidence Interval for mean (95% CI)

These confidence intervals (CI) are ranges of values that are likely to contain the true values of the mean responses for the term levels in the model.

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 corresponding mean response. 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.

## T-value (fitted mean)

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

### Interpretation

Minitab uses the t-value to calculate the p-value, which you use to test whether the mean 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 rejection is the same no matter what the degrees of freedom are. For more information on using the t-value, go to Using the t-value to determine whether to reject the null hypothesis.

## P-Value – fitted mean

The p-value is a probability that measures evidence against the null hypothesis. The null hypothesis is that the mean response is 0. Lower probabilities provide stronger evidence against the null hypothesis.

### Interpretation

To determine whether the mean is statistically different from 0, compare the p-value 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 the mean response is not equal to 0 when it actually is.
P-value ≤ α: The mean is significantly different from 0
If the p-value is less than or equal to the significance level, you reject the null hypothesis and conclude that the mean response is significantly different from 0.
P-value > α: The mean is not significantly different from 0
If the p-value is greater than the significance level, you do not have enough evidence to conclude that the mean response is significantly different from 0.

## Data Mean (covariate)

The mean of the covariate is the average of the covariate values, which is the sum of all the observations divided by the number of observations. The mean summarizes the sample values with a single value that represents the center of the covariate values.

### Interpretation

This value is the mean of the covariate. Minitab holds the covariate at the mean value when calculating the fitted means for the factors.

## Standard Deviation (StDev)

The standard deviation is the most common measure of dispersion, or how spread out the individual covariate values are around the mean.

### Interpretation

Use the standard deviation to determine how much the covariate varies around the mean. Minitab holds the covariate at the mean value when calculating the fitted means for the factors.

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