Select the *Robust*
tab of the Descriptive
Statistics dialog box to access options to calculate robust estimates
of location that are insensitive to outliers in the data.

**Summary: statistics.** Click this button to produce
a spreadsheet containing the statistics selected in the *Location*
group box of this tab. Robust statistics, such as those calculated here,
can give useful results even when certain model assumptions (e.g., normality)
are not met. Because they are insensitive to extreme values in the data,
robust location statistics should be used when outliers are present in
the data.

**Location.** Use the options in this group box to
specify which location statistics to calculate.

**Trimmed mean.**
Select this check box and enter a percentage value to use in calculating
the trimmed mean. Unlike the *Winsorized
mean* (which replaces a percentage of values from the top and bottom
of the data set), the *Trimmed
mean* is calculated by removing a percentage of values from both ends
of the data set. A trimmed mean, therefore, is the arithmetic average
after x-percentage of values has been removed from the highest and lowest
ends of the data set.

**Winsorized
mean.** Select this check box and enter a percentage value to use in
calculating the Winsorized mean. The Winsorized mean is the mean computed
after the x-percentage highest and lowest values are replaced by the next
adjacent value in the distribution. For example, consider an ordered data
set with 100 observations: *x _{1}*,

When the data are taken from a symmetric distribution, the Winsorized mean is an unbiased estimate of the population mean. However, the Winsorized mean does not have a normal distribution even if the data are normally distributed.

**Grubbs test
for outliers.** Select this check box to include the results for Grubbs
outlier test (Grubbs 1969; Stefansky 1972) in the robust statistics spreadsheet.
Based on the assumption of normality, this test can be used to detect
a single outlier at a time. It is not recommended for use on samples with
less than 7 observations.

Grubbs test statistic (G) is calculated as the ratio of the largest absolute deviation from the sample mean to the sample standard deviation. That is,

_{}is an outlier if G is greater than the
critical value,

Where:

is the sample mean

s is the sample standard deviation

N is the sample size, and

is the critical value from a t distribution
with N-2 degrees of freedom and a significance level of _{}.