**PART 1: What is the difference between the Median Trace
and Median Run smoothing?
Part 2: What are the two ways to calculate the Moving Averages
technique?**

**Median Trace**

**Immediately below, one
can see an example of the Median Trace. The raw data (symbolized as
letters) is plotted on a time series. Data smoothing is completed
vertically. That is the median is calculated by identifying
the center number for each point in time.**

**Median Run**

**Immediately below, one can see an example of the
Median Run. The raw data (symbolized as letters) is plotted on a time
series. Data smoothing is completed horizontally. The
median is calculated by selecting the center number among three consecutive data
points. For the first set of data points, a, b and c, c is the
median. We point c on our smoothed chart. For the second set
of data points, b, c and d, d is the median (b = d), so it is plotted.
When we complete the smoothed chart, we immediately notice that we lose some
data.**

**What are the two ways to
calculate the Moving Averages technique?**

The term Moving Averages is employed to describe two different calculations for data smoothing. The most common method for calculating the Moving Averages technique is to calculate the average at each point in time. This is identical to the Median Trace -- EXCEPT we calculate the mean not the median. The less common method for calculating the Moving Averages technique is found in the problem related to autocorrelation in Single System Designs. Here, the Moving Averages technique is calculated in the same manner as the Median Run -- EXCEPT, of course, we calculate the mean not the median. Following is an illustration of the Moving Averages technique for Single System Designs:

This marital counseling data is autocorrelated and the data points are fluctuating or cyclical. Therefore the Moving Averages technique is deemed most appropriate for smoothing the data.

**Directions: **

•Add
point 1 and point 2

•Divide
the sum by 2

•Add
point 2 and point 3

•Divide
the sum by 2

•Add
point 3 and point 4

•Continue
this pattern until all points are added and divided

•Test
for autocorrelation

•If
NOT autocorrelated use the MAT method on the treatment data set

•Plot
the new data set on a graph and use a statistic.

**The specific math is illustrated below:**