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: