The effect size *m* can be considered unstable when much of the pushing or pulling of *m* come from the extremities of data. That is when a collection of extreme data points have a high influence on m in an equation such as *y=mx+b *for that effect size is *Unstable*.

The Influence of Extremities Factor has been devised to measure the instability of the effect size m.

In *Y _{i} = mX_{i} + b*, Y

_{i}and X

_{i}are vectors of data with Real Entries.

*m* is the regression coefficient and is calculated via least squares. This is termed as simple linar regression.

*(x,y) _{i}* denotes the

*i*point of the data.

_{th}In equation (5.1) *inf _{i}* is the influence of the point

*i*in calculating

*m*. This is defined as the following:

*m _{U}* is

*m*with all points in the dataset, where U denotes the entire dataset.

*m _{U-i}* is

*m*calculated without the

*i*data point.

_{th}We then sort the data by values of descending *inf _{i}*. The set of data comprising of the top 10% of

*inf*is labelled as “UL” for the upper limit and the bottom 10% of

_{i}*inf*is labelled as “LL” or lower limit.

_{i}By removing the UL set of data we calculate *m _{{U-UL}}*.

By removing the LL set of data we calculate *m _{{U-LL}}*.

By removing data that is pushing up “*m*” (i.e. high *inf _{i}*) we get

*m*which is lower than

_{{U-UL(10%)}}*m*.

_{U}

By removing data that is pulling down “m” (i.e.low *inf _{i}*) we get

*m*which is higher than

_{{U-LL(10%)}}*m*.

_{U}

Influence of Extremities Factor at 10% intervals would be:

A low IEF indicates a stable effect size m. A high IEF indicates an unstable effect size m. By stable, the value of *m* is not overly influenced by a few data points and by unstable, the value of m is overly influenced by a few data points. Datasets that are stable are more representative of the entire cohort and datasets that are unstable are likely not representative of the entire cohort.