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week units of analyses and we feel confident that this mitigates any systematic effect, if any at
all, variation in don’t know responses may have.
Measure of Approval Volatility: Approval is the percent of individuals surveyed responding in
the affirmative. Plotted as a trend line are the approval scores at 96 points across the term. This
trend line is smoothed using T4253H smoothing (standard SPSS for windows). At any given
point, the distance in percentage points between the smoothed line and the actual approval trend
line provides the residual. The residual is plotted for each unit of analysis and appears as spikes
in Figures 2 and 3. The average volatility for any given quarter is calculated as the average of
these residuals. For illustrative purposes, a smoothed line through these residuals is placed in the
Figures.
Measure of Approval Buoyancy: Approval Buoyancy for any given president is the difference
between that president’s Approval Score and the average approval score or the seven remaining
presidents. This difference is calculated for each president at 96 points across the term. Thus,
AB
t1...t96
= AS1
{
( AS2…AS8)
÷
7
}
, where AB
t1…t96
is Approval Buoyancy at any of the 96
points in the term and AS1 is the Approval Score for the first of the modern presidents and AS8
is the Approval Score for the last of the modern presidents. AB may be calculated using either
in- or out-party Approval Scores.
Measure of Approval Polarization: Approval Polarization for any given president is the absolute
value of the Approval Difference between the In- and Out-Party Approval relative the average
Approval Difference for the seven remaining presidents. This difference is calculated for each
president at 96 points across the term. Thus, AD1
t1..t96
= IPA1 – OPA1 , where AD1
t1..t96
is
Approval Difference for the first of the modern presidents at any of the 96 points in the term,
IPA1 is the In-Party Approval for this president, and OPA1 is the Out-Party Approval for this
president. And thus, AP1
t1..t96
= AD1
{
( AD2…AD8)
÷
7
}
, where AP1
t1..t96
is Approval
Polarization for the first of the modern presidents and AD2…AD8 are the approval difference
scores for the remaining seven presidents.
Convention