A Step by Step Guide for SPSS and Exercise Studies

Statistical tests 125
outliers in other analyses (e.g., MANOVA). In such cases, the dependent
variable should be a separate column in the data file with the case numbers.
Cook’s distance shows how much the regression coefficients would change if a
particular case was omitted. Norusis (1998) suggests that Cook’s distances
greater than 1 usually deserve scrutiny, as they may be too influential. Leverage
values also measure multivariate outliers. This distance measure ranges from 0
to close to 1, with greater values indicating potential outliers. Norusis (1998)
suggests, as a rule of thumb, to look at values greater than 2p/N, where p is the
number of independent variables and N is the number of cases. However, this
rule of thumb identifies too many cases in small samples.
The Save option also contains a number of Influence Statistics. These
statistics identify cases which exert considerable influence on the calculation of
various coefficients. DfBeta(s) show how much the regression coefficient of
each independent variable and the constant term would change if a particular
case was excluded from the analysis. Standardized DfBeta(s) contain the same
information for standardised regression coefficients. Norusis (1998) proposes
another rule of thumb, which states that cases p should be scrutinised if they have
absolute standardised values greater than 2 N . DfFit shows the change in the
predicted value of a dependent variable if a particular case is omitted.
Standardized DfFit shows p the standardised changes in the predicted values.
Again, you can use the 2 N rule to identify influential cases.
In Dialog box 82 click Plots (Dialog box 86). This option can be used to
examine the assumptions underlying the regression analysis and to identify
outliers and influential cases. A number of scatterplots can be plotted using the
dependent variable (DEPENDNT), the standardised predicted values of the
dependent variable (ZPRED), the standardised residuals (ZRESID), the residuals
for a case when this case is excluded from the regression (DRESID), the
predicted value of a case when the latter is excluded from the regression
(ADJPRED), the studentized residuals (SRESID), and the studentized residuals
for a case when it is excluded (deleted) from the regression (SDRESID). To
obtain a bivariate scatterplot with any of the above variables, move one of them
into the Y box and the other into the X box. To create more than one scatterplot,
use the Next button.
Norusis (1998) suggests a number of scatterplots to examine the assumptions
of regression analysis. For example, to check the assumption of homoscedasticity,
you can create a plot of ZPRED against the DEPENDNT. However, it is
easier to examine this assumption if you plot the residuals against the predicted
values. Norusis (1998) recommends the use of SRESID, as these should be
normally distributed with a relatively large sample size. SRESID can be plotted
against ZPRED (for an example of a similar plot, see Figure 25). Note that if you
save the residuals in the data file (using the Save option), you could plot them
against each of the independent variables. To create such plots, use the Simple
Scatterplot in the Graphs menu. If the linearity assumption is met, such plots
should not show any patterns. If they do, the relationship between the dependent
variable and the particular independent variable is probably not linear.