RESEARCH METHOD COHEN ok

540 QUANTITATIVE DATA ANALYSIS
of 110 and who studies for 30 hours per week. The
formula becomes:
Examination mark = (0.65 × 30) + (0.30 × 110)
= 19.5 + 33 = 52.5
If the same student studies for 40 hours then the
examination mark could be predicted to be:
Examination mark = (0.65 × 40) + (0.30 × 110)
= 26 + 33 = 59
This enables the researcher to see exactly the
predicted effects of a particular independent
variable on a dependent variable, when other
independent variables are also present. In SPSS
the constant is also calculated and this can be
included in the analysis, to give the following, for
example:
Examination mark = constant + β study time
+β intelligence
Let us give an example with SPSS of more than
two independent variables. Let us imagine that
we wish to see how much improvement will
be made to an examination mark by a given
number of hours of study together with measured
intelligence (for example, IQ) and level of interest
in the subject studied. We know from the previous
example that the Beta weighting (β) givesusan
indication of how many standard deviation units
will be changed in the dependent variable for each
standard deviation unit of change in each of the
independent variables. The equation is:
Level of achievement in the examination
= constant + β Hours of study + β IQ
+β Level of interest in the subject.
The constant is calculated automatically by SPSS.
Each of the three independent variables – hours of
study, IQ and level of interest in the subject – has
its own Beta (β) weighting in relation to the
dependent variable: level of achievement.
If we calculate the multiple regression using
SPSS we obtain the results (using fictitious data
on 50 students) shown in Box 24.34.
Box 24.34
AsummaryoftheR,RsquareandadjustedR
square in multiple regression analysis
Model summary
Adjusted SE of the
Model R R square R square estimate
1 0.988 a 0.977 0.975 2.032
a. Predictors: (Constant), Level ofinterestinthesubject,
Intelligence, Hours of study
The adjusted R square is very high indeed
(0.975), indicating that 97.5 per cent
of the variance in the dependent variable
is explained by the independent variables
(Box 24.34). Similarly the analysis of variance
is highly statistically significant (0.000), indicating
that the relationship between the independent
and dependent variables is very strong
(Box 24.35).
The Beta (β) weighting of the three
independent variables is given in the ‘Standardized
Coefficients’ column (Box 24.36). The constant is
given as 1.996.
It is important to note here that the Beta
weightings for the three independent variables
are calculated relative to each other rather than
independent of each other. Hence we can say
that, relative to each other:
The independent variable ‘hours of study’
has the strongest positive effect on the level
of achievement (β = 0.920), and that this
is statistically significant (the column ‘Sig.’
indicates that the level of significance, at 0.000,
is stronger than 0.001).
The independent variable ‘intelligence’ has a
negative effect on the level of achievement
(β =−0.062) but that this is not statistically
significant (at 0.644, ρ>0.05).
The independent variable ‘level of interest in
the subject’ has a positive effect on the level
of achievement (β = 0.131), but this is not
statistically significant (at 0.395, ρ>0.05).