RESEARCH METHOD COHEN ok

538 QUANTITATIVE DATA ANALYSIS
Box 24.30
Ascatterplotwithgridlinesandregressionline
Hours of study
6
5
4
3
2
1
0
20
30
40
50
60
Level of achievement
line. In fact this is all calculated automatically by
SPSS.
Let us look at a typical SPSS output here
(Box 24.31).
This table provides the R square. The R square
tells us how much variance in the dependent
variable is explained by the independent variable
in the calculation. First, it gives us an R square
value of 0.632, which indicates that 63.2 per
cent of the variance is accounted for in the
model, which is high. The adjusted R square
is more accurate, and we advocate its use, as
it automatically takes account of the number of
independent variables. The adjusted R square is
usually smaller than the unadjusted R square, as it
also takes account of the fact that one is looking at
Box 24.31
AsummaryoftheR,RsquareandadjustedR
square in regression analysis
Model summary
Adjusted SE of the
Model R R square R square estimate
1 0.795 a 0.632 0.625 9.200
a. Predictors: (Constant), Hours of study
70
80
asampleratherthanthewholepopulation.Here
the adjusted R square is 0.625, and this, again,
shows that, in the regression model that we have
constructed, the independent variable accounts
for 62.5 per sent of the variance in the dependent
variable, which is high, i.e. our regression model
is robust. Muijs (2004: 165) suggests that, for a
goodness of fit with an adjusted R square:
0.5: strong fit
Second, SPSS then calculates the analysis of
variance (ANOVA) (Box 24.32). At this stage
we will not go into all of the calculations
here (typically SPSS prints out far more than
researchers may need; for a discussion of df
(degrees of freedom) we refer readers to the
earlier section). We go to the final column here,
marked ‘Sig.’; this is the significance level, and,
because the significance is 0.000, we have a very
statistically significant relationship (stronger than
0.001) between the independent variable (hours
of study) and the dependent variable (level of
achievement) (Box 24.32).
This tells us that it is useful to proceed with
the analysis, as it contains important results.
SPSS then gives us a table of coefficients, both
unstandardized and standardized. We advise to
opt for the standardized coefficients, the Beta
weightings. The Beta weight (β) istheamount
of standard deviation unit of change in the
dependent variable for each standard deviation
unit of change in the independent variable. In
the example in Box 24.33 the Beta weighting
is 0.795; this tell us that, for every standard
deviation unit change in the independent variable
(hours of study), the dependent variable (level of
achievement) will rise by 0.795 (79.5 per cent)
of one standard deviation unit, i.e. for every
one unit rise in the independent variable there
is just over three-quarters of a unit rise in the
dependent variable. This also explains why the
slope of the line of best fit is steep but not quite 45
degrees – each unit of one is worth only 79.5 per
sent of a unit of the other (Box 24.33).