Immersion, Presence, and Performance in Virtual Environments
4.1 Statistical Analysis for Immersion and Presence
Here the issue is the relationship between presence and the two main independent
variables, immersion and environment. The dependent variable (p) was taken
as the number of 6 or 7 answers to the three questions as stated above.
This situation may be treated by logistic regression (Cox,
1970), where the dependent variable is binomially distributed ("number
of successes out of 3 trials"), with expected value related by the
logistic function to a linear predictor (Appendix
A).
Immersion was significant at the 5% level as an independent variable for
p, which was significantly higher for the egocentric compared to exocentric
case. (The change in deviance was 5.623, which should be compared with a
c2 deviate on 1 d.f. = 3.841). However, the environment variable was not
significant. When the analysis was repeated using the principal components
score for presence, the inclusion of immersion was similarly significant
at the 5% level provided that the spatial ability test score was included
in the model. Interestingly, there was a small but statistically significant
negative association between presence and the SAT score for those in the
egocentric group.
4.2 Statistical Analysis for Performance
Table 3
Mean and Standard Deviations of Proportions of Correct Moves
Immersion: | Exocentric | Egocentric | | Plain |
0.50 ± 0.26 | 0.80 ± 0.22 |
| Garden |
0.61 ± 0.39 | 0.93 ± 0.12 |
Performance was measured by the variable "Correct" (C), the
number of correct moves made by subjects out of 7 or 9. The mean proportion
of correct moves was 0.70±0.30. There were no significant differences
in number of correct moves regarding those subjects who were given 7 or
9 moves to remember. Table 3 shows the means and standard deviations for
the proportions of correct moves. This suggests that the task performance
improves with egocentric compared with exocentric, and with the richer environment.
However, this does not take into account the influence of other possible
factors, so we use logistic regression for more thorough analysis.
Table 4
Logistic Regression of Number of Correct Moves
Overall fit: Deviance = 17.626 on 16 d.f Variable | Parameter
Estimate | Standard Error | Change in Deviance | | Overall
mean | 0.9535 | 2.022 | |
| Egocentric
Immersion | 1.127 | 0.4538 | 6.61 |
| Garden
Environment | 1.820 | 0.5420 | 12.41 |
| No Previous Chess | -2.477 | 0.8459 | 9.36 |
| Practise | 0.5608 | 0.2292 | 9.16 |
| Female | -13.47 | 4.476 | 11.84 |
| SAT (female) | 0.1909 | 0.06631 | 11.15 |
Now treating C ("correct") as a response variable, we may consider
it as a binomially distributed variable being the number of correct moves
out of n (= 7 or 9) possibilities, and use the logistic regression model
outlined in Appendix A. The null hypothesis is
equivalent to the subjects simply guessing moves at random, rather than
based on their gained understanding of the spatial layout and the moves
themselves. The independent variables (immersion, environment) and each
of the explanatory variables of Table 2 were considered in the analysis.
The results are shown in Table 4, and the null hypothesis is rejected. For
a good fit of the data to the logistic regression model, the overall deviance
should be small, so that a value of less than the tabulated value is significant.
Indeed the overall deviance is approximately equal to the degrees of freedom,
which is what is expected for a good fit. No term can be deleted from the
model without significantly increasing the deviance. This is shown in the
last column of the table. The values are the increases in deviance that
would occur were the corresponding term to be deleted from the model. These
should be compared with the tabulated c2 deviate on 1 d.f. = 3.841. Further
analysis is presented in Appendix B.
4.3 Interpretation of Results
The results suggest the following - that other things being equal:
- Performance as measured in this particular experiment is positively
associated with egocentric immersion in comparison with the exocentric screen
based viewpoint;
- Performance is positively associated with a more realistic (garden)
environment compared with an empty environment;
- Females do not do as well as males in this particular experiment,
but
- In the case of females a higher SAT score is associated with increased
performance, whereas for males the SAT score is not associated with performance.
These results also take into account that (other things being equal):
- Previous knowledge of chess is associated with better performance;
- Better performance is achieved the greater the number of practice
sequences.