Appendix 6 – Statistical Analysis
The interdependence of factors in 5.2.3 is analysed applying formal statistical techniques in this appendix.
As one of the dimensions in the cross-tabulation (objectives for environmental improvement) allows for multiple choices, the single counts in the matrix can not be regarded independent; in example the conditions to apply a standard chi-square test for homogenous distribution are not fulfilled.
Therefore, the focus of this analysis is narrowed down to a hypothesis where p1, p2 and p3 represent the proportions of the respondents for local, national and international businesses having stakeholder satisfaction (SS) as part of their environmental objectives:
H0: p1=p2=p3
A chi-square test has been applied with a level of significance of 5%.
Chi-square test for Homogeneous distributions
Level of significance: 0.05
Test-i:
International, National and Local
![](https://johnsohn.dk/wp-content/uploads/2016/12/Test-i.png)
Test-ii:
National and Local
![](https://johnsohn.dk/wp-content/uploads/2016/12/Test-ii.png)
The table above (Test-i) shows that the proportions are significantly different (p-value 0.017%) for any reasonable choice of significance-level.
Comparing only the local and national responses (Test-ii) the difference between those are not significantly different (p-value 31.5%), in example the difference could be random.
Further to quantifying the findings 95% confidence-intervals are created for the proportion of international businesses having stakeholder satisfaction (SS) objectives as well for the anticipated common proportion for national and local respondents.
Confidence interval for population
![](https://johnsohn.dk/wp-content/uploads/2016/12/Confidence-interval-for-population.png)
The resulting intervals (59%-85%) and (26%-45%) corresponding with standard deviations for the p-estimates on 6.7% and 4.9% shows that the uncertainty in estimating the proportions are rather big. A bigger sample size could reduce this uncertainty.
Calculations are made in excel based on a template originating from Sid Sytsma, Ferris State University.