Multiple comparison and random effect model on cocoa production in Ghana (from 1969/70 to 2010/11 production years)

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The study analyses the production of cocoa in Ghana from 1969/70 to 2010/11 .The study area ( Ashanti, Western,Brong Ahafo, Central, Eastern and Volta regions) were particularly chosen for this study because of their prime places in cocoa production in Ghana. The descriptive statistics used to analyze the results showed that majority (56.33%) of cocoa produced in the country comes from western region of Ghana with the mean annual production of 142823.9 metric tonnes while the lowest production(0.5%) of cocoa comes from volta region with mean annual production being 4897.00 metric tonnes. The ANOVA analysis revealed that there is significant difference(significance= 0.0001) between the mean production of cocoa in the country and further analysis using the multiple comparison (pair wise tests) also showed that the mean annual production of cocoa differ in terms of the six region of cocoa production in the country. Multiple comparison to detect where the difference lies using the three the comparison tests in the study(Tukey,LSD,Scheffe and Bonfferoni) showed that the mean difference between Ashanti and Western region was not significant but the mean difference between Ashanti and Central, Eastern, Volta ,Western were significant with mean difference of 53679.23,39441.73,83654.48 and -54272.38 respectively. Further analysis using mixed effect model also revealed that from 1969/70 production, all the six regions with the exception of Volta region experienced increasing cocoa production trend as time increased. Western and Ashanti regions had the highest production over the years. Random intercept with variance-covariance assumption also showed that the different regions had variations in the mean cocoa production.
A thesis submitted to the Department of mathematics, Kwame Nkrumah University of Science and Technology, Kumasi, in partial fulfilment of the requirements for the award of Master of Philosophy Degree in Mathematics,