Testing for differences in the monthly mean prices of selected food items in Lagos and Ogun states using doubly multivariate [formula omitted] statistic

Abstract

The work investigates differences in the mean vectors of the monthly prices of ten selected food items (crate-of-egg, brown-bean, local-rice, frozen-chicken, white-cassava flakes, yellow-cassava flakes, agriculture-rice, tomato, yam, and palm-oil) in Lagos State and Ogun State. The paired multivariate T2 statistic (also referred to as the doubly multivariate T2 statistic) was used to test the hypothesis of equality of the population mean vectors for prices of these ten selected food items using monthly prices between January 2017 and February 2020. The application of this multivariate test procedure will help to understand whether the combined prices of the food items are significantly different in the two states. The effect of each food item in the presence of other food items can also be discovered.The arrangement of the data was such that food prices were paired according to the months they were collected. Diagnostic tests of assumptions for the T2 statistic were conducted prior to the application of the test. The result shows that T2=218.17 with a p-value of 0.000, indicating a statistical difference in the monthly prices of the fooditems between the two states. However, the results of the univariate paired sample t-tests indicate significant difference at 5% level for only brown-bean, local-rice, tomato and palm-oil. The coefficients of the standardized discriminant function for each food item revealed that brown-bean has the largest contribution in the separation of the prices of food items in the two states.