A Management Decision-Making and Index Number Paper Example

Question 1: The concept of sign test when comparing two dependent populations

The sign test encompasses a statistical technique used to test for any consistent differences between the pairs of observations like the weight before and after treatment of particular subjects. Based on the pairs of observations for each of the subjects, the sign test helps in determining if a given member of the pair such as post-treatment is greater or less than the other one like pre-treatment. X and y values may be used for the paired observations. Ideally, the expression of the comparisons would be in the form of x>y (x is greater than y), x=y, or x<y (x is less than y hence showing the vitality of the sign test. However, in case the observations depict their expressions as numeric quantities, the paired t-test will have greater power as compared to the sign test for detection of consistent differences. The sign test will also be crucial in testing if the median of different numbers is significantly less or even greater as compared to a given specified value (Zhang et al., 2014).

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Zhang, L., Dong, X., & Xu, X. (2014). Sign tests using ranked set sampling with unequal set sizes. Statistics & Probability Letters, 85, 69-77.

Question 2: What is an index number, its characteristics, and reasons for computing an index number?

An index number refers to a figure that reflects the price or quantity compared with a particular base or standard value. It shows a measure of the relative price change in a variety of variables. One of the characteristics of an index number is that it is expressed in the form of numbers thereby making it easy to calculate the manner in which the value tends to change over time. Other characteristics comprise of the comparative nature and universal utility of the index number. The principal reason for computing an index number is because it shows the averages for measuring the change in price, quantity, or variables over a period. Computing the index number occurs through calculation of the ratio of current value to base value (Allen, 2017).

Allen, R. G. D. (2017). Index numbers in economic theory and practice. London: Routledge.

Question 3: A management decision-making perspective in the following topics

a. Non-parametric methods; analysis of ordinal data

Ordinal data is always crucial for a perspective of practical decision support. In essence, much of the ordinal data collected requires non-parametric statistics to enhance valid analysis. The aspect of ordinal data brings forth a range of business applications that facilitate the decision-making process. The ordinal information helps in estimating numerical values, attribute weights or event probabilities. In decision-making, the ordinal data would facilitate the development of a generalized rank-sum thereby allowing for the incorporation of the concept of degree of importance. The simulation results will compare the generalized-rank sum with other formulas like the rank order centroid technique. Computation with the ordinal data begins with conversion of the natural perceptions of how acceptable or unacceptable the outcomes of the process would be depicted. At circumstances, it may be difficult to assign the utility scores on interval scales to help represent the nature of outcome acceptability or even unacceptability (Chen et al., 2017).

Atanassov, K. T. (2016). Index matrices: towards an augmented matrix calculus. New York City: Springer.

b. Index numbers

In the perspective of decision-making, the index numbers are practical in the measurement of changes in cost of living and trends of production. The index numbers are also crucial in the measurement of changes in money value in the sense that a rise or fall in search value would determine the direction of production of a particular quantity. As such, it would facilitate any future payments and identify the changes in real income of various groups of individuals. In the analysis of markets for different commodities, the index numbers would enhance the identification of such markets to help realize the best outcomes within the platform of operation. The weights assigned to the commodities tend to govern the markets. For instance, when the value of production increases or decreases, the index numbers will be used to determine the rates through a significant comparison to the base year (Atanassov, 2016).

Chen, B., Choi, J., & Escanciano, J. C. (2017). Testing for fundamental vector moving average representations. Quantitative Economics, 8(1), 149-180.

c. Time series and forecasting

Usually, datasets depend on time thereby bringing forth the concept of time series. In the perspective of decision-making, this concept will be critical in studying the past behavior in the sense that one can consider investing money on a particular organization. Moreover, it would establish the trend of different aspects such as the profits realized over a particular period. On the other side, it becomes easy to utilize forecasting when time series is in place since it becomes efficient to establish the history and brings about a proper decision on whatever would happen in the future, which might have either positive or adverse effects on the operational standards. For instance, the time series may make it easy for the evaluation process hence facilitating the incorporation of an appropriate strategy to deal with what would cause adverse consequences (Osmanoglu et al., 2016).

Osmanoglu, B., Sunar, F., Wdowinski, S., & Cabral-Cano, E. (2016). Time series analysis of InSAR data: Methods and trends. ISPRS Journal of Photogrammetry and Remote Sensing, 115, 90-102.

d. Concept of moving average and its use

Moving average depicts the succession of particular averages that emanate from successive segments and show a range of values, which originate from statistical analysis. In the decision-making process, this concept is useful in creating different average values for subsets of full data sets. In essence, it would smooth out the noise occurring from random outliers, as well as emphasizing the trends over a long period. As the index values become unpredictable and volatile, it serves efficient to establish any advantage that would enhance risk reduction while increasing profitability across a broad spectrum. The moving average is also useful in determining the past trends of price within a particular system. Since the moving averages are flexible, it always becomes efficient to forecast the price movements and trades of a given place, which consequently helps in the interpretation of relationships of spot trends of the data sets. As such, they confirm the trends after their establishment to an extent of monitoring momentum (Iannario, 2014).

Iannario, M. (2014). Modelling uncertainty and overdispersion in ordinal data. Communications in Statistics-Theory and Methods, 43(4), 771-786.

References

Allen, R. G. D. (2017). Index numbers in economic theory and practice. London: Routledge.

Atanassov, K. T. (2016). Index matrices: towards an augmented matrix calculus. New York City: Springer.

Chen, B., Choi, J., & Escanciano, J. C. (2017). Testing for fundamental vector moving average representations. Quantitative Economics, 8(1), 149-180.

Iannario, M. (2014). Modelling uncertainty and overdispersion in ordinal data. Communications in Statistics-Theory and Methods, 43(4), 771-786.

Osmanoglu, B., Sunar, F., Wdowinski, S., & Cabral-Cano, E. (2016). Time series analysis of InSAR data: Methods and trends. ISPRS Journal of Photogrammetry and Remote Sensing, 115, 90-102.

Zhang, L., Dong, X., & Xu, X. (2014). Sign tests using ranked set sampling with unequal set sizes. Statistics & Probability Letters, 85, 69-77.