SBLC4002 Statistical Sampling Techniques

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SBLC4002 Statistical Sampling Techniques

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SBLC4002 Statistical Sampling Techniques

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Course Code: SBLC4002
University: University Of Wales Trinity Saint David

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Country: United Kingdom

Question:

Tasks
Who is untrained in quantitative techniques, has asked you to explain the following using modern business related examples to illustrate your explanation:

a) Averages and measures of dispersion.
b) Regression and correlation analysis.

Answer:

Introduction
In the business scenario, each aspect of the regular living, quantitative techniques are used to help in decision making. In order to perform efficiently in a modern business company, whether the company is a private commercial, a government organization, a state industry or other, managers should be capable to use quantitative techniques in a positive way and efficient manner. Quantitative techniques refers to those methods which give the decision, makes a organized and strong means of analysis which is formed on quantitative information. It is a technological technique employed for issue solving and decision making by the administration. The quantitative techniques enable the decision maker to expand policies for accomplishing the pre-determined goals and. This report explains all the quantitative techniques in business by using modern business related illustrations. The main objective of the report is to explain and differentiate between the several kinds of averages and measure of dispersion, differentiate between regression and correlation analysis and the critical evaluation of the techniques in the business.
Description and differentiation various types of averages and measure of dispersion
According to Anderson et al. (2012), quantitative strategies mean those procedures that can be evaluated in unquestionably units of estimation. These techniques refer to features whose progressive estimations yield quantifiable perceptions. There are mainly three types of averages which is mean, median and mode which are explained below:
Mean: According to Ayyub & McCuen (2011), the mean is the average of the numbers which is ascertained as focal estimation of an arrangement of numbers. In other words, mean is what you acquire by adding up of all the numbers by dividing how many numbers were in the list. In some other ways, the mean is the equitable average If the numbers are all combined together and then allocate equally.
Median: According to Cadle et al. (2014), the median is a statistical expression that is one way of calculating the average of a set of data points. In short words, the median is the center value in a data set.  
Mode: The mode is the most ordinary outcomes. It is a statistical term that states to the most much of the time happening number found in an arrangement of numbers. The mode is started by gathering and arranging the data so as to compute the recurrence of every result. The result with the biggest events is the mode of the set.
Measure of dispersion: According to Chatterjee & Hadi (2015), dispersion is the degree to which the extents or magnitudes of the items vary the level of assorted variety. The word dispersion may also be utilized to demonstrate the spread of the information. The fundamental property of dispersion as a value that directs the extents to which all other values are dispersed about the focal value in a specific allocation. The qualities of a favorable measure of dispersion are:
It should be easy to understand
It should be simple to calculate
It should be rigidly characterized.
It should be depend on every individual thing of the conveyance
It should have inspecting soundness (Cohen et al., 2013).
On the other side, the measures of dispersion are classified into two categories that are absolute and relative. According to Darlington & Hayes (2016), absolute measures of dispersion present in the same units in which the real data are present. Relative measures of dispersion are the proportion or the percentage of a measure of dispersion to a suitable average.
Differentiation between types of average and measure of dispersion

Types of Averages

Advantages

Disadvantages

Mean

All the information is utilized to find the solution.
 
It is basic and simple to compute.
 
It is minimum affected by the variance of testing.
 
It can be computed regardless of the possibility that the total designation is not known but rather a portion of the perception and number of the perception are known.

Very major and little values can false the outcome.
 
It can never be recognized by investigation or by graphical area.
 
It is excessively influenced by extraordinary perceptions and thus it is not satisfactorily speak to information comprising of some extreme point

Median

Large and little values does not affect it
 
It is simple measure of the central tendency of the arrangement
 
Median values are dependably a specific particular incentive in the arrangement
 
Median values is genuine value and is a superior agent estimation of the arrangement compared to arithmetic mean average, the estimation of which may not exist in the arrangement by any stretch of the imagination.
 
 

It requires a long investment to discover for a major arrangement of data
 
Median neglects to be illustrative measure if there should be an occurrence of such arrangement the diverse estimation of which is wide separated from each other.
 
Median is not prepared to do promote arithmetical treatment.

Mode

The main average that can utilize when the arrangement of data is not numerical
 
Mode is extremely basic measure of focal inclination.
 
Mode can be found graphically with the assistance of histogram.

There may be more than one mode
It may not be properly portray the information
Mode is an uncertain and vague of the central tendency.
Mode is not capable of further algebraic treatment.

Description and distinguish between regression and correlation analysis
Regression analysis: According to Draper & Smith (2014), regression analysis is the estimation of the average relationship between more than two variables in terms of the real units of the date. In other words, regression analysis is a statistical tool with help in understanding the theory of functional relationship between the variables and thus, it gives a procedure for assuming or forecasting. The variable which is use to assume the other variable is known as independent variable ( explanatory variable). In the regression analysis, the dependent variable is indicated by X and the independent variable is indicated by Y. According to Huston (2010), the analysis utilize in regression is known as simple linear regression analysis. The reason behind its simplest form is that there is only one independent variable. The regression analysis is classified into two categories:
Linear regression: According to Jankowitsch et al. (2011), linear regression is a kind of regression which utilizes the free factor with a specific end goal to depict or accept the needy variable.
Multiple regression: Multiple regression is a sort of regression which utilizes at least two than two autonomous variable so as to depict or accept the reliant variable.
Correlation analysis: According to Manikandan (2011), correlation analysis is a quantitative technique of statistical calculation use to comprehend the positive aspects of a relationship between two, numerically measured and continuous variables. Correlation analysis has enormous use in real life because of the following reasons:
Correlation analysis enables business to get a particular value in order to measure the extent of relationship exists between the variables.
Correlation analysis helps business to comprehend the economic behavior.
Correlation analysis helps the business executives to calculate the price, cost and other variables.
Correlation analysis can be used as a basis for the study of regression.
Correlation analysis enables the business to decrease the scope of uncertainty connected with decision making. The assumption depends on correlation analysis is always near to reality.
Correlation analysis is classified into three categories which are explained as follows:
Positive and negative correlation: According to Mardia (2014), when all the variables are diverse in a similar track, it is known as positive relationship. On the other, when the factors are differentiating in the switch course, it is known as negative correlation.
Simple, partial and multiple correlation: According to McNeil et al. (2015), simple correlation states that the study of any two variables in the correlation analysis is known as simple correlation. Multiple correlation studied the three or more variables concurrently in a correlation analysis is known as multiple correlation. Partial analysis refers that in a correlation analysis, business identify more than two variables, but consist only one independent variable and the remaining independent variables are constant.  
Linear and non-linear correlation: According to Montgomery et al. (2012), if a proportion of change between the two sets of variables is similar in a correlation analysis, then it is known as linear correlation. On the other side, if a quantity of change in one variable does not give the same proportion of change in another variable, it is known as non-linear correlation.
Difference between regression and correlation analysis:

Basis

Correlation

Regression

Variables

Both X and Y variables are random variables.

In a regression analysis, x is a random variable and y is a fixed variable.

Relationship

Correlation analysis obtains the extent of relationship between two variables.

Regression analysis specifies the cause and effect relationship between the variables and builds a functional relationship.

Value

The coefficient correlation is a relative estimation

Regression coefficient is an absolute figure.

Objective

The objective of correlation analysis is to identify a numerical value which represents the relationships between variables.

The objective of regression analysis is to evaluate the values of random variable on the basis of the fixed variable values.

Examples of quantitative techniques use in business applications
Averages:
For example:  consider the wages of staff at a factory below and calculate the mean, median and mode of this data.
Staff    1           2         3        4         5       6      7       8       9      10
Salary15k    18k       16k      14k    15k   15k  12k  17k   90k   95k
The mean salary for these ten staff = 307/10
= $30.7k
Median = According to Moore et al. (2011), company have to take the 5th and 6th score in our data set and average them to get a median of 16k.
Mode= The mode is the most frequent score in our data set. The model value of the wages in a factory ranges of 15k.
Measure of dispersion
Example: Consider the following information on two stocks X and Y:

Year

Return on X (%)

Return on Y (%)

2008

12

10

2009

18

16

The standard deviation of return from each of the stocks:
Stock A: Variance= 0.5 (10-13)2+0.5 (18-15)2= 9
Standard deviation = square root of 9 = 3%
Stock B: Variance = 0.5 (12-15)2+ 0.5 (18-15)2 = 9
Standard deviation: 3%
To co-variance of return from the stocks:
Co-variance of stocks A and B = COvAB= 0.5 (10-13) (12-15) + 0.5 (16-13) (18-15)
Correlation analysis and regression analysis:
For example, XYZ Company wants to promote their product in the market. In the given table, if the advertisement increases, the sales revenue also increase and product will be familiar both in market and customer mind. According to Newbold et al. (2012), the correlation and regression equation of XYZ Company are calculated as follows:

Correlation & Regression

Data

X-Data

Y-Data

Observation

Ads

Sales

Observation 1

20

45

Observation 2

13

35

Observation 3

10

32

Observation 4

33

65

Observation 5

16

39

Observation 6

8

15

Observation 7

10

24

Observation 8

15

30

Observation 9

18

48

Observation 10

6

14

Regression Statistics

Observations

10

Correlation coefficient (r)

0.948

Coefficient of determination (r-squared)

90%

Standard error of the estimate

5.238

Regression Equation

Slope

1.900

Intercept

6.385

Sales = 6.385 + 1.9 (Ads)

Predicting With The Regression Equation

X value

20

Confidence Level

95%

Predicted Y value

44.392

          Confidence Interval

44.392

          Prediction Interval

44.392

Hypothesis Test For Correlation

Null hypothesis:  Slope = 0 (no correlation)

Level of Significance

0.05

t-Statistic (computed)

8.4530

p-value

0.0000

Decision

Avoid the null hypothesis

Conclusion

Conclude that correlation exists.

Evaluation of different methods
According to Reynolds et al. (2010), the critical evaluation of the above methods is explained are as follows:
Averages:
Measures of Central Tendency give a layout measure that attempts to depict a whole course of action of data with a single regard that addresses the middle or center of its flow.
Wages of the employees is considered to be range from 15k to 90k. It shows that wages of staff members are allocated between range of 15-95k.
Measure of dispersion
The standard deviation shows the average separation between a perception esteem, and the mean of an informational collection. Along these lines, it indicates how well the mean speaks to the qualities in an informational collection. Like the mean, it is suitable to utilize when the informational collection is not skewed or containing exceptions. The raw measure of dispersion, prior to a statistical analysis and processing of the results, is the observation of the grouping of the impact points on target. If all rounds are fired toward the same aim point, assuming that the same equipment is used for all the rounds, then the proximity, or the grouping, of the impact points obtained after repeated firings is the first observation one can make on the level of performance of given two stocks.
Correlation analysis and Regression analysis
According to Tonidandel & LeBreton (2011), the examination shows a critical evaluation of intensification efficiency assurance, which uncovers that conceivably extensive underestimations happen when exponential mathmatics is connected to the log-direct locale. This error was found to come from misjudging the source of the log-straight locale, which is gotten not from invariant enhancement effectiveness, yet rather from an exponential misfortune in intensification rate. In contrast, least restrictive environment examination created Emax estimates that corresponded nearly to that got from a standard curve, result implies that standard efficacy investigation is established upon exponential science. According to Wegner (2010), this confusing outcome suggests that the quantitative viability of positional-construct investigation depends not upon the exponential character of continuous PCR, but instead with respect to the capacity to correctly characterize the relative position of an intensification profile (Zhang et al., 2012). An evaluated regression and correlation condition might be utilized for an expansive assortment of business application, for example,
Taking a gander at the impact on an association’s advantages of an extension in benefits.
Perceiving how touchy an association’s arrangements are to changes in advancing employments.
Seeing how a stock cost is impacted by changes in financing costs..
Regression examination may likewise be utilized for estimating purposes; for instance, a relapse condition might be utilized to gauge the future interest for an organization’s items.
Conclusion
From this report, it has been concluded that quantitative techniques in business provides a systematic approach for the evaluation of phenomenon in business economics and economics in general terms. Mostly business are depend upon quantitative techniques which concentrates on the significance of these techniques also from the theoretical viewpoint. This report explains the importance of quantitative techniques which enable the manager of an company in facing up to this stress and hurdles in the decision-making process which should be considered seriously. This report explains the various methods of quantitative techniques such as type of averages, measure of dispersion, correlation and regression analysis, distinguish between all these methods. The report also provides the various examples of the different methods and their use in the business and the evaluation of the methods so that manager can focus on objectives, identify and keep the various kinds of decision variables that affect goals and objectives, determine and record interactions between trade-off decision variables and to record requirements on the qualities that factors may expect.
References
Anderson, D.R., Sweeney, D.J., Williams, T.A., Camm, J.D. & Cochran, J.J., 2012. Quantitative methods for business. Cengage Learning.
Ayyub, B.M. & McCuen, R.H., 2011. Probability, statistics, and reliability for engineers and scientists. CRC press.
Cadle, J., Paul, D. & Turner, P., 2010. Business analysis techniques: 72 essential tools for success. BCS, The Chartered Institute.
Chatterjee, S. & Hadi, A.S., 2015. Regression analysis by example. John Wiley & Sons.
Cohen, J., Cohen, P., West, S.G. & Aiken, L.S., 2013. Applied multiple regression/correlation analysis for the behavioral sciences. Routledge.
Darlington, R.B. & Hayes, A.F., 2016. Regression analysis and linear models: Concepts, applications, and implementation. Guilford Publications.
Draper, N.R. & Smith, H., 2014. Applied regression analysis. John Wiley & Sons.
Huston, S.J., 2010. Measuring financial literacy. Journal of Consumer Affairs, 44(2), pp.296-316.
Jankowitsch, R., Nashikkar, A. & Subrahmanyam, M.G., 2011. Price dispersion in OTC markets: A new measure of liquidity. Journal of Banking & Finance, 35(2), pp.343-357.
Manikandan, S., 2011. Measures of dispersion. Journal of Pharmacology and Pharmacotherapeutics, 2(4), p.315.
Mardia, K.V., 2014. Statistics of directional data. Academic press.
McNeil, A.J., Frey, R. & Embrechts, P., 2015. Quantitative risk management: Concepts, techniques and tools. Princeton university press.
Montgomery, D.C., Peck, E.A. & Vining, G.G., 2012. Introduction to linear regression analysis (Vol. 821). John Wiley & Sons.
Moore, R.A., Mhuircheartaigh, R.J.N., Derry, S. & McQuay, H.J., 2011. Mean analgesic consumption is inappropriate for testing analgesic efficacy in post-operative pain: analysis and alternative suggestion. European Journal of Anaesthesiology (EJA), 28(6), pp.427-432.
Newbold, P., Carlson, W. & Thorne, B., 2012. Statistics for business and economics. Pearson.
Reynolds, C.R., Livingston, R.B., Willson, V.L. & Willson, V., 2010. Measurement and assessment in education. Pearson Education International.
Singh, T.N., Kainthola, A. & Venkatesh, A., 2012. Correlation between point load index and uniaxial compressive strength for different rock types. Rock mechanics and rock engineering, 45(2), pp.259-264.
Tonidandel, S. & LeBreton, J.M., 2011. Relative importance analysis: A useful supplement to regression analysis. Journal of Business and Psychology, 26(1), pp.1-9.
Wegner, T., 2010. Applied business statistics: Methods and Excel-based applications. Juta and Company Ltd.
Zhang, J., Zhang, Z., Xiao, X., Yang, Y. & Winslett, M., 2012. Functional mechanism: regression analysis under differential privacy. Proceedings of the VLDB Endowment, 5(11), pp.1364-1375.

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