Trade-off involved with regard to sample size

Discuss about the Probability and Hypothesis Testing System.

A key problem that researches often face is with regards to determining the sample size which would be required for conducting the research. It should be noteworthy that the key objective of the sampling process is that the chosen sample should be representative of the actual population. As a general rule, it is better that a higher sample size is selected as it enhances the chance of the sample being representative of the population even though this depends on the underlying sampling method deployed. However, a higher sample size leads to a smaller standard error which captures the difference between the population parameter and sample statistic. But a key problem associated with a large sample is the high amount of time and resources that would be required in collecting and analysing data collected from such large sample (Hair, et.al., 2015).

Hence, the above theoretical discussion clearly reflects that there is an inherent trade off involved with regards to sample size whereby on one side the higher sample size can potentially deliver higher precision and accuracy but at a higher cost while on the other side a lower sample size would lower the accuracy but the cost involved would be lesser. In this trade off, it is imperative that a suitable middle ground be attained. In this regards, the following formula for minimum sample size is useful (Lind, et.al., 2012).

It is apparent from above that the minimum sample size depends on the level of accuracy desired coupled with the level of heterogeneity in the population data. The higher the heterogeneity level, higher would be the minimal sample required. MOE requires the margin of error and the sample is inversely related to the square of the MOE (Flick, 2015).

For the given case, the population comprises of 69000 employees and out of these about 21% employees or 15,000 employees have been chosen for the sample. The sample size does not seem high to me considering that the underlying population seems to be heterogeneous considering that in total this has employees from 63 banks and additionally different levels. Hence, considering the number of organisations and levels involved, it makes sense to choose a higher sample size as lower sample size can potentially lead to misrepresentation of some banks and underrepresentation of others. Thus, these sampling errors can potentially have an adverse impact on the reliability of these results. Hence, it would be fair to conclude that such a large sample size would be necessary for the given study (Lind, et.al., 2012).

Minimum sample size formula

The current sampling method that has been deployed in the given study is simple random sampling. This is a sampling method where requisite samples are randomly selected and each element of the sample has an equal chance of getting selected. Thus in order to conduct simple random sampling, the various employees can be numbered from 1 to 63000 and then 15,000 random numbers can be generated and the corresponding employees would form the sample. Like other sampling techniques, simple random sampling method has certain advantages and disadvantages which have been outlined below (Hair, et.al., 2015).

Advantages of simple random sampling

• A key advantage of simple random sampling is the ease of use which is involved. This is especially relevant considering the given sample size of 15000 employees and thereby convenient implementation is imperative.
• Another key advantage is that this method is free from errors related to classification since no classification of data is required to implement the same.
• It usually leads to the selection of a representative sample especially if the sample size is large enough. This representative sample through the use of inferential statistical tools can then be yield to derive useful conclusions about the population (Lieberman, et.al., 2013).

Disadvantages of simple random sampling

• This method is not very useful with regards to data that is heterogeneous and has significant attributes attached. Take the example of the current research. In this case, there are  significant attributes that are involved such as bank name, level of employees, gender etc. which need proportionate representation. However, this seems difficult in random sampling as it may so happen that a particular bank has large representation in the sample while other lower. Further, in case there is a bank with only limited employees such as 500, then it might be possible that no representation from the same may be available despite the larger sample size (Flick, 2015). Thus, in this case, it is better to choose stratified sampling method which involved sorting the population in accordance with the key attributes that require representation. Once the sorting of data is done, then the sample can be selected randomly in a manner that each requisite attribute has the same representation in the sample as compared to the population.
• The simple random sampling method can lead to higher standard error especially if the population is not homogeneous and hence the stratified sampling is more suitable as has been explained above (Lieberman, et.al., 2013).

The discussion on the reliability and validity of the given variables is carried out as highlighted below (Fehr, & Grossman, 2003).

• Quantitative job insecurity – For the given variable, the reliability is measured through the cronbach’s alpha which has a value of 0.89. Considering that a value above 0.8 is considered to be quite acceptable for quantitative variables, hence for the given variable reliability is not an issue. Thus, even when the study is repeated with different sample, it would be expected to yield a comparable result for this particular variable. In relation to the validity of the given variable, the measure seems objective and has a basis in a previous study which implies that it can suitably measure the given variable.
• Qualitative job insecurity – For the given variable, the reliability is measured through the cronbach’s alpha which has a value of 0.87. Considering that a value above 0.7 is considered to be quite acceptable for qualitative variables, hence for the given variable reliability is not an issue. Thus, even when the study is repeated with different sample, it would be expected to yield a comparable result for this particular variable. In relation to the validity of the given variable, the measure seems credible considering the previous use of the items in reputed studies. Hence, neither reliability nor validity is concern for this measure (Hair, et.al., 2015).
• Psychological distress – The reliability is not an issue with this variable also as the cronbach alpha is greater than 0.8. Hence, even if the study is repeated with a different sample of participants, it would be expected that the result would be similar. The validity of the 12 item measure is also present since the measure has been previously used in a study. However, one concern may arise in relation to validity is the relevance of the measure considering it was used in a study which dates back to almost four decades. This hence needs to be considered.

Besides another measure used was job satisfaction which deploys the standard scale from 1 to 5 in term of increasing satisfaction levels. Hence, from the above discussion, it is apparent that the given variables used in the study are both valid and reliable for the underling purpose.

It is apparent that the objective of the study is to highlight the potential association between the qualitative and quantitative measures of well-being and job insecurity. However, it is interesting to note that additional variables in the form of gender, age and education level have also been considered. It makes sense to consider these variables as these are control variables and the change in these could adversely impact the validity of the results obtained from the study. It is imperative to note that the control variables are not the primary concern of the researcher as the objective is to measure the relation between independent and dependent variable. However, the control variables have the ability to alter or skew the underlying relationship if kept unchecked. As a result, the researcher ensures that the control variables are kept constant throughout the study so as to ensure that the underlying relationship between the dependent and independent variables is not altered by these variables (Medhi, 2001).

In the given study, the impact of change in these variables can easily be highlighted. For instance consider the variable age. For employees with higher age, it is expected that the quantitative measures would be more significant considering that after working for quite a long period,  the employees may not have the inclination to work at other places and also might fear that they may not get a job easily. Further, these employees would be less concerned with the qualitative measures of job dissatisfaction as over time, they would have got used to the working conditions and associated policies of the organisation. For the younger age, it would be expected that the qualitative measures of job dissatisfaction would be comparatively more vital considering that they would have higher mobility in the job market owing to their young age and adaptability. Their concern with the quantitative variables would be comparatively less as they would be confident of securing employment elsewhere (Medhi, 2001).

Similarly, the gender and education level would potentially make a huge difference. The highly educated employees would have higher expectations and hence qualitative measures of job dissatisfaction would be more critical considering the fact that they would have very less trouble in finding another job. Hence their dissatisfaction with the quantitative measures is comparatively lesser in comparison to the educated people. Further, considering the gender roles, quantitative factors should be more significant for males since they tend to act as the primary bread earner in most families. For the female employees, it is the qualitative variables that are supposedly more pivotal. Hence, considering the above, it makes sense to have these control variables so that valid results can be obtained between the requisite variables of primary interest to the researcher (Hair, et.al., 2015).

The research design that has been used for the given study is a correlational research design. The various advantages and disadvantages associated with this research design are outlined below.

Advantages of correlational research design

• One advantage is that it allows the researchers to collect more data that in case of other experimental studies. This is because the objective is to understand the trend and strength o the association between the given variables and hence potential causal relationships between different variables can be identified (Eriksson & Kovalainen, 2015).
• Another advantage is that this design could serve as potential starting ground for other researches which can then explore a particular aspect of the potential causal relation between two given variables and explore the same in detail using a descriptive research design.
• Further, the correlational studies allow simplification of future studies since the direction and strength of relation between given variables is determined which can then contribute to model building and testing based on the results obtained from correlational research design (Hillier, 2006).

Disadvantages of correlational research design

• One major disadvantage of correlation research design is that it merely discover the direction and nature of association relationship but does not provide any conclusive reason for the association observed. Also, the association relationship does not automatically transfer into a causal relationship which is a key limitation. Additional studies are required to build on the results that are derived from these studies.
• These studies can only be used when there are two variables that can be measured on a scale. Correlational studies cannot accommodate a higher number of variables for which other research designs are required (Hastie, Tibshirani & Friedman, 2011).

References

Eriksson, P. & Kovalainen, A. (2015). Quantitative methods in business research (3^rd ed.). London: Sage Publications. 

Fehr, F. H., & Grossman, G. (2003). An introduction to sets, probability and hypothesis testing (3^rd ed.). Ohio: Heath. 

Flick, U. (2015). Introducing research methodology: A beginner’s guide to doing a research project (4^th ed.). New York: Sage Publications. 

Hair, J. F., Wolfinbarger, M., Money, A. H., Samouel, P., & Page, M. J. (2015). Essentials of business research methods (2^nd ed.). New York: Routledge. 

Hastie, T., Tibshirani, R. & Friedman, J. (2011). The Elements of Statistical Learning (4^th ed.). New York: Springer Publications.  

Hillier, F. (2006). Introduction to Operations Research. (6^th ed.). New York: McGraw Hill Publications.

Lieberman, F. J., Nag, B., Hiller, F.S. & Basu, P. (2013). Introduction To Operations Research (5^th ed.). New Delhi: Tata McGraw Hill Publishers.  

Lind, A.D., Marchal, G.W. & Wathen, A.S. (2012). Statistical Techniques in Business and Economics (15^th ed.). New York : McGraw-Hill/Irwin. 

Medhi, J. (2001). Statistical Methods: An Introductory Text (4^th ed.). Sydney: New Age International.