Sociology

According to Feinstein (1996) correlation is a statistical analysis which is used to measure a linear relationship that exists between two variables. Correlation coefficients are the values for correlation. These correlation coefficients are usually represented by the letter r. The possible values of r range between -1.0 and 1.0. A negative relationship between variables is represented by numbers that are less than zero while a positive relationship between variables is represented by numbers that are greater than zero. The value of r is thought of almost like a percentage.
Appendix 1 shows an output from a correlation engine which shows how one can use correlation for a customer or employee satisfaction analysis. Any Likert rating scale system item can be chosen (for example five-point rating) from an analysis and all the statistically considerable correlations viewed with the viewed item.
While using a correlation engine, the following will be observed at the bottom of the page
Correlations(r) considerable at p  0.05. This is a traditional indication of the possibility that the correlations observed are an outcome of chance. For this case this probability (p) is set in a manner that the threshold should not be more than 5 percent. There is not more than a 0.05 possibility that the correlations which are listed are as an outcome of chance.Whenever the correlations are viewed, it is very vital to be keen with the p-level. One does not need a more understanding than the one explained here. One is only required to know that p  0.05 is the most used threshold standard for statistical importance.
The n column on the appendix represents the number in total for all respondents. This is very vital for statistical importance because when one has a big value of n, then a smaller correlation is still very significant statistically. On the other hand when one has a small value of n, then heshe requires a much bigger correlation for statistical importance. When two sets of correlations contain very dissimilar number of respondents are being looked at, one cannot contrast the coefficients of correlation to one another from each list. One requires observing each list on its own and coming to conclusions of each list independently.
In the appendix 1 example, there is closeness between the correlations i.e. the range from one correlation to the other is small. In the example below (Appendix 2), the ranges between subsequent correlations are much bigger. When a couple of things at the top have much higher correlation coefficients (r) as compared to the others, then followed by a large drop in r for the items to follow, attention should be focused more on those items at the top.
According to Schafer (1997), if there are a number of items that are close to each other, one should still begin at the top of the list. One should then give more equitable credence to those items that come next after the items at the top. A natural cut-off-point is usually somewhere where there is a big drop in r on the list. This idea should be used by the analyst as a logical point for analysis limitation.
Considering the example in appendix 2, there is a gap which is large after the first item. Therefore a conclusion can be drawn that competence is the first factor which determines the satisfaction of the individuals by their supervisor. The second and third items might also be looked at because they are too strong correlations that provide additional information which is useful. In a matter of fact, there would be need for considering all the items down to the biggest change in r where it falls from 0.58 to 0.51.
Correlation is commonly used in many analyses to find out matters most among individuals by correlating items of analysis with some measure of satisfaction in overall. As it can be seen from the above examples, this is method that can be used safely free of any worry of the technical stuff .

The noise is filtered out and only those correlations that are statistically significant are shown. What is important is that one should always begin with the top items on the list to identify what matters most. High negative correlations at the bottom of the list should also be looked at as they give an indication of the converse relationship between the items.
Multivariate analysis
This analysis is based on a principle of statistics known as multivariate statistics. This involves observing and analyzing many statistical variables simultaneously. The technique is used in design and analysis to carry out studies of trade across many dimensions and at the same time noting the effects of all variables on interest responses. This area of statistical analysis is among the most productive areas of important achievements for the past few decades.
Multivariate analysis can be used to design that is capability based inverse design in which all variables are considered independent alternatives survey  the concepts selection to fulfill the need of a customer analyze the concepts according to changing situations and identify significant design drivers as well as levels of hierarchy.
Multivariate analysis becomes complicated when used together with physics-based analysis. This combination is used to estimate the impact of hierarchical systems-of-systems variables. Studies that frequently make use of multivariate analysis are caught up by the complication of the problem. These problems are usually dealt with by use of surrogate models. These are high accurate estimates of the code that is physics-based .
These surrogate models are evaluated more easily because they use equations.
This enables large-scale MVA learning. Doing a Monte Carlo simulation in design space is usually hard while using physics- based codes but it usually becomes easier by use of surrogate model.