IF I understand your question properly, it is more inclined at finding the return on investment from the perspective of the firm which invests in training its workforce in anticipation that it might increase efficiency / decrease slack and so on and so forth. 

It can be found by the usage of z test or t test, depending upon the number of observations that one possess, if at all there is any positive impact post training than pre training in terms of performance output. Having a large number of observations would make the distribution "Gaussian/Normal" as per the central limit theorem, making it a candidate on which z test can be applied. If there is a significant and positive increase in the production out, then the firm can certainly be sure about the success of its training program. In order to establish the result further, the same test can be applied with a control group this time and if the result does not alter much, the firm can be sure of its investment success.

Now, to check for the exact return on investment can get a little trick as the exact amount of financial proceeds generated as a result of that training is difficult to establish. If a reliable estimate can be made about the benefits arising out of the training that the employees underwent, then return on investment of the company can certainly be found by the formula:

ROI = (Gains from the training - Cost of training)/ Cost of training.

Since return on investment is a concept mainly rooted in financial side of a business, other non financial benefits arising out of the training would have no bearing on the ROI. As far as any previous article relevant to this study is concerned, I am unaware of it. 

Dear Naseem,

I am afraid not having understood the first part of your answer ( what and how should Student test measure the ROI of training in a particular company ?). For the second part, I agree, about your remarks on the possible non financial benefits arising out of the training. Nonetheless, it's worth, I think, to try to calculate, even, at minima, the financial ROI for that type of spending by the company.

What I fundamentally wanted to convey in the first part was that the Students t test can be used to test if the mean performance variable (such as units produced per hour, clients issue addressed per day etc.) improved post training of the employees than pre training on an average. In simple terms, the company ideally should be in a position to claim that "On an average the performance/output has increased or cost has decreased post undergoing the training. I hope you get my point.

Dear Naseem,

Okay, I capture what you meant and thank you for it. What you suggest is about the productivity of training expenses. The relationship between productivity and training is precisely the core of all the literature about the importance of training. Nonetheless almost all of this literature is centered around sectors or clusters of companies, as well as about the sharing of benefits between labourers and companies ( see Ann Bartel &  Rahmah Ismael papers enclosed). I don't know about that type of approach and calculation for A Single Company. That's why I set up my question.Thanks for your help.

Is the following assumption too simple? Calculate the profit per employee for the company. Assume the profit is proportional, so that if the average compensation is 50,000, and the profit per employee is 75,000, then a manager who earns 100,000 is assumed to result in 150,000 in profit. Track salary history after training, as a proxy for increased profitability, and compare to cost of training.

Dear Richard,

Thanks a lot for your contribution. The problem with this way, is that there could be many intangible investments, other than training expenses, that would enhance or not profitability. So you can not isolate the specific influence of Training costs on profit.