Dear All,

I need an help to define the satistically valid call audit sample - for a call centre where daily answered call count is appx. 2.3 lacs.

The Process is a Telecom Process. Required Minimum & Maximum Sample Size. And also the baseline Satistical Theory.

Please advice.

Regds,

Partha

 

 

Hi Partha,

Your question mentions about needing to define a statistically valid call audit sample for a call centre / BPO, with the baseline statistical theory behind it. Before doing an audit one needs to know the topic for audit first. Per your question, in a typical call centre scenario where the call volume is huge on a day-to-day basis, one should identify the subject of audit first before going in for sample size calculations, test checks & the like, which escapes mention in your question.

In a call center / BPO, periodical audits are conducted on calls for a variety of reasons. For eg, Call Quality audit, AHT audit, Fatal error audit, etc., per the organisation's policy or depending on the affected (among the above & more) area(s) for review, analysis & improvement. Your question doesn't mention the subject & purpose of audit, without which it becomes difficult to give a proper or near precise answer. The population size (for eg,no of calls/day) to be audited in a call center is normally very huge, as illustrated by your question. Furthermore, certain guidelines (eg-taking calls per script given, free hand given on calls after adhering to privacy policy, etc) also decide on the distribution of data. Depending on it, there can be outliers occuring very or not very frequently. The statistically valid call sample that is chosen is expected to represent the diverse characteristics of the population to ensure a fair test.

Generally speaking, a near normal population will have a near normal sampling distribution of the mean for small sample sizes. Weirder populations will require larger sample sizes for the sampling distribution of the mean to be nearly normal. Statisticans usually consider a sample size of 30% or more to be sufficiently large.

Would solicit more information from your end for a clear picture, to elicit a better response from one & all here. Also, the sample size calculator uploaded in the file cabinet herein, by SJ sir should be useful to you.

NOTE: Sampling error is the error resulting from using a sample instead of the entire population to estimate a population parameter.

Thanks & rgds.

Manian: Is it 30 or 30%.?

Partha: For unknown or very large poulation proportion ( current situation) of count data, 

a sample size of 384 should be sufficient for a Confidence Level of 95% and an Error Margin of 5%.

If you need different  confidence level and margin of error , then the sample size will be different.

Further, in this case, one can safely assume the binomial distribution of the discrete count data approaching a normal distribution as the population is very large ( much like the binomial distribution of the outcomes of a dice game approaching a normal distribution for increased draws).

 

Regards,

Ari

 

Hi Ari sir,

           Thanks for pointing it out. It is 30 & not 30% as got mentioned inadvertently. Furthermore, one also needs to keep an eye on the nature & type (generally  discrete)  of data while deciding on the sample size. For eg, is the data homogenous or hybrid in nature, as different types (variety) of call audits involve scrutiny of data with varying nature. For instance, while doing an audit on fatal errors committed on calls, the data is normally homogenous along with its type (types of fatal error) being limited. However, while doing an audit on call quality, both nature of data (reasons for scoring/marking down on quality) & its type (quality scores) are variable.

Thanks & rgds. 

 

Dear Ari Sir,

Thanks for the following input:

"a sample size of 384 should be sufficient for a Confidence Level of 95% and an Error Margin of 5%"

It would be really great if you advice the Sample Call Quality Audit Count - for 230000 answered calls - considering Confidence Level at 95% & Error Count of 3%.

Regds,

Partha

 

Hi Ari sir,

         Futrher to you answering the subsequent question asked by Partha, would also appreciate if you could enlighten us in the statistical reasoning (with / without asumptions) behind arriving at the sample size (including the figure of 384 for an unknown / very large population proportion, as opined by you) in the absence of clear indicators for calculation of the same for the population proportion (of 2,30,000). Viz., std deviation, hypothesis proportion, present sigma level. 

Thanks & rgds.

Hi Partha,

          Per your question to Ari sir (sample size for a population of 2.3 lacs with a confidence level of 95% & error margin of 3%), the calculated sample size arrives to 1064, using the sample size calculator available in the file cabinet herein . 

        Following were the assumptions made in the absence of specific inputs from you on Hypothesis proportion & Power of test in the calculation.

1) Sample size has been calculated for poulation proportion (not population mean as would need std dev for that or we can do acceptance sampling).

2) Hypotheses proportion has been kept as 50%.

3) Power of test (you desire in your results) has been taken as 50%, and

4) The alternate hypothesis as ' not equal to '. 

Note - If you want to keep power of test at 90% with the remaining assumptions as same, then the sample size calculated for a population of 2.3 lacs comes to 2879.  

     You may please cross check the above at your end.

Thanks & rgds.

 

Dear Partha & Manian:

I regret my belated reply.  I am very busy with my training schedules and other meetings/ tour programs.Besides, I moderate several membership groups for PM, Leadership, Six sigma etc . Hence, I will be able to post when I get some spare time and I request you to bear with my punctuated respones.

Now, coming to your questions,

The formula for sample size for estimating the population proportion is

n = (z^2)*p*(1-p)/(E^2)

SITUATION 1:

Sample size for a Confidence Level of 95 % and  Error margin of 5% :

Using the above formula,

Confidence Level = 95 % (needed to calculate the z value from

standard normal dist)

Margin of Error (E) = + or - 5%,

then for maximum sample size, the value of p should be =0.5 and the

sample size will work out to be

n = 1.96^2 * 0.5 *0.5 / (0.05^2) = 384

Hence, a minimum of 384 calls are to be sampled randomly to state results

at 95% Confidence level and within margin of error of + or - 5%.

SITUATION 2:

For CL = 95% and E = 3% ; 

Confidence Level = 95 % (needed to calculate the z value from

standard normal dist)

Margin of Error (E) = + or - 3%,

Then, for maximum sample size, the value of p should be =0.5 and the

sample size will work out to be

n = 1.96^2 * 0.5 *0.5 / (0.03^2) = 1067  which will be normally rounded off to 1100

Hence, Sample size = 1100 for 95 %CL & 3% Error margin .

Hope, this answers Manian's request for the formula and Partha's request for the SS for  a margin of error of 3%.

Partha may please note that the sample should be selected randomly especially using a stratified random sample to include samples from various types of calls stated by you.

Regards,

Ari

 

Hi again Ari sir,

                Thanks for your precise response & clarification.

Rgds.

Dear Ari Sir & Manain,

Thank you for your support. Would take help from you, after getting revert from Clients.

Thank You...

Regards,

Partha