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Significance Of Net Income
Posted By: andy on 10/10/2005 11:08 PM (CST) 125 Points
I work in a Direct Mail environment where there are plenty of signifiacnce tests for response rates. If I send a pack which increases response and average value but costs more how can I measure if the increse in net income is also significant.

Many thanks

Posted by: mbarber Member Response
10/10/2005 11:23 PM (CST)
Gidday Andy - you'll probably want to work backwards from the end of your campaign so that, say 5 weeks or so from when you sent the packs out, you work out the actual sales.

Subtract the overall cost of the packs from the overall value of sales and divide by the number of packs sent.

To compare, go back to a previous campaign and crunch the numbers usnig the same approach.

The '5 weeks later' is an abritary time. Use whatever is appropriate for you product, just make sure you use the same time scale for the comparison.

I'm not sure if this is the type of 'net' figure you want because you might be asking to iclude all oncosts like salaries, expenses etc - if you are you'll need all of that data too for each of the offerings.

Also are you saying the pack costs more to produce, to send or both?
 
Posted by: andy Author Response
10/10/2005 11:32 PM (CST)
Thanks for the reply, I don't think I was clear in my question.
Calculating the net income isn't a problem although some oncosts may be. The problem I need to address is if I split test two packs, one cheap and one expensive (one example I have done is more expensive to produce & send), can I calculate and report back and say the net for the expensive pack is significantly better than the cheaper pack ie combing Response, ave value and costs.
 
Posted by: ASVP/ChrisB Member Response
10/11/2005 2:00 AM (CST)
Andy - Sure you can, provided you know which sales are derived from which packs, and you can separately analyse the Net on each sale.

ChrisB
 
Posted by: andy Author Response
10/11/2005 2:21 AM (CST)
Hi Chris,

The crux of what I am asking is is there a significance test, like the common response rate significance tests which can be applied to net income or net income per 1000 or net income per contact. For example if I mail two packs to 5,000 people each and PAck 1 gets 10% resp and pack 2 gets 15% response I can say withh 99% confidence that pack 2 response will be better next time. If pack 2 costs more so the income net income from Pack 1 is, say, $10,000 and the net income from Pack 2 is $11,000 is there a ststistical test to say that in 90/95/99% of cases I will get more net income from Pack2? I realise the income is a function of average value and response but it is the cost factor that throws me.

Any help will be appreciated.
 
Posted by: DWomack Member Response
10/11/2005 7:53 AM (CST)
Hi Andy.

I'm not a statistician but I think a t-test for independent samples will work, assuming you are comparing means from two groups and your data are normally distributed.

For a more thorough and expert answer, check out the Statsoft electronic textbook at:

http://www.statsoft.com/textbook/stathome.html

You may find what you need under their statistical advisor tab.

Good luck,

Dan
 
Posted by: wnelson Accepted Answer
10/11/2005 10:06 AM (CST)
Hi, Andy,

Dan’s comment about the “t-test” is close but statistically incorrect. t-test is used for small samples – typically 30 or less.

This problem is interesting because as we all learned statistics, we studied all there is to know about means and standard deviations. But, when we became marketers and started sending out direct mail, eMail, etc, and measuring responses, we forgot that the world isn’t only proportions, but parametric also. Parametric statistics involves things we measure with each unit. In this case, a unit is a customer who receives your pack. The parameter of interest is net income. So, think of the problem in terms of net income per response. Let’s look at Pack 1:

In your example, you said that your response rate is 10% for a sample of 5000. Total net income is $10,000. The average net income per unit is then $2 for the entire sample.

Keep in mind someone might tell you that average net income for those who responded is $20. This is a cool statistic, but not relevant to the problem. You can tell that to the person who brings this up and also add that the sky is blue because of the shorter wavelengths of light are scattered by the air molecules, allowing only the longer reds and yellows to come through. Since our eyes see color based on the absence of the frequency, we see blue in the sky. Also, add that if our atmosphere were made up of a different composition of gases, the sky would be a different color. The point: The net income per respondent is higher, yes, but if the pack were different, the total net income and the net income per respondent would be different – and that is what we are testing.

Back to the test: The average income per respondent is $2 - $10,000 from 500 people and $0 from 4500. What we want to do is calculate the net income for each of the 500 respondents so we can also measure the variance for the net income. To do this, you want to take the contribution margin for each respondent (product revenue minus product cost) and subtract the cost per pack. The average will still come out the same, but this allows you to calculate variance. To calculate variance, input the 500 net incomes into Excel and subtract the mean for the entire sample of 5000 from each (in the example, subtract $2). Sum the difference, square it, divide by 5000, and then take the square root of the result. See the formula for variance

http://davidmlane.com/hyperstat/desc_univ.html

Or if you’re not comfortable with this, input the net income data for the 500 respondents into Excel, along with 4500 rows of zeros and use the Excel function for standard deviation. Do this calculation for each sample of 5000. Then, to test the significance of the net income per pack, use the following formula:

z = (x-bar1 – x-bar2)/sqrt((v1 – v2)/n)

where:
z - z-score for the standard normal statistic
x-bar1 – mean of the net income for the first pack
x-bar2 – mean of the net income for the second pack
sqrt – is the square root function
v1 – is the variance of the net income for the first pack
v2 – is the variance of the net income for the second pack
n – is the sample size – 5000 in this case.

To test the significance, use the z-table at http://www2.sjsu.edu/faculty/gerstman/EpiInfo/z-table.htm to read the significance of the difference between the two average net incomes. If the probability us low, this tells you that the difference of the average net incomes for the two packs is not significant.

I hope this helps.

Wayde
 
Posted by: andy Author Response
10/11/2005 8:01 PM (CST)
Thanks v much Wayde, just the info I was after.
 
Posted by: wnelson Member Response
10/11/2005 8:10 PM (CST)
Glad to be of help, Andy! Any time.

Wayde
 


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