What Hypothesis Test do I use?

Question

I have a problem where we submit amounts for debit orders internally, we calculate an overall success rate as successful debit order amount divided min(net salary of the client,arrears amount outstanding) to give us an overall success rate between two different strategies. My question now is which test I should use to relate the two success rates given different strategies (and volumes associated to these strategies).

Please assist me with this.

Answer 1

Well, Marla is certainly correct that the data are not paired. It would also appear that the data do not have a truly normal distribution as they do not encompass the set of Real numbers in that they are limited to positive values.

Still, this is a common limitation and within limits an assumption of normality of the individual measurements here is probably valid. (note: contrary to Marla's comments about Gosset's t-distribution , the t-test and the t-distribution are applicable ONLY to normally distributed variables)

So, assuming normality within the range of interest as a starting requirement, statistical tests on the means of multiple measurements of a normally distributed variable can only be made if there ARE multiple measurements. Where the success rate as defined by the poster is applied to EACH individual, then one would have a number of success rate values which can be combined into two sets (one for each strategy) and the mean success values (SV) can be compared using a t-test or an ANOVA.

Where SV = SDO / min(NCS, AAO).

If there is only a single overall value calculated for each strategy, then no tests can be made. Hypothesis testing is generally on the means or expected value of a measure, not a single shot measure.

note:

SDO = successful debit order amount

NCS = Net client salary

AAO = client Arrears amount outstanding

Answer 2

Best I can tell, your data isn't paired. I'm not very familiar with the terminology you use, but look at your endpoint(i.e. success rate).

Is it continuous? If 'Yes', then how many data points do you have: is it enough for the you to use the "law of large numbers" to assume it's normally distributed? If both are true you can use the Z-test, if you can't assume normality, then use the Student's t-test instead. If your endpoint is a ratio, you might want to consider expressing it as a decimal or percentages, so you can compare them on a level field, then the same advice would hold, what's the distribution of the data (normal or not), and how much data do you have (Can you use the Law of Large Numbers, if needed)?

That should give you a good start, Good luck working through the details.