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I don't understand when to use which statistics. Please explain.

So I have the customer data with columns like registration and tenure. Registration column values are 'yes/no' and tenure is a continuous variable with number of months they are with us.

Total number of customers - 500k Registered ones - 110k Non-Registered ones - 390k

My NULL Hypothesis - Registration has no effect on tenure

Alternate Hypothesis - Registration has positive effect on tenure (In other words,registered customers are staying with us for long)

I did descriptive statistics and compared the mean of both groups (registered and non registered), it shows that the registration has negative effect on tenure. Mean or median of registered customers is less than non registered ones. However, I am not sure if I can confirm the negative effect. Questions are,

  1. Can i trust the descriptive statistics in this scenario?
  2. What I have is sample data or population? I have all our customers.
  3. Distribution behind the tenure is not normal, it looks like the below one. If I have to do inferential statistics to test my hypothesis. what tests i should consider?

Registration was not always an option for the customers. We started this few years ago and so the mean of registered customers is lower than the non registered ones. Is there any other way to look at this problem to find the loyalty of customers?

enter image description here

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    $\begingroup$ If you have data for your whole population (all the individuals of interest - all the customers) then you have no need for inferential statistics, descriptive statistics is enough. In that case there are no hypotheses, you merely estimate means (for ex.) and then you decide if these are different enough, again you have to decide what is a "big enough" difference. $\endgroup$ – user2974951 Dec 4 '18 at 9:50
  • $\begingroup$ Thanks. Let's assume I dont have the entire customer list, can you answer the other questions. I am trying to understand. $\endgroup$ – ds_user Dec 4 '18 at 9:55
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    $\begingroup$ Can you show us the plots for the registeres and non-registered plots separately? Also what is that plot that you included? $\endgroup$ – user2974951 Dec 4 '18 at 10:11
  • $\begingroup$ Can you explain more about registration, and your dataset? Eg has registration always been an option, or was it introduced recently? In order to trust the statistical inference, one has to have clear understanding of how data was collected. E.g. If registration only started 1year ago and unregistered 5years ago, then your mean tenure would be lower for registered customers? $\endgroup$ – seanv507 Dec 4 '18 at 17:51
  • $\begingroup$ Yes. You are right. Registration was introduced few years ago and that is affecting the mean of registered ones. And the plot I have included above is the tenure distribution in months. $\endgroup$ – ds_user Dec 4 '18 at 17:54
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  1. Descriptive statistics don't tell you whether something is 'significantly' different -they are not a statistical test of your hypotheses and can't tell you the 'probability' of your alternative hypothesis being correct, but they do help you understand your data. The distribution plot is a good way of understanding your data too. You have some very large numbers for tenure (e.g. 483) that will be strongly influencing your mean in the groups they turn up with.

  2. It depends how you're defining your population. You have the entire population of your customers so far. But your customers so far are just a sample of the population that is all of your potential customers.

  3. A couple of thoughts to consider before you start using statistical tests - firstly, your distribution isn't continuous if you are measuring it in whole numbers of months, it is discrete (number of months). You may be able to approximate it to a continuous distribution though, and transform the data to make it more normal.

    Secondly, what is the big peak in tenure at 7 months? Was there a campaign to get new customers? What potential bias might this introduce to your analysis (e.g. is there something different about the customers recruited in that month?), and is there a way you can deal with that?

    I would consider something like a Mann Whitney/Wilcoxon test, because that won't be influenced as much by outliers and I think it will work for discrete data so long as you use a version of the test that can deal with tied values (i.e. then you won't need to transform your data to use it).

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  • $\begingroup$ Thanks for your answer. 1. Yes you are right. Outliers impact the mean, so I am thinking of using median here. 2. I am still trying to understand this, registration is a process which started few years ago and so the registered number of customers will keep changing over the period. So not sure if I can take this as my population or as sample 3. Not sure If there was a campaign before 7 months, I can check that. $\endgroup$ – ds_user Dec 4 '18 at 18:01
  • $\begingroup$ If you are trying to understand how registration affects the tenure of your potential (future) population of customers, then your customers so far are just a sample of that. So I would be inclined to treat this as a sample of an infinitely large population. $\endgroup$ – Izy Dec 5 '18 at 11:51
  • $\begingroup$ I agree with seanv507 that you should only consider customers since registration began - remove other customers from the dataset. Also consider other things that could be introducing bias to the dataset - such as campaigns etc. Have you considered whether customers sometimes leave and then return after a gap in tenure - if so how do you deal with that? Once you've filtered down your dataset, have another look at the distribution and decide whether you can approximate and transform it to a continuous normal distribution - if so you could carry out a t-test. Otherwise, consider a Mann Whitney. $\endgroup$ – Izy Dec 5 '18 at 11:55

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