Our contact center offers digital marketing solutions. Our client has asked to test the hypothesis that if the first call to a customer is longer (than a specific time) then the customer will most likely not answer the follow-up calls i.e the second and/or the third call. Can this be really tested? What kind of data should I look at? I am new to stats, please help me understand the technique and solve this problem.
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$\begingroup$ What of it? Record the length of the first call and whether they pick up on subsequent calls. $\endgroup$– tripleeeCommented Aug 11, 2021 at 12:08
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1$\begingroup$ As a starter you can do some visualisation of your historic data, plot first call time vs % of second calls, what does it tell you? $\endgroup$– Dirk NCommented Aug 11, 2021 at 15:29
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$\begingroup$ Thanks, that part has already been done. there is a difference like 52/48, but the client wants something statistical $\endgroup$– Mridul BhardwajCommented Aug 12, 2021 at 1:06
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1 Answer
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There are a bunch of more sophisticated ways to do this, but the quick solution is to be quite literal.
You have a binary predictor: if the call lasts longer than some amount of time.
You have a binary outcome: if the customer answer follow-up calls.
This is a classic situation for something called the chi-squared test. There are four outcomes.
Short call, follow-up answered
Short call, follow-up ignored
Long call, follow-up answered
Long call, follow-up ignored
Arrange these in a grid as references for the chi-squared test describe (I recall liking the Wikipedia article). The test then tests if the proportions of follow-up calls answered vs ignored differs between the long-call and short-call groups, exactly what you want to know.
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$\begingroup$ A more sophisticated approach could be to do away with dichotomization based on the threshold and analyze how follow-up responsiveness is influenced by call length. // As you mature as a statistician or analyst, you will get comfortable with answering questions from your boss or customer but also telling them that there is a better question to ask (and answering that question). $\endgroup$– DaveCommented Aug 11, 2021 at 12:33
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$\begingroup$ This is a good partial answer. There remains the (important) question of how to select calls for the dataset. In order to justify a chi-squared test, for instance, some form of randomization is required. $\endgroup$– whuber ♦Commented Aug 11, 2021 at 13:26
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$\begingroup$ Thank you Dave for the detailed answer, this really helps me understand the approach needed. $\endgroup$ Commented Aug 12, 2021 at 1:07
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$\begingroup$ @whuber - Can I not use the entire log for the last, say 6 months? is it like mandatory to draw a sample? $\endgroup$ Commented Aug 12, 2021 at 1:09
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1$\begingroup$ If you’re doing a hypothesis test, you are inferring something about a greater population, based on the observed sample. WHuber is, if I interpret the comment correctly, saying that you need to know the population from which your sample (which might be all of your points over the past six months) is drawn. // I should have picked up on this earlier, but time series issues could be in play. That can seriously wreck this kind of analysis of you do not consider that possibility or dismiss it but are incorrect. $\endgroup$– DaveCommented Aug 12, 2021 at 1:15