# How to use statistical hypothesis testing to find if associations between discretised account balances and campaign conversion rates

Background

I have a situation where I have data on bank balances of various respondents, and a flag for whether they completed a desired action (i.e., whether they purchased a loan or not). The data on savings/money has been discretised, however.

Problem statement

A concern has been raised that the bank balances of respondents might not be the actual ones, but updated (updated bank balance = original balance + loaned amount).

How to verify this? I have tried formulating an approach below.

Solution formulation

Since I only have discretised data, I thought I could set up a statistical hypothesis test for proportions.
Hypothesis: If the proportion of success/loan purchasers increases drastically as we move up higher in account balance groups, it would indicate the balances are inclusive of loans.

As shown in the image, there is an unexpected increase in success rate, and at this point, it seems no statistical test is needed?

My questions:

1. Is the aforesaid sufficient evidence? How can I make it more thorough (statistically), assuming I will not get the actual balances?
2. If I did get actual balances, how can I gather evidence to verify that there is/is not a group of people whose balances are inflated due to loan amount

I am extremely interested in understanding Stats. application to such problems, and understanding the Statistical theory, so I would be indebted to understand the wrongs of my way.

Data

``````structure(list(finalClass = c("Reject/Cancel", "Success", "Reject/Cancel",
"Success", "Success", "Reject/Cancel", "Reject/Cancel", "Success",
"Reject/Cancel", "Success", "Reject/Cancel", "Success", "Reject/Cancel",
"Success", "Success", "Reject/Cancel", "Success", "Reject/Cancel",
"Reject/Cancel", "Success", "Reject/Cancel", "Success", "Reject/Cancel",
"Success", "Success", "Reject/Cancel", "Reject/Cancel", "Success",
"Success", "Reject/Cancel", "Success", "Reject/Cancel", "Success",
"Reject/Cancel", "Reject/Cancel", "Success", "Reject/Cancel",
"Reject/Cancel", "Success"), balance_new_bracket = c("01. <= 10k",
"01. <= 10k", "02. 10k - 20k", "02. 10k - 20k", "03. 20k - 30k",
"03. 20k - 30k", "04. 30k - 40k", "04. 30k - 40k", "05. 40k - 50k",
"05. 40k - 50k", "06. 50k - 60k", "06. 50k - 60k", "07. 60k - 70k",
"07. 60k - 70k", "08. 70k - 80k", "08. 70k - 80k", "09. 80k - 90k",
"09. 80k - 90k", "10. 90k - 100k", "10. 90k - 100k", "11. 100k - 200k",
"11. 100k - 200k", "12. 200k - 300k", "12. 200k - 300k", "13. 300k - 400k",
"13. 300k - 400k", "14. 400k - 500k", "14. 400k - 500k", "15. 500k - 600k",
"15. 500k - 600k", "16. 600k - 1M", "16. 600k - 1M", "17. 1M - 2M",
"17. 1M - 2M", "18. 2M - 3M", "19. 3M - 6M", "19. 3M - 6M", "20. > 6M",
"20. > 6M"), N = c(18232L, 5115L, 1697L, 819L, 364L, 761L, 476L,
245L, 308L, 137L, 210L, 108L, 155L, 89L, 77L, 137L, 52L, 108L,
103L, 39L, 569L, 260L, 233L, 182L, 1597L, 156L, 109L, 817L, 590L,
116L, 817L, 100L, 51L, 62L, 9L, 1L, 3L, 4L, 1L), percent = c(0.780914036064591,
0.219085963935409, 0.674483306836248, 0.325516693163752, 0.323555555555556,
0.676444444444444, 0.660194174757282, 0.339805825242718, 0.692134831460674,
0.307865168539326, 0.660377358490566, 0.339622641509434, 0.635245901639344,
0.364754098360656, 0.35981308411215, 0.64018691588785, 0.325,
0.675, 0.725352112676056, 0.274647887323944, 0.686369119420989,
0.313630880579011, 0.56144578313253, 0.43855421686747, 0.911009697661152,
0.0889903023388477, 0.117710583153348, 0.882289416846652, 0.835694050991501,
0.164305949008499, 0.890948745910578, 0.109051254089422, 0.451327433628319,
0.548672566371681, 1, 0.25, 0.75, 0.8, 0.2), tots = c(23347L,
23347L, 2516L, 2516L, 1125L, 1125L, 721L, 721L, 445L, 445L, 318L,
318L, 244L, 244L, 214L, 214L, 160L, 160L, 142L, 142L, 829L, 829L,
415L, 415L, 1753L, 1753L, 926L, 926L, 706L, 706L, 917L, 917L,
113L, 113L, 9L, 4L, 4L, 5L, 5L), conf_low = c(0.775552136317493,
0.213794081502295, 0.65578046562415, 0.307220804467065, 0.296264735635882,
0.648227521218143, 0.624326658051425, 0.305255642604346, 0.646947176024304,
0.265253980427813, 0.60544358384926, 0.287709357961987, 0.571443652323727,
0.304282016481803, 0.295522603420615, 0.571952527712148, 0.25317409400087,
0.596551368545636, 0.64420157566435, 0.203150823708409, 0.653560936603063,
0.282154345692913, 0.51220524670192, 0.390195953557052, 0.896698056863425,
0.076072772673856, 0.0976559949418072, 0.859767702403072, 0.80626156910148,
0.137713232814479, 0.868959355941994, 0.0896127959455879, 0.357541357583628,
0.452272456810347, 0.663732883120057, 0.00630946320970987, 0.194120449683243,
0.283582063881911, 0.00505076337946806), conf_hi = c(0.786205918497705,
0.224447863682507, 0.692779195532935, 0.34421953437585, 0.351772478781857,
0.703735264364118, 0.694744357395654, 0.375673341948575, 0.734746019572187,
0.353052823975696, 0.712290642038013, 0.39455641615074, 0.695717983518197,
0.428556347676273, 0.428047472287852, 0.704477396579385, 0.403448631454364,
0.74682590599913, 0.796849176291591, 0.35579842433565, 0.717845654307087,
0.346439063396937, 0.609804046442948, 0.48779475329808, 0.923927227326144,
0.103301943136575, 0.140232297596928, 0.902344005058193, 0.862286767185521,
0.19373843089852, 0.910387204054412, 0.131040644058006, 0.547727543189653,
0.642458642416372, 1, 0.805879550316757, 0.99369053679029, 0.994949236620532,
0.716417936118089)), row.names = c(NA, -39L), class = "data.frame")
``````

PS. This is a cross-post from Twitter, where I tried having a discussion about this (and Frank Harrell kindly advised on getting actual balances) but I realised it is a lengthy one, not suitable to Twitter.

There arenâ€™t any BIO-statistical issues in your problem, so Cross-Validated would be the best place for discussing it.

That said, even if the pattern in the data seems to fit your hypothesis, I can think of 3 other possible explanatory hypotheses for such a pattern, and Iâ€™m an amateur in this field. With data pre-aggregated to this level, you canâ€™t do much.

The best solution is to ASK THE PEOPLE WHO PREPARED THE DATA to explain exactly what the Balance figure is. Was it â€śbalance at the time of loan offerâ€ť, or something else.

If confirming the data definitions with the source is not possible, then preface your analysis with â€śusing data as givenâ€ť and explain the implications or limitations.

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