The Statistical ‘Pyaar’

The Statistical ‘Pyaar’

Rishabh was a random boy of our neighbourhood who right from his teenage was attracted towards a random girl, Lisa of the same locality. People often felt Rishabh’s behavior was far from normality and Lisa perhaps could not be fit into any parametric distribution.

After days of day dreaming and admiring the beauty of Lisa, one day Rishabh decided to express his love for her, but Rishabh was a true statistician. He wanted a conclusive and a definite answer for his proposal and so before proposing, he decided to check the results based on a random sample of events. Only those events were selected where only 2 independent entities Lisa and Rishabh were present excluding the entire outer world. This resulted in formulation of two hypotheses:

H0: Lisa did not love Rishabh

H1: Lisa loved Rishabh

 

The parameters for love chosen by Rishabh were the following:

(i)                Amount of time spent on telephone by her with him

(ii)              Number of messages/calls made by her where she made the initiation

(iii)            How many times did she agree to go out with him for dinner

(iv)            Number of times the expression of her eyes indicated love

(v)              Number of other hints given by her which might become a cause to believe she loved him

Out of these, the (iv) one according to him was the best proxy for love though he was himself not very convinced about it.

Rishabh had the data for all these facts and so he tried to test the hypothesis. As per the data availability, the p-value was much greater than 0.05 provoking Rishabh to reject his H0 with 95% or 99% level of significance. Thus the sample results were in favour of Rishabh. He also fitted a model using the independent variables from (i), (ii), (iii) and (v) and the dependent variable being (iv). He got a reasonably good R-square value and he was convinced about the goodness of his model fit.

The next morning, Rishabh was very fresh and happy. He already knew the answers of his proposal. His test was of very high power and he felt there was negligible chance of his rejection. He had used his statistical sense in his love life and had successfully drawn inference and also predicted the love of Lisa.

He went to Lisa and opened up his mind. But, to his surprise several other factors unexpectedly cropped up

(i)                She had a strict family and she didn’t have the courage to go against them.

(ii)              She was a catholic and couldn’t go against religion.

(iii)            She was not ready for any kind of serious relationship now as she was busy focusing on her career

On top of it Rishabh’s mother appeared from no where and started with her harsh words holding Lisa responsible for his poor performance in studies. This random error was least expected and disturbed the fundamental distribution. Noise became superior to the random boy and the random girl- Rishabh and Lisa. Rishabh had not accounted for this error and hence realized that the model was highly flawed.

Also, Rishabh learnt that Lisa had an ex-boy friend who was also a catholic and Rishabh needed to conduct a paired t test to find who would be more suitable for her. This would require collecting information about her ex as well. He had to on an average better than the ex-boyfriend. Again the newly found factors needed to be borne in mind while modeling. The chances of wrong decisions were the following

(i)                Accept Rishabh| ex was better

(ii)              Reject Rishabh| Rishabh was better

Thus, Rishabh considered false positive to be far more superior and hence he tried focusing on minimizing (ii). He was of very ethical in nature and would not mind much if Lisa rejected him given that ex-was better.

Rishabh once again tried after changing the model and the approach. He tried to fit his love model on Lisa. He checked the multicollinerarity and hetroskedasticity problem.  He introduced dummy variables in the models like gifts, promises, beliefs and trust of having a bright and a happy future. He then tried predicting the love of Lisa for him. This new model with lots of expensive gifts seemed to fit better. The R-square and the adjusted R-square value were greater than the earlier. This time the predicted value was again close to acceptance and this time Rishabh was more confident. He had induced refinement both in his model as well as in his relationship.

Rishabh was again set to propose the girl. Lisa this time melted and from two mutually exclusive and completely disjoint sets, they became overlapping set with some amount of their heart common to both. Thus Lisa did not have sufficient evidence in her favour to reject him. But, Rishabh was yet not satisfied. He aimed for a sure event and wanted to arrive at a discrete inference. Hence, he waited to get a job for himself which could fetch him extra points. He tried and impressed her parents who after a little more efforts accepted him with wider confidence interval. Lisa’s heart flew and she was impressed too. He began more interactions and associations with her. Rishabh’s degrees of freedom those days were just the same as the degrees of freedom of Lisa. The consistency, the efficiency and the sufficiency test all held good for Rishabh and she had negligible probability of rejecting Rishabh with probability of e-16.

Both Lisa and Rishabh tied their knots on the Statistics Day, 29^th June and two different scatter plots of them successfully evolved in having a correlation coefficient of  0.98- too much a couple could ask for. 

Rishabh’s statistical sense didn’t stop at this juncture. He knew the post marriage success mostly depended on the equation P(X<Y)=P(X>Y) where X and Y represents Rishabh and Lisa. Any dis-balance in the equation will result in the dis-balance in the stress and strength of the marriage. Rishabh believed that any distribution tends to behave normally when n-->∞. He thus tried to equate all his behavior, pattern etc to that of Lisa’s  to the extent possible. He knew that his rank was not a full rank and that was the sole aim of Rishabh post marriage because he knew every girl desired to have the highest rank for his husband and Rishabh strove hard for it.

Very soon both Rishabh’s and Lisa’s were able to successfully resolve minor differences that persisted and both of their ideas came closer and closer and merged at ∞. And they lived happily for n number of years where n-->∞.

Each love story is special and perfect in its own way and his one was statistically significant too!