# Probability and Likelyhood for Business —Increase revenue

In marketing and business intelligence, A/B testing is a term for a random experiment with two variants, A and B, probability of events occurring and it also looking at all the possibilities the event can occurs in N number of time in a given time period.

So remembering your basic Math theory Probability where gravity does not come to play. In term of Marketing A/B testing sometimes called bucket test or split-run testing. It not called bucket test for no reason has you can test more than two variants at anyone time in any given time period.

**A/B testing formulas are like so**:

1. fn(S) = 1, then fn(A ∩ B) = fn(A) + fn(B). where S is the certain event;

2. If A ∩ B = ∅ then fn(A ∪ B) = fn(A) + fn(B). - this the relative frequency of an event in a given time period.

So let consider the following **A/B split test = ****#Likethepicture**** or ****#Dislikethepicture**** **and I am going to demonstrate to you that it is based on the Math Theory Probability and Gravity does not come to play has the information is static. **Please take part in our fun experiment below and click on link like or dislike to express your opinion**.

Click on the picture you like or dislike or click on relevant link under the picture

** Click if you**__ like__** or **__dislike__** me Click if you **__like__** or **__dislike__** me**

S= (Like) , (Dislike) - is an event which happens with certitude at each repetition of an experiment.

A={(like),(Content), (Conversion)}

B={(Dislike),(Content),(Conversion)}

The possible outcome is this sample distribution (A) & (B) - If A is the set of results which represent an event, then the set {A (the complementary of A) is the set of results which represent the contrary event.

We have seen that the fact that the event A implies the event B means that whenever A takes place, B takes places as well. Therefore, the set of results representing the event A is included in the set of results representing the event B: A ⊂ B.

(A)U( B) = Like picture or dislike picture - The union A∪B of two events A and B is the event which takes place when at least one of the events A or B occur.

The intersection A ∩ B of two events A and B take place when content is looked at and when conversion happen.

**Now let me show you how the frequency of this AB split test is part of basic math probability theory**

Let’s consider the following AB split test and an event (A,B) associated to this test. We repeat the experiment n times (in given conditions) and we denote by α the number of occurrences of the event (A,B). **The number of occurrences of the event A¯ is n − α**

The number fn(A,B) = α n is called relative frequency of the event AB

To test the absolute frequency it is said The number α, called absolute frequency of the event AB, is between 0 and n; α = 0 if during n repetitions of the experiment, the event AB did never occur;

α = n if the event AB occurred at every repetition of the experiment. Therefore 0 ≤ α ≤ n and 0 ≤ fn(AB) ≤ 1, ∀n ∈ N ?

**Probability of Event in set (A, Like, content, conversion) (B, Dislike. content, conversion)**

As these two events like and dislke are equally possible, it is natural to estimate (to measure) the chance of occurrence of each of them by 1/2 = the inverse of the number of elementary events from A (the relative frequency 50% = 1/2 of each of the two events).

**Conclusion**

So you see how our example experiment apply to the theory of probability and gravity does not come to play as the information is static. If you understand this likelihood of events, when looking at your analytic you will understand the result gathered by Google, Bing, or Social Media Analytic they are using probability theory and hypothesis including the likelihood this events will happen and that enable to develop software that use predictive behavioural pattern such as Watson from IBM cognitive analytic it took then 10 years to developed.

**A/B split testing can be use virtually on anything you want to do or test and get meaningful result such as conversion, lead and paying customers.**

In online settings, such as ** web design** (especially user experience design), the goal of A/B testing is to identify changes to web pages that increase or maximise an outcome of interest (e.g., click-through rate for a

**).**

__banner advertisement__

Formally the current web page is associated with the null hypothesis. A/B testing is a way to compare two versions of a single variable typically by testing a subject's response to variable A against variable B, and determining which of the two variables is more effective.

As the name implies, two versions (A and B) are compared, **which are identical except for one variation that might affect a user's behaviour**. Version A might be the currently used version (control), while version B is modified in some respect (treatment).

For instance, on an e-commerce website the purchase funnel is typically a good candidate for A/B testing, as even marginal improvements in drop-off rates can represent a significant gain in sales. Significant improvements can sometimes be seen through testing elements like **copy text, layouts, images and colours, but not always**.

Simple A/B tests are not valid for observational, quasi-experimental or other non-experimental situations, **as is common with survey data, offline data, and other, more complex phenomena.**

A/B testing has been marketed by some as a change in philosophy and business strategy in certain niches, **though the approach is identical to a between-subjects design, which is commonly used in a variety of research traditions.**

A/B testing as a philosophy of web development brings the field into line with a broader movement toward evidence-based practice. The benefits of A/B testing are considered to be that it can be performed continuously on almost anything, especially since most marketing automation software now, typically, comes with the ability to run A/B tests on an on-going basis.

This allows for ** updating websites** and other tools, using current resources, to keep up with changing trends.

Thank you for taking part in our experiment Trisha Amable (girlfridayz)