##### What is a Hypothesis?

At its core, a hypothesis is an educated guess. It's a statement that suggests a potential answer to a question or a possible solution to a problem. It is tentative in nature and serves as a starting point for further investigation.

Hypotheses are used primarily in scientific methods applied to research. In case of product management, we are making assumptions about product/customers/market and want to have proof

They pave the way for experiments and studies. Once a hypothesis is formed, researchers then set out to test its validity. The results of their experiments will either support the hypothesis, modify it, or disprove it entirely.

##### Different Types of Hypotheses

When we have assumptions this is important to formulate 2 types of hypothesis.

**Null Hypothesis (H0)**:

This asserts that there is no difference or effect.

When conducting a hypothesis test, our aim is to challenge the null hypothesis and our experiment is constructed so we **try to reject the null hypothesis**

It serves as a default position.

For instance, let's consider the commonly accepted idea that the average adult body temperature is 98.6 degrees Fahrenheit. If we were to test this, our null hypothesis might state, “The average body temperature for healthy adults is 98.6 degrees Fahrenheit.” Not rejecting this hypothesis simply maintains our current belief that a typical healthy adult has a temperature of 98.6 degrees. It doesn't verify it as a fact.

**Alternative Hypothesis (Ha)**:

This is essentially the opposite of the null hypothesis. It posits that there is a difference or effect.

When conducting a hypothesis test, if statistics show us that there is statistical significance **we reject null hypothesis**

For instance, let's consider the commonly accepted idea that the average adult body temperature is 98.6 degrees Fahrenheit. If we were to test this, our alternative hypothesis might state, “The average body temperature for healthy adults is not 98.6 degrees Fahrenheit.” It created by just adding not in the Null hypothesis.

**Funny language:**

In statistic world, it could be awkward how we describe the hypothesis tests results correctly, but these are commonly used ways to say our results. We can :

a) Reject null hypothesis (it means our experiment shows that our assumption is correct and there is significant difference)

b) Failed to reject null hypothesis (it means our experiment shows that our assumption is incorrect and there is no significant difference)

**Mathematical addition to hypothesis:**

In scientific world almost every time you can see they hypothesis are supported by mathematical formulas corresponding to the type of hypothesis.

When we assume that there is no difference(null hypothesis) we can say Option **"="** Population

When we assume that there is difference, it could be >, >=, <, <= or ≠

We use >, >=, <, <= for 1-sided hypothesis tests (you can read about it in post about hypothesis testing)

We use ≠ for 2-sided hypothesis tests (you can read about it in post about hypothesis testing)

##### How to Form a Hypothesis

**1. Start with the assumption:** The birthplace of any hypothesis is a simple question. This question could be something you've always wondered or it could arise from observing a pattern or trend.

*Example Question*: Does daily listening to classical music affect a person's concentration levels?

*Example question 2: Some users users are more likely to buy child clothes for newborns?*

**2. Conduct Preliminary Research:** Before you form a hypothesis, it's important to have a basic understanding of the subject. Delve into existing research and studies to gain insights.

**3. Make it Specific:** A hypothesis should be clear and precise. Vague statements can make testing and validation difficult.

*Vague Hypothesis*: Music affects concentration.

*Specific Hypothesis*: Listening to classical music for 30 minutes daily increases a person’s concentration levels.

*Vague Hypothesis 2*: Some users buy more child clothes.

*Specific Hypothesis 2*: *Users in age between 20 to 30 years are more likely to buy child clothes for newborns?*

**4. Ensure it's Testable:** A good hypothesis should be testable. This means you should be able to design an experiment or study to determine its validity.

**5. Keep it Simple:** While a hypothesis should be specific, it doesn't need to be overly complex. Avoid adding too many conditions or variables because it can over complicate tests(see point 4).

**6. Formulate Null and Alternative Hypothesis: **Make sure you write down Null and Alternative hypothesis

##### Examples of Hypotheses:

These examples where taken from Penn state: Eberly college of science.

*Example 1:*

**Research Question**: *A financial analyst believes there might be a positive association between the change in a stock's price and the amount of the stock purchased by non-management employees the previous day* (stock trading by management being under "insider-trading" regulatory restrictions).

**Variables**: Daily price change information (the response variable) and previous day stock purchases by non-management employees (explanatory variable). These are two different measurement variables.

**Null Hypothesis**: The correlation between the daily stock price change ($) and the daily stock purchases by non-management employees ($) = 0.

**Alternative Hypothesis**: The correlation between the daily stock price change ($) and the daily stock purchases by non-management employees ($) > 0. This is a one-sided alternative hypothesis (about 1-2 sided hypothesis you can read in next post)

*Example 2: *

**Research Question**: *Does the data suggest that the population mean dosage of this brand is different than 50 mg?*

**Response Variable**: dosage of the active ingredient found by a chemical assay.

**Null Hypothesis**: On the average, the dosage sold under this brand is 50 mg (population mean dosage = 50 mg).

**Alternative Hypothesis**: On the average, the dosage sold under this brand is not 50 mg (population mean dosage ≠ 50 mg). This is a two-sided alternative hypothesis.

*Example 3: *

**Research Question**: *Does the data suggest that, on the average, people are able to lose more weight on a low carbohydrate diet than on a low fat diet?*

**Response Variable**: Weight loss (pounds)

**Explanatory (Grouping) Variable**: Type of diet

**Null Hypothesis**: There is no difference in the mean amount of weight loss when comparing a low carbohydrate diet with a low fat diet (population mean weight loss on a low carbohydrate diet = population mean weight loss on a low fat diet).

**Alternative Hypothesis**: The mean weight loss should be greater for those on a low carbohydrate diet when compared with those on a low fat diet (population mean weight loss on a low carbohydrate diet > population mean weight loss on a low fat diet). This is a one-sided alternative hypothesis.

*Example 4:*

**Research Question**:* Is there a linear relationship between the amount of the bill ($) at a restaurant and the tip ($) that was left. Is the strength of this association different for family restaurants than for fine dining restaurants?*

**Variables**: There are two different measurement variables. The size of the tip would depend on the size of the bill so the amount of the bill would be the explanatory variable and the size of the tip would be the response variable.

**Null Hypothesis**: The correlation between the amount of the bill ($) at a restaurant and the tip ($) that was left is the same at family restaurants as it is at fine dining restaurants.

**Alternative Hypothesis**: The correlation between the amount of the bill ($) at a restaurant and the tip ($) that was left is the difference at family restaurants then it is at fine dining restaurants. This is a two-sided alternative hypothesis.

## Conclusion

Formulating a hypothesis is a foundational step in the scientific method. It’s more than a mere guess; it’s an educated assumption that directs the course of research. By making predictions and then testing them, we not only learn more about the world around us but also refine our understanding and knowledge. The beauty of a hypothesis is in its simplicity, specificity, and testability.