Does the thought of p-values and regressions cause you to run off in an exceedingly cold sweat? There is no need to get worked up - We, at **3rd Eye Advisory®** are here to provide you with the answers to a number of consuming statistical queries that keep you awake, 87.9% of the night.

**Know about 'Hypotheses'**

The statistical practice of hypothesis testing is prevalent not only in Statistics, but also throughout the natural and social sciences.

From business POV, hypothesis test might be set up with a specific end goal to clarify how much an expansion in labour influences profitability. Thus, hypothesis testing serves to investigate the relationship between at least two factors in an exploratory setting. Business managers may then use the results of a hypothesis test when making management decisions. Hypothesis testing enables business managers to inspect causes and effects before settling on a vital management decision.

Example: Determining if the average daily return, of any stock listed on XYZ stock market, around New Year's time is greater than 2%.

- H
_{0}: Null Hypothesis: mean = 2% - H
_{1}: Alternative Hypothesis: mean > 2% (This is what we want to prove)

- H
**Data Collection**

As hypothesis testing is absolutely a statistical exercise, data is quite often required before carrying out a test. Data might be acquired from economic research offices or management consultancy firms, who may even complete the hypothesis testing for the benefit of the business. Data are assembled for a given hypothesis. So if a business wishes to investigate how economic growth influences a company or firm's profitability, the management consultancy will probably gather data concerning GDP growth and the net revenues of the organization in the course of the last 10 or 20 years.**The Hypothesis Process**

After collecting sufficient data, we usually fit a linear model**→ y=ax+b**where in this example-

x: Economic Growth

y: Company Profits, as our motive is to test the effect of change in 'x' on 'y'.

The fascinating parts of the equation, y = ax+b are 'a' and 'b', where-

a: y- intercept & b: Slope of the equation.

We may have certain conditions:

- If 'a' is large → then a small change in economic growth would significantly influence company profits and vice-versa.
- If a=0 → No effect of economic growth in company's profits.

In the second case, the null hypothesis, H0 will be accepted as there will be no effect or association between economic growth and profits of the association. Rejecting the H0 would mean that economic growth does in fact have an effect on profits.

Hypothesis testing is performed with expert statistical software packages like SPSS, R, Stata etc. Association between factors of very large samples is analyzed by these statistical software packages. Data are fed into the framework and the program does the rest. It is up to the analyst to decipher the outcomes.**Level of Significance**

A standout amongst the most widely recognized numbers you unearth in Statistics is alpha (α). Alpha means the fixed significance level. It is the probability of rejecting the H_{0}, when it is true for a given hypothesis test. One of the main variables an analyst looks for is the critical values. Critical values vary depending on the type of statistical test is performed, but usually values represent significance levels of 1, 5 or 10 %.

For instance, a significance level of 0.05 indicates a 5% risk of assuming that that there is an impact of economic growth on the net revenues of the company, when actually there is no effect. Before beginning with any statistical experiment, alongside stating the hypotheses, you fix a level of significance you're testing at.

In the above mentioned example of economic growth and its effect on profitability of the company, rejecting H_{0}at 1 % significance level infers absolute confidence that "x" has no impact on "y." On the contrary, if the analyst can't reject the null hypothesis, H_{0}even at 10 % level of significance, then he could state with a reasonable level that "x" has an effect on "y," and at a magnitude of "a."

For financial calculations (including behavioral finance), 5% is the generally the accepted limit.**Type I Error (Producer's Risk) and Type II Error (Consumer's Risk)**

There are two sorts of errors, which by its nature can't be evaded, and we should know that these errors exist. The errors are given quite common names of type I and type II errors.

- Type I errors happen when we reject a true null hypothesis. It is also called Producer's Risk or α Error. Producer's Risk is the probability that a good product will be rejected as a bad product by the consumer.
**Example of a Type I Error:**

Suppose on the basis of data, the research team of a firm concluded that more than 50% of the total customers like the new service started by the company, which is, in fact, less than 50%.- Type II errors happen when we don't reject a false null hypothesis. Can be also called as Consumer's Risk or β Error. It is the imminent risk found in all consumer-oriented commodities, that a product not meeting quality standards will pass undetected through the manufacturer's quality control system and enter the consumer marketplace.
**Example of a Type II Error:**

Assume that on the basis of sample results, the research team of a company claims that less than 50% of the total customers like the new service started by the company, which is, in fact, more than 50%.

**p-Values**

When you perform a hypothesis test in Statistics, a p-value helps you decide the significance of your outcomes. All hypothesis tests eventually utilize a p-value to measure the quality of the confirmation (what the data are enlightening you regarding the population). The p-value is a number in between 0 and 1 and construed in the following way-

- p-value (generally ≤ 0.05) indicates strong confirmation against the null hypothesis, so you reject the null hypothesis.
- A large p-value (> 0.05) indicates weak evidence against the null hypothesis, so you don't reject the null hypothesis.
- p-values, very close to the cut-off (0.05) are considered to be marginal (could go either way).

Always report the p-value so your readers can draw their own conclusions.

For instance, suppose:

- Pharmaceutical company XYZ claims their anti-flatulent product cures acidity in 5 minutes or less on an average but you think it's more than that.
- You conduct a hypothesis test because you believe the null hypothesis-

H_{0}: mean time in which the acidity is cured is at most 5 minutes, is incorrect.

Your alternative hypothesis-

H_{1}: mean time is greater than 5 minutes, which is correct. - You randomly sample some time durations in which the product had cured acidity previously and run the data through the hypothesis test, and your p-value turns out to be 0.002, which is much less than 0.05.
- In real terms, there is a probability of 0.002 that you will mistakenly reject the pharmaceutical company's claim that their product cures acidity in less than or equal to 5 minutes.
- Since, generally we are willing to reject the null hypothesis when this probability is less than 0.05; you conclude that the pharmaceutical company is wrong.
- In fact, their anti-flatulent product takes more than 5 minutes on an average to cure acidity.
- But, you could also be wrong by having sampled an unusually high number of cases in which it took more than 5 minutes to cure acidity, just by chance.

Statistics can observe accurate relationships. A cautious audit of data can uncover links between two factors, for example, particular sales offers and changes in income or dissatisfied clients and products purchased. Diving into the data further can give more specific speculations about the associations with test, which can prompt more control over consumer loyalty, rehash buys and consequent sales volume.

Alright! So, maybe that's not 'everything' you need to know about Statistics as it is a subject as vast as an ocean, but here, the null hypothesis that there is no effect of this article on your Statistical knowledge can be safely rejected in favour of the alternative hypothesis that there is definitely an effect of this article on your Statistics know how.

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