Table of Contents

Toggle__Probability:__

- Probability expresses the chance of an incident occurring.
- Literally, probability means the possibility.
- It gives an idea on the certainty or uncertainty of any random incident.

### Formula for assessing Probability:

Probability (P) = Favourable outcomes/Total number of outcomes

- Probability value comes in between 0 & 1 in decimals.
- Its value can never be negative.

For eg, in the case of coin toss, the outcome would be either head or tails.

Hence, here, total number of outcomes is 2.

If we check the Probability of getting heads in each toss,

P=1/20

P=0.5

Thus, it can be concluded that there is 50% chance of getting either head or tail in each toss.

### Terminology in relation to Probability

Term | Meaning |

Experiment | An activity whose outcomes are not known |

Random Experiment | An experiment for which the set of possible outcomes is known |

Trial | The various attempts in the process of an experiment |

Event | A trial with a well-defined outcome |

Outcome | Result of a trial or an experiment |

Sample Space | Set of outcomes of all the trials in an experiment |

Sample Point | One of the possible results of a trial |

Eg:

Term | Meaning |

Experiment | Causes for a disease |

Random Experiment | Type of Shareera prakriti (7 outcomes: ekadoshaja, dvandvadoshaja, sannipataja) |

Trial | Checking various parameters to assess prakriti |

Event | Assessing Hair density & prakriti (dense, sparse, thin) |

Outcome | Dense hair in case of dominance of kapha dosha |

Sample Space | Shareera Prakriti = Vataja, Pittaja, Kaphaja, Vatapittaja, Pittakaphaja, Kaphavataja, Sannipataja |

Sample Point | Marking each parameter of prakriti to all the questions in a subject. |

### Events in relation to Sample Space:

- Equally likely Events

If the events have the same probability of occurrence, then they are called equally likely events.

Eg:

- Getting 1 and 6 on throwing die.
- Vipaka of a drug being either madhura, amla or katu.

- Complementary Events

If there are just two events, and one event is exactly opposite to the other event, that is termed as complementary events.

Eg:

- Getting pass or fail in an exam.
- A disease being either curable or incurables.

- Impossible Events

The event that cannot happen is called an impossible event.

Eg:

- Getting 9 on throwing a die.
- The symptom daha occurring due to kapha dosha.

**Mutually Exclusive Events**

Two events are said to be mutually exclusive events if they cannot occur at the same time.

Eg:

- Getting heads and tails at the same time on tossing a coin.
- Getting both adanakala and visargakala features in a single ritu.

## Test of Significance:

- A test of significance is a prescribed method for comparing observed data with a claim (hypothesis), the truth of which is being assessed.
- Significance is crucial to reject or form a precise interpretation, based on the available data and values.
- This is more like a testing process to accept or reject a claim (hypothesis) in a study, and hence the name “Tests of Significance”.

Steps in applying test of significance:

Step 1 | Stating Research Hypothesis (Alternate) |

Step 2 | Stating Null Hypothesis |

Step 3 | Choosing Error or Probability Level |

Step 4 | Computation using appropriate Tests of Significance |

Step 5 | Interpretation of Obtained Result |

### Types of Errors:

#### Type 1 Error:

- Reality: Null Hypothesis is to be accepted & Alternate rejected
- Error Done: Alternate Hypothesis is accepted & Null rejected.

Eg: A clinical experiment was done to compare the agnideepana efficacy of standard pancakola choorna with only pippali choorna.

Here:

- Alternate Hypothesis: Pippali choorna is more efficient in agnideepana when compared with pancakola choorna.
- Null Hypothesis: Pippali choorna is not as much efficient as pancakola choorna in performing agnideepana.
- After the result, let us assume that in reality, Pancakola choorna is more efficient in agnideepana when compared with only pippali.
- Thus, Null hypothesis should have been rejected and alternate accepted.
- But, the researcher accepts Alternate Hypothesis & concludes that Pippali choorna is more efficient in agnideepana when compared with pancakola choorna.
- This is an example for Type 1 Error.

#### Type 2 Error:

- Reality: Alternate Hypothesis is to be accepted & Null rejected
- Error Done: Null Hypothesis is accepted & Alternate rejected.

Eg: A clinical experiment was done to compare the virecana & vamana for pittashamana.

Here:

- Alternate Hypothesis: Virecana is more efficient in pittashamana when compared with vamana.
- Null Hypothesis: Virecana is not as much efficient as vamana in doing pittashamana.
- After the result, let us assume that in reality, Virecana is more efficient in pittashamana when compared with vamana.
- Thus, Alternate hypothesis should have been accepted and Null rejected.
- But, the researcher accepts Null Hypothesis & concludes that Virecana is not as much efficient as vamana in doing pittashamana.
- This is an example for Type 2 Error.

Conclusion:

- Tests of significance involve the acceptance or rejection of a sample data collected from the target population
- Errors are possible during this process and it can be Type 1 or Type 2.
- Only 5% chance error is possibly allowed for any research.

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