"Day 35 of My Learning Journey: Setting Sail into Data Excellence! Today's Focus: Mathematics for Data Analysis (Stats Day -14)
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Published: 2024-02-27 12:56:41

STATISTICS FOR DATA ANALYTICS - 14



MAKING A DECISION - REJECT OR FAIL TO REJECT NULL HYPOTHESIS.


Lets take an example :- 

Claim : average score in cricket = 70 ( based on his past games.)
Play 5 games of cricket together.
Avg score = 20 → less likely to believe the claim
Avg score = 65 → more likely to believe the claim
What score between nd 65 is the boundary, that made me change my decision. This point is called the critical point.

20 can be taken as LCV (LOWER CRITICAL POINT )

65 can be taken as UCV (UPPER CRITICAL POINT )


HOW WE MAKE DECISION?
IF THE SAMPLE MEAN LIE IN THE CRITICAL REGION MEANS MORE THE UCV AND LESS THAN LCV.

WE FAIL TO REJECT NULL HYPOTHESIS WHEN ITS VALUE IS IN WHITIN IN THE RANGE. MEANS BETWEEN UCV AND LCV.





TYPE OF ERROR 

TYPE 1 & TYPE 2 ERROR

Disclaimer: in this  example I don’t use any Jargon so that you can understand it.
We never say accept, we only say reject or fail to reject the null hypothesis.






ACTUAL VALUE ( NULL HYPOTHESIS ) 
PREDICTED VALUE


TRUE 
FALSE 
DO NOT REJECT 
( ACCEPT)
CORRECT DECISION
FALSE BUT ACCEPT
 ( TYPE 2 ERROR )
REJECT
TRUE BUT REJECT
 ( TYPE 1 ERROR )
CORRECT DECISION






MOSTLY WE GIVE THIS COLUMN ANSWER BASED ON THE PREDICTED VALUE NOT ON THE ACTUAL VALUE.

LET'S TAKE AN EXAMPLE :- 




Loan giving suggestion :- 

True accept - machines suggest giving loans to them and in actuality we must give them.

False accept - machines suggest giving loans to them and in actuality we must not  give them loans. ( type 2 error )

True reject - machines suggest not to give loans to them but in actuality we must give them loans ( type 1 error )


False reject - machines suggest not to give  loans to them and in actuality we don’t give them loans.




If you don’t understand with above example Another example :- 


Type 1 and Type 2 Error

Reality : Null hypothesis is True or  Null hypothesis is False
Decision : Null hypothesis is True or Null hypothesis is False.


Outcome 1 :- We reject the null hypothesis when in reality it is false —-------- Good

Outcome 2 :- We reject the null hypothesis when in reality it is True —-------- Type 1 error

Outcome 3 :- We retain the null hypothesis when in reality it is false —-------- Type 2 error

Outcome 4 :- We retain the null hypothesis when in reality it is True —-------- Good



Which error is more dangerous ?
It depends on the industry and the expert.

Both errors are manageable but inversely proportional to each other..




Significance value.

The risk of committing this error is the significance level ( alpha ) , chosen by us.

Ways to decrease the error
Decreasing type 1 error  ( alpha ):- 
Lower the significance value.

Decreasing type 2 error ( beta ) :- 
Increase sample size
Increase the significance value


Alpha increase Beta decrease  (vice verse ) inversely proportional. 



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