"Day 38 of My Learning Journey: Setting Sail into Data Excellence! Today's Focus: Mathematics for Data Analysis (Stats Day -17)
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Published: 2024-03-04 13:10:50

STATISTICS FOR DATA ANALYTICS - 17


Hypothesis testing and statistical Analysis

Type of Hypothesis 

Z-test - ( for numerical DATA )
Methods
Critical Value 
P-value method
	
T-test - ( for   numerical DATA )
Methods
One-sample mean test
Paired Two- Sample Mean Test
Unpaired Two-Sample Mean Test
Two-Sample Proportion Test
A/B Testing.	

Chi Square Test - ( for categorical DATA )	
Methods
Independent Test
Goodness of Fit

Anova Test - (  variance ) : F test
Method 
One-way ANOVA
Two-way ANOVA	






When to consider Hypothesis testing ?

When we have a previous mean of the previous data ( historic data )  and we want to predict the future value from it then we do hypothesis testing.



Z-test - numerical 

Conditions :- 

Standard deviation is given  & Sample above 30.
Standard deviation is not given  & Sample above 30.
Standard deviation is given  & Sample below 30.
We apply z-test.

Critical value method 
	
Two tail test

It is a value on both sides which creates boundaries.

Step 1 :- 

 UCV (UPPER CRITICAL POINT )
 	 
 UCV = 1 - ( ALPHA / 2 )
 

Step  2 :- 

With the value of UCV from z-table we get the z-score 
In we find a Z-score.
 the z-score is calculated for the critical points


Step 3 :- 

Calculator the following to get range.





LCV (LOWER CRITICAL POINT )

With the formula.

UCV (UPPER CRITICAL POINT )


Value between this ( upper and lower value ) is the acceptance value.

 

One tail test

	Example 

	Null hypothesis : mean <= 350 units ( based on previous data )

	Alternate Hypothesis : mean > 350 units ( prediction ) 

	One tail test ( specially a upper tailed test ) 

In this case we don’t divide the value of alpha by 2.

 
 UCV = 1 - ( ALPHA  )

Get the z value from z table. 

But why the upper tailed test ?
Because the mean value in alternate hypotheses is greater.


	




P-value method
This method is more frequently used in the industry.
	
Step 1 :-
	In this case we start by finding out the Z-value for a given sample mean.

With formula and then finding its value from the z-table.

	In the p-value method, the z-score is calculated for the sample mean.

	In the critical method , the z-score is calculated for the critical points.







What is P-value ?

P-value as the probability that the null hypothesis will not be rejected.

The higher the p-value, the more will be the observed data point closer to the mean or acceptance area,more chances of accepting the null hypothesis or failing to reject a null hypothesis.

The lower the p -value, the higher is the probability of the null hypothesis being rejected.

Step 2 :- 
P value = 1 - z score 
P value = ( 1- z-score ) * 2 for 2 tail test
P value = ( 1- z-score ) * 1 for 1 tail test

Step 3 :- 
If the p value is more than alpha ( acceptance value ) we accept the null hypothesis.

My conclusion :- 

Normally in standard deviation we use Empirical formula to get the answer likewise in z score we use z table.

T , Z, F and other  tests all find the value between mean and other standard deviations like 1st sd dev , 2nd sd dev etc and which test to use is dependent on the type of data and sample size of the data.


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