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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