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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