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Test of Significance – An Overview

The methods used for comparing the sample data or information obtained by the observational study with the hypothesis which should be analyzed is called the test of significance.

How does it Start?
Usually, the tests of significance start with two values,
H0 = Null Hypothesis
Ha = Alternate hypothesis
Let me explain it with the simple example,
Let us assume that the clinical trial for a drug is being carried out,

Where H0 = the new drug is no way better than the existing drug.
  Ha = the new drug has an alternative effect that is it may have either better or negative effect when compared to the existing one.
We always conclude by saying that either reject H0 or accept H0 in favour of Ha . But we never say either reject or accept  Ha.

Mathematical Parameters
The hypothesis is usually analyzed using the value mean μ.
Alternative Hypothesis can be two types either one-sided or two-sided. If one-sided it can be either greater than or less than the value given by the null hypothesis.
In the second case, it is not equal to the value given by the null hypothesis.
Case 1,
H0 μ = K

Ha μ > K
 OR
Ha μ < K

Case 2,
H0 μ = K
Ha μ (not equal) K
Overall Process Explained in 5 Steps:

  1. Consider and state the overall reason for which the process is carried out.
  2. Determine the null and alternative hypothesis.
  3. Analyze the known parameters according to the formulae and the probability of error level.
  4. Determine the type of significance test to be carried out.
  5. Conclude the results and interpret them.

Types of Errors,

Type 1 Error ( Alpha Error ) – Rejecting the Null Hypothesis
Instead of accepting the null hypothesis and rejecting the alternate hypothesis the opposite occurs.

Type 2 Error ( Beta Error ) – Accepting the Null Hypothesis
Instead of rejecting the null hypothesis and accept the research hypothesis, but the opposite occurs.
Probability of committing type 1 error is called P-value, 
Z – test
Find out the Z- Score

Z – Score can be calculated by the below-mentioned formula,
z = .
Then determine the p-value, and interpret.
Example
100 People treated with medicine A for a fever recovered 90 %
100 People treated with medicine B for a fever recovered 80 % . Determine Medicine A is better than Medicine B ?
H= There is no significant difference between medicine A and B
Ha = Medicine A is 1.125 times better than Medicine B
In this case, z score will be 2, P-value will be less than 0.05, so reject the null hypothesis and accept the alternate hypothesis.

Chi-Square Test

  1. Make the table with all frequencies.
  2. Determine E value.
  3. Find O – E value.
  4. Calculate X2 Value 

  X2 = (O-E)2 / E

  1. Add all X2 Values
chi suare.PNG

    Diagrammatic representation of the Chi- square test ( Values are just demonstrated )

Calculate the degree of freedom, DOF = ( R – 1 ) x ( C – 1 )
Find out P-Value from table.
By comparing the x2  value with the P-Value and interpret the result.

T – Test for quantitative data

  • Calculate the t – value using the formula 
  • Calculate degree of freedom determine the value from table
  • Compare the table value with t – value and interpret the results.
  • If calculated t value is higher than table value reject null hypothesis.
  1. In unpaired T-test t value is determined by,
Capture.PNG
  1. In the cases of paired T – Test,

t = Mean / Standard Error
Degree of freedom can be calculated by the formula, DOF = n -1 
Get the P-Value from table and compare to predict the results. 

References

  1. https://www.slideshare.net/imran14zaheer/test-of-significance-58261779
  2. https://www.slideshare.net/shubhanshug1/tests-of-significance-40805085
  3. https://byjus.com/maths/tests-of-significance/
  4. https://web.csulb.edu/~msaintg/ppa696/696stsig.htm

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