Hypothesis Testing

Hello guys, WELCOME BACK to my Blog!!! This week I have learnt about hypothesis testing in class and would like to share with you guys my experience on applying it to DOE practical that I did in school. 

What is Hypothesis Testing?👀

A statistical hypothesis is an assumption about a population parameter. This assumption may or may not be true. Hypothesis testing refers to the formal procedures used by experimenters or researchers to accept or reject statistical hypotheses.

DOE PRACTICAL TEAM MEMBERS:

1. Nander (Iron Man)
2. Tzer (Thor)
3. Ashwati (Captain America)
4. Nikkisha (Black Widow)
5. Daryl (Hulk)
6. NIL (Hawkeye)
 
Data collected for FULL factorial design using CATAPULT A

Data collected for FRACTIONAL factorial design using CATAPULT B

Iron Man will use Run #2 from FRACTIONAL factorial and Run#2 from FULL factorial.
Thor will use Run #4 from FRACTIONAL factorial and Run#4 from FULL factorial.
Captain America will use Run #5 from FRACTIONAL factorial and Run#5 from FULL factorial.
Black Widow will use Run #7 from FRACTIONAL factorial and Run#7 from FULL factorial.
Hulk will use Run #4 from FRACTIONAL factorial and Run#4 from FULL factorial.
Hawkeye (NIL)

The QUESTION	The catapult (the ones that were used in the DOE practical) manufacturer needs to determine the consistency of the products they have manufactured. Therefore they want to determine whether CATAPULT A produces the same flying distance of projectile as that of CATAPULT B.
Scope of the test	The human factor is assumed to be negligible. Therefore, different user will not have any effect on the flying distance of projectile.   Flying distance for catapult A and catapult B is collected using the factors below: Arm length = 31 cm Start angle = 5 degree Stop angle = 60 degree
Step 1: State the statistical Hypotheses:	State the null hypothesis (H0):   Catapult A produces the SAME flying distance of projectile as that of Catapult B. State the alternative hypothesis (H1):   Catapult A and Catapult B produce DIFFERENT flying distance of projectile.
Step 2: Formulate an analysis plan.	Sample size is 8 in which n<30. Therefore t-test will be used.     Since the sign of H is a ≠, two tailed test is used.     Significance level (α) used in this test is 0.05 because the results to be analysed has a less stringent requirement and it is used as the default significant level in school for projects.
Step 3: Calculate the test statistic	State the mean and standard deviation of sample catapult A: State the mean and standard deviation of sample catapult B: Compute the value of the test statistic (t):           At significant level of 0.05, t0.975 =  ±2.145 when v = 14 (Appendix 1)
Step 4: Make a decision based on result	Type of test (check one only) 1.     Left-tailed test: [ __ ]  Critical value tα = - ______ 2.     Right-tailed test: [ __ ]  Critical value tα =  ______ 3.     Two-tailed test: [  ✓  ]  Critical value tα/2 = ± 2.145   Use the t-distribution table to determine the critical value of tα or tα/2   Compare the values of test statistics, t, and critical value(s), tα or ± tα/2   Since the test statistic, t = -5.619 lies in the rejection region, the null hypothesis, Ho is rejected.
Conclusion that answer the initial question	Since Ho is rejected, at the significant level of 0.05, Catapult A and Catapult B produce different flying distance of projectile. Hence, there is a inconsistency of the products that the manufacturer have manufactured.
Compare your conclusion with the conclusion from the other team members.   What inferences can you make from these comparisons?	Similar to my result, the other members also concluded that there is a inconsistency of the products that the manufacturer have manufactured.   It can be inferred that the catapult that they have manufactured will always give rise to inconsistency in the flying distance of projectile even when the same settings are used.

Reflection

It is my first time learning hypothesis testing and I think it is a useful skill for me because I know that in the future, I will be conducting my own experiment and to test the hypothesis, it is important that the right procedures are used. 

During the class, I was taught about the hypothesis testing with some examples but still I wasn't confident in applying it. Luckily, there were some practice questions and after I went through those questions, I was able to understand hypothesis testing better. While doing the questions, I encounter some problem but the lecturer went through some important point and I was able to understand and solve them easily.

Next up, I was tasked to apply hypothesis testing for DOE experiment on catapult and by doing it, I understand more about the usefulness of hypothesis testing. For instance, I realize that by using hypothesis testing, I can easily find out whether the product that the manufacturer have manufactured have the same consistency in flying distance of the projectile and from the result,  I can then suggest way for improvement so as to achieve a more accuracy in consistency.

I am pretty sure I will use this skill next semester for final year project and I think this skill is extremely useful to test hypothesis along with design of experiment.