Hypothesis testing

 For this blog, I will be doing hypothesis testing on the results obtained from the Designs of Experiments (DOE) practical. In the practical, two catapults was used to conduct fractional factorial and full factorial each, the data collected will be used.

Contents of this post:

1. Team Members
2. Data collected for Full Factorial design using Catapult A
3. Data collected for Fractional Factorial design using Catapult B
4. Runs each member is using
5. Hypothesis testing (using template provided)
6. Reflection

DOE PRACTICAL TEAM MEMBERS:
1. Steward (Iron Man)
2. Wayne (Thor)
3. Jiayu (Captain America)
4. Xin Ni (Black Widow)
5. Nick (Hulk)
6. - (Hawkeye)

Data collected for FULL factorial design using CATAPULT A :

Data collected for FRACTIONAL factorial design using CATAPULT B :

Runs each member is using:

1. Steward (Iron Man) will use Run #2 from FRACTIONAL factorial and Run#2 from FULL factorial.
2. Wayne (Thor) will use Run #3 from FRACTIONAL factorial and Run#3 from FULL factorial.
3. Jiayu (Captain America) will use Run #5 from FRACTIONAL factorial and Run#5 from FULL factorial.
4. Xin Ni (Black Widow) will use Run #8 from FRACTIONAL factorial and Run#8 from FULL factorial.
5. Nick (Hulk) will use Run #3 from FRACTIONAL factorial and Run#3 from FULL factorial.

Hypothesis testing (using template provided):

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 = 32 cm Start angle = 30 degree Stop angle = 90 degree
Step 1: State the statistical Hypotheses:	State the null hypothesis (H0): Catapult A and Catapult B produces the same flying distance of projectile, so products manufactured are consistent. State the alternative hypothesis (H1): Catapult A and Catapult B does not produce the same flying distance of projectile, so products manufactured are not consistent.
Step 2: Formulate an analysis plan.	Sample size is 8 Therefore t-test will be used. Since the sign of H1 is ≠, a two tailed test is used. Significance level (α) used in this test is 0.05 .
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):
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 t=-0.71, Therefore, H0 is accepted while H1 is rejected since it lies in the acceptance region, 2.145 > t=-0.71 > -2.145.
Conclusion that answers the initial question	At 0.05 level of significance, it is found that the catapult products manufactured are consistent as Catapult A and Catapult B produced the same flying distance projectile.
Compare your conclusion with the conclusion from the other team members.   What inferences can you make from these comparisons?	All the team members have concluded that both catapults at a specific run produced the same flying distance so products manufactured were consistent. It can be inferred that even at different factor levels, the flying distance projectile remains the same for all. This further proofs the null hypothesis that Catapult A and Catapult B produces the same flying distance of projectile, so products manufactured are consistent.

Reflection:

 Overall, I found hypothesis testing a really useful tool that can help to test an assumption using the data collected from previous experiments. Although it is very useful, it was initially very difficult to understand at first. This is because there were many steps that I have never done before and sometimes the steps were hard to understand so it made it hard for me to apply what I learnt. 

One such step is determining whether the statistical test is a one-tailed or two-tailed test by the sign (≠, >, <) used in the alternative hypothesis. To determine the sign used, we have to understand what the question is really asking for. For example, "The manufacturer claims a breaking strength of 8000 kg", for this the < sign is used for the alternative hypothesis. This is because if the rope has a breaking strength less than that of 8000kg, it shows that his claim is wrong. If the breaking strength is above 8000kg, then the manufacturer's claim cannot be proven false or true properly. This step took a lot of practise before I could finally get an idea on how I should go about deciding on the sign to use for the alternative hypothesis.

Another difficulty was the significance level, I was not sure whether to choose 0.05 or 0.01 level of significance. I did not really know what each level means. From what I learnt from my lecturer, α=0.01 is used when error cannot be tolerated and accuracy is very important. For example, in studies or research about the human body and in the medicinal field, α=0.01 has to be used to ensure accuracy as the cases stated above involves humans. α=0.05 is normally used when doing hypothesis testing which is why I used 0.05 level of significance for the above hypothesis testing exercise.

Having learnt more about doing hypothesis testing by doing the practice questions given, I was slightly more confident than before when doing this hypothesis testing exercise. I was able to apply everything I learnt in the tutotial lesson and practice questions. This allowed me to complete the exercise without much trouble.

All in all, this was yet another new and insightful topic that I managed to learn and practice to apply it properly. I am sure that I will have to use it again in the future so I am glad that I was able to understand and use this method of testing assumptions using data collected.