Hypothesis Testing

For this blog, I will be using the DOE experimental data that my practical team has collected for both the FULL and FRACTIONAL Factorial methods.

There are 4 people in my group:

1. Cyane (Iron Man)

2. Clarence (Thor)

3. Rydrew (Black Widow)

4. Derrick (Hulk) ~~ this is me

Data collected for FULL factorial design using CATAPULT A:

Data collected for FRACTIONAL factorial design using CATAPULT B:

Since I am "Hulk", I will be using Run#3 from both the FULL and FRACTIONAL factorial methods for hypothesis testing.

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 =  22 cm Start angle = 24 degrees Stop angle = 57 degrees
Step 1: State the statistical Hypotheses:	State the null hypothesis (H0):  Mean of sample for A = Mean of sample for B At arm length of 22 cm, start angle of 24 degrees and stop angle at 57 degrees, the mean flying distance of the projectile using catapult A and catapult B have no difference. State the alternative hypothesis (H1): Mean of sample of A ≠ Mean of sample for B At arm length of 22 cm, start angle of 24 degrees and stop angle at 57 degrees, the mean flying distance of the projectile using catapult A and catapult B are different.
Step 2: Formulate an analysis plan.	Sample size is 5 for catapult A and 8 for catapult B. Therefore t-test will be used. Since the sign of H1 is  ≠ (not equal to), a two tailed test is used. Significance level (α) used in this test is 0.01
Step 3: Calculate the test statistic	State the mean and standard deviation of sample catapult A: Mean = 98 cm Standard Deviation = +/- 6.65 cm State the mean and standard deviation of sample catapult B: Mean = 112.1 cm Standard Deviation = +/- 4.18 cm 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 = ± 3.106   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 Critical Value,  tα/2 = +/- 3.106 t = -4.318 t does not fall between -3.106 and 3.106. Therefore Ho is rejected.
Conclusion that answer the initial question	Since null hypothesis is rejected, alternative hypothesis which states that "At arm length of 22 cm, start angle of 24 degrees and stop angle at 57 degrees, the mean flying distance of the projectile using catapult A and catapult B are different.". Because the mean flying distance of both catapults are different from each other, I conclude that the catapults produced by the manufacturer are inconsistently manufactured.
Compare your conclusion with the conclusion from the other team members.   What inferences can you make from these comparisons?	Cyane's null hypothesis was rejected and thus she concluded that the catapults were produced inconsistently. Rydrew's testing proved otherwise and he concluded that there was consistent production of the catapults. Cyane and I came to similar conclusions while Rydrew's analysis gave opposing conclusions. An inference I can make from the comparisons is that results are more likely to differ from one another when we single out individual sets of data instead of looking at the whole picture.

Reflection

I was tasked to comduct a hypothesis testing with the results yielded from the DOE practical. I think that this activity serves as good practice because I believe being able to conduct hypothesis testing will be a uuseful skill.

Hypothesis testing is important, especially when conducting analysis because it can help to save time. For example, after collecting a set of data and conducting hypothesis testing, one can easily determine whether the analysis of data is reliable or valid. Once this has been established, one can decide whether it is worth to conduct analysis in the future, based on the statistical significance of the data collected.

I used to think that hypothesis testing was very easy. Meaning, one can just state a hypothesis and test its validity purely by doing experiments. Now, I realise that there is more to hypothesis testing than meets the eye. Many calculations are involved, which is reasonable, because you can mathematically prove a statement's validity. Next, when I happen to need to conduct analysis of data, when I have the time to, I will conduct hypothesis testing to clear doubts about a certain something, whether it be indentifying differences in performances of tires, or determining if Thor or The Hulk is stronger.