Bokena Series pt 2 blog 5: EH MY ASSUMPTION CORRECT MEH

 Hello everyone, and welcome back to another bokena series blog, where today I will be talking about how I applied the full and fractional factorial design into my recent experiment. In this experiment I will go through the calculations and the basic concepts that we had used as a team to produce our results in our hypothesis testing. From the previous blog, where I explained the 2 different types of factorial designs and how they are to be applied we can see that fractional factorial design is used when the data size needed to be collected is small and there are many factors to be considered. 

So first off, what is hypothesis testing?? We use hypothesis testing when we make an statistical hypothesis, which is an assumption made about a population perimeter. As it is an assumption, many time we are not able to confirm if the hypothesis is correct which is where hypothesis testing comes in. We use hypothesis testing, a formal procedure used by experimenter and researcher, to verify is our original hypothesis is correct.

There are 2 types of statistical hypothesis that we can make;

Null hypothesis (H0): When the original variable and the new variable changed cause no difference in the outcome 

Alternate hypothesis (H1): When the original variable and the new variable changed produce different outcomes 

Ideally, we to ensure that the assumption is correct we examine the entire population to confirm if they hypothesis is valid. However, in situations where sample sizes are very big the better option would be to take a few random samples in the population to validify the hypothesis.

So I've mentioned how hypothesis testing works but what kinda questions do they actually answer?? 

Examples of questions that hypothesis testing can answer are

- Is the new material stronger than the previous one used?

- Does our product last longer than of our competitors?

- Does the new method of production actually increase the efficiency of the making process?

- Is the component replaced working as well as the original component

- Does the product work better after the changes implemented?

There is of course a downside of choosing random samples, to conduct hypothesis testing. As the random samples do not completely represent the entire population, there could decision errors when determining if the hypothesis is valid. There are 2 types of errors that can be made;

Type I error: Where the researcher rejects the null hypothesis (H0) when it is true, and the probability of committing this error is called the significance level (α)

Type II error: Where the researchers fails to reject the null hypothesis (H0) when it is false, and the probability of committing this error is called beta (β)

Table above is the results produced from our Design of Experiment (DOE) practical. We will be using these values to confirm the validity of our hypothesis by conducting hypothesis testing.

Our has been distributed into 5 different roles;

1. Eng Kiat (Iron Man)

2. Matthias (Thor)

3. Sreenithi (Captain America)

4. Abhishek (Black Widow)

5. Jun Yi (Hulk)

And each role will have to take 2 different runs to compare one of the 3 factors;

Iron Man will use Run #1 and Run#3. To determine the effect of projectile weight.

Thor will use will use Run #2 and Run#4. To determine the effect of projectile weight.

Captain America will use Run #2 and Run#6. To determine the effect of stop angle.

Black Widow will use Run #4 and Run#8. To determine the effect of stop angle.

Hulk will use Run #6 and Run#8. To determine the effect of projectile weight

As I am Black Widow, unironically, I will be using Run#4 and Run#8 which will be used to determine the effect of the stop angle (A) on how far the ball travels.

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 is collected using the factors below:

Arm length (A) = ____cm

Projectile weight (B) = _____ grams

Stop angle (C) = _____ degree and ______ degree

State the statistical Hypotheses:

Run#4: Low value of Stop Angle (A)

Run#8: High value of Stop Angle (A)

Null Hypothesis (H0): 

Assuming that Run#4 and Run#8 had produced the same outcome of travelling the same distance 

μ4= μ8

Alternate Hypothesis (H1): >

Assuming that Run#8 causes the ball to travel further than and Run#4 as Run#8 has a larger stop angle compared to Run#4

μ4 > μ8

Calculating of the test statistics

Run#4

Mean (x̄1): 116.6

Standard Deviation(S1): 0.78

Run#8

Mean(x̄2): 81.6

Standard Deviation(S2): 0.98

Significance Level (α) used for calculation will be 0.05
As the sample size is only 16 (n1= 8 & n2= 8), the t - test will be used.

As H1 has the symbol ' > ', the right tail of the hypothesis testing graph is used.

σ = [[8(1.44)2 + 8(0.99)2] / (8 + 8 - 2)]0.5

= 6.529

t = (81.7 - 77.5) / σ( 8-1 + 8-1 )

= 2.573

Type of test

1. Left-tailed test: [ __ ] Critical value t_α = - ______

2. Right-tailed test: [✅] Critical value t_α = 2.573

3. Two-tailed test: [ __ ] Critical value t_α/2 = ± ______

Since t > tα (lowest value in α), H0 is rejected

Therefore, H0 is false.

Conclusion that answer the initial question

From this hypothesis testing, I have confirmed that the larger the stop angle the further the ball travels and the smaller the stop angle the lesser the ball travels.

Compare your conclusion with the conclusion from the other team members.

• Black widow (Matthias) - A lighter projectile leads to the projectile flying a larger distance while the heavier projectile causes the projectile to travel lesser
• Thor (Sreenithi) - With a smaller stop angle , the projectile travels a larger distance while the larger the stop angle the lesser the projectile travels
• Hulk (Jun Yi) - the lighter projectile causes the a larger flying distance while the heavier projectile prevented the ball from travelling far
• Ironman (Me) -  a larger arm length causes the ball to travel lesser compared a shorter arm length 

Inference from these comparisons

After looking at all the different conclusions, we have noticed that our objective is to get the furtherest travel distance for the ball. Therefore, we should use a lesser weighted ball with a shorter stop angle and short arm length to get maximum efficiency.

Learning Reflection

During the lesson, I was hella confused with what was going on, so we already had learnt Design of Experiment (DOE) so why is there hypothesis testing??? However, later on when actually applying it myself I had to noticed that even before we had started the experiment that we had to make an assumption and we had to confirm whether it is right or wrong. That is the whole point of hypothesis testing.

Despite seeming to be easy, hypothesis testing actually takes a lot of time and analysis to ensure that there is no bias in the validating the hypothesis. Especially when the answer you are looking for is not the correct one. The only things that we have to always look out for is the integrity and loyalty to our research. The fact that we are wrong should be considered a small step to achieve a better product and not to cut short the learning process.

The hypothesis testing is a very essential tool for us to use as it allows many different industries to apply this method to clarify their hypothesis. Learning this skill is more of a lesson on how to be adaptable in different situations. Giving us different areas where hypothesis testing can be use allows us to be more open minded about the scenarios where they can be used. 

And lastly to me I feel like hypothesis testing is the prefect tool to settle debates amongst classmates to see who's idea is better. Instead of ending on a compromising note. Adding more fuel and excitement to the debate.

That's all for todays bokena series blog and thank you all for sticking with me. Do stay tune for the next blog as I will be going through my final product for this module and I'm sure you'll love it.