Hypothesis Testing

 Objectives:

1. Able to apply Hypothesis Testing Statistical Methodology to a scenario 

(i.e Based on DOE Practical --> if 2 different catapults give the same flying distance)

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Background:

DOE Practical 🔎

For this practical, we investigated 3 factors that would effect the flying distance of a catapult at 2 levels using DOE. The objective of this practical is to investigate the effect of the individual factors and identify the factor that has the most significant effect on the response variable. 

We were tasked to collect and perform full factorial design with 8 replicates and fractional factorial design with 8 replicates. We were split into 2 smaller groups within our group, 1 team doing full factorial and the other doing fractional factorial. We then analysed our sample results using DOE for both full and fractional factorial sets and compared our conclusions. 

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Hypothesis Testing 🔬

In general, a statistical hypothesis is an assumption about a population which may or may not be true. Hypothesis testing refers to the formal procedures used to accept or reject statistical hypotheses. Essentially, it is the method of testing a hypothesis by comparing it with the null hypothesis and finally coming up with a conclusion.

Blog Assignment

This week we were tasked with applying the hypothesis testing method taught to our results in the DOE practical. 

Members in DOE Practical:

1. Iron Man (Person A) : Serena

2. Person B (Thor) : Trisyia

3. Person C (Captain America) : Jun Xiang

4. Person D (Black Widow): Kai Rong

5. Person E (Hulk)

6. Person F (Hawkeye): Jerome

Data collected for FULL factorial design using CATAPULT A 

Data collected for FRACTIONAL factorial design using CATAPULT B 

USE THIS TEMPLATE TABLE and fill all the blanks

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 =  28 cm Start angle =  20 degree Stop angle = 60 degree   Let Catapult A be from Full factorial & Catapult B be used from Fractional Factorial Runs respectively. Since I am Iron Man, (Person A) I will use: Run #2 from FRACTIONAL factorial and Run#2 from FULL factorial.
Step 1: State the statistical Hypotheses:	State the null hypothesis (H0): H0  =   H1      Catapult A & B produces the same flying distance of projectile. State the alternative hypothesis (H1): H0  ≠   H1   Catapult A & B produces different flying distances of projectile.
Step 2: Formulate an analysis plan.	Sample size is 8.  Therefore t-test will be used. Since the sign of H1 is    ≠    , a left/two/right 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:  Mean (x̄) = 116.5 cm Standard deviation (σ) = 6.30 cm State the mean and standard deviation of sample catapult B: Mean (x̄) = 138.5 cm Standard deviation (σ) = 2.97 cm   Compute the value of the test statistic (t): n1 = 8 n2 = 8 x̄1 = 138.5 cm x̄2 = 116.5 cm s1 = 2.97 cm s2 = 6.30 cm v = 8 + 8 – 2 = 14
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 =  ______        Use the t-distribution table to determine the critical value of tα or tα/2       At α/2= 0.975, V=14, tα/2 = 2.145 3.     Two-tailed test: [ _✔_ ]  Critical value tα/2 = t0.975                                                                              = ± _2.145_____ Compare the values of test statistics, t, and critical value(s), tα or ± tα/2 Since t = 8.357 > t0.975 = 2.145, it lies within the rejection region. Therefore, Ho is rejected and H1 is accepted.
Conclusion that answer the initial question	Since t > t0.975, Ho is rejected. This means that the alternative hypothesis H1 that states Catapult A & B produces different flying distances of projectile is correct. This means that the products the company manufactured are not consistent and identical in performance.  In conclusion, Both Catapults A and B have different flying distance.
Compare your conclusion with the conclusion from the other team members.   What inferences can you make from these comparisons?	My conclusion:  Both Catapults A and B have different flying distance. VS Teammates' conclusions: Person B (Trisyia): Both Catapults A and B have different flying distance. Person C (Jun Xiang): Both Catapults A and B have different flying distance. Person D (Kai Rong): Both Catapults A and B have same flying distance. Person F (Jerome): Both Catapults A and B have same flying distance. Inferences made: 3 out of 5 of us (Majority) reached the same conclusion, that is, both catapults have different flying distance which meant that the products the company manufactured are not consistent and identical in performance as compared to 2 out of 5 of us (Minority) which had the conclusion that the catapults have the same flying distance. The 2 members i.e. Person D and F who reached the same conclusion was because they both analysed the same set of runs :  " (Person D) Black Widow will use Run #8 from FRACTIONAL factorial and Run#8 from FULL factorial. (Person F) Hawkeye will use Run #8 from FRACTIONAL factorial and Run#8 from FULL factorial." Also: The difference in the results shows that the assumption of human factors not affecting the flight distance is wrong. Another factor that could have led to this differences in results would be air resistance. Hence it can be taken that 3/4 conclusions from the hypothesis tests found that the 2 types of Catapults gave different flying distance and proven that the performance of Catapult A and B are not consistent nor identical.

Reflection:

This blog assignment is linked to a practical which was done with the purpose of us applying Design of Experiments skill. In this assignment we had to apply a newly learnt skill Hypothesis testing to test and see if our hypothesis i.e. the catapults used in the practical had the same flying distance because in the practical the data we recorded from launching the balls from the catapult was the flying distance so we made use of the average data from 1 run from Full factorial set and 1 run from the Fractional factorial set to test the above mentioned hypothesis. From this assignment I realised and experienced first-hand how we could integrate the concepts learnt because only with DOE knowledge we could make the full and fractional data tables and then make use of that data to test out a hypothesis for me this was the most interesting aspect of the assignment. This task was important because it allowed us to apply our knowledge into a real-life scenario which we had done ourselves (practical) instead of just answering a problem sum question (i.e. Hypothesis testing practice questions) so the conclusions and the steps we were doing was more meaningful and made more sense. In general, i feel hypothesis testing itself is very important, one of the most useful and important skills ive learnt in fact from this module because it really helps to substantiate statements we make loosely. For example if someone guessed how our prototype would work if a certain parameter was changed that person is actually making a hypothesis and hence without testing it we wouldnt know it its actually true which could help improve our prototype. This is also why this skill is important for CP5070 project and also for FYP. I think DOE and hypothesis testing go hand in hand to a certain extent and would be especially useful for FYP whereby after conducting tests on my prototype i can make sense of the data and verify if a hypothesis made which could potentially improve its performance is valid or not. Essentially these skills help me to make sense of data. In conclusion, I used to think that DOE and hypothesis testing sounded daunting and methodologies which would be hardcore scientific and hence difficult to comprehend. But as I went through the lecture slides, the practice questions i realised the main purpose of doing them was to make sense of the data and substantiate data and solidify questions we might have with proven conclusions. So now I think they are very useful although tedious and next I will use them in my internship and especially FYP to help solidify questions we might have on potential ways to improve our project.