Hypothesis Testing

 HYPOTHESIS TESTING TASK📝

For this assignment, We are tasked to use the DOE experimental data that your practical team has collected both for FULL Factorial and FRACTIONAL Factorial.

DOE PRACTICAL TEAM MEMBERS (fill this according to your DOE practical):

1. Bjorn Lim

2. Darren

3. Gwyn

4. Cui Han

5. Hai Jie

Data collected for FULL factorial design using CATAPULT A (fill this according to your DOE practical result)

Data collected for FRACTIONAL factorial design using CATAPULT B (fill this according to your DOE practical result): 

Bjorn will use Run #1 from FRACTIONAL factorial and Run#1 from FULL factorial.

Darren will use Run #7 from FRACTIONAL factorial and Run#7 from FULL factorial.

Gwyn will use Run #6 from FRACTIONAL factorial and Run#6 from FULL factorial.

Cui Han will use Run #4 from FRACTIONAL factorial and Run#4 from FULL factorial.

Hai Jie will use Run #4 from FRACTIONAL factorial and Run#4 from FULL factorial.

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 =  24.5 cm Start angle = 5 degree Stop angle = 45 degree
Step 1: State the statistical Hypotheses:	State the null hypothesis (H0): Catapult A and B produce the same flying distance of the projectile. 𝜇A = 𝜇B Assuming µ is the flying distance of the projectile. State the alternative hypothesis (H1): Catapult A and B do not produce the same flying distance of the projectile. 𝜇A ≠ 𝜇B Assuming µ is the flying distance of the projectile.
Step 2: Formulate an analysis plan.	Sample size is 8 runs. Since 8 runs is a small sample size, 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: Number of runs = 8 runs Mean = 229.2cm Standard Deviation = 5.78cm State the mean and standard deviation of sample catapult B: Number of runs = 8 runs Mean = 144.4cm Standard Deviation = 11.03cm Compute the value of the test statistic (t): At a significance level of 0.05, percentile is the 97.5th
Step 4: Make a decision based on result	Type of test (check one only) Left-tailed test: [ __ ]  Critical value tα = - ______ Right-tailed test: [ __ ]  Critical value tα =  ______ Two-tailed test: [ ✓ ]  Critical value tα/2 (t0.975) = ± 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 = 18.02 lies in the rejection region, the null hypothesis is rejected. At 0.05 level of significance, Catapult A and B do not produce the same flying distance of the projectile Therefore Ho is rejected.
Conclusion that answer the initial question	Since the null hypothesis is rejected, the alternative hypothesis is accepted. Catapult A and B do not produce the same flying distance of the projectile.
Compare your conclusion with the conclusion from the other team members. What inferences can you make from these comparisons?	My conclusion is the same as the conclusion from my other team members. However, my t calculated is much higher than the t calculated by my other team members. This creates a larger margin in my t calculated and the t0.975 value. This shows that Run #1 from FRACTIONAL factorial and Run#1 from FULL factorial has a much more significant difference in the flying distance produced by catapult A and B. Since our conclusion is consistent for all the runs, the comparison shows that catapult A and B do not produce the same flying distance even when the settings (arm length, start angle, stop angle) are changed.

Conclusion:

For this task, we were able to use the data we collected in our previous DOE practical to perform hypothesis testing. We were already able to practice hypothesis testing during our tutorial lesson however, I was not able to grasp the reason for using this tool. This exercise really helped me to understand how and when to utilize this tool as we were able to perform the calculations using real data we collected. During the DOE practical, I already hypothesize that the 2 catapults produce very different launch distances however by looking just at the pure data, it is not easy to prove the significance of my hypothesis. By using the hypothesis testing tool and calculating the values, I am able to prove my hypothesis. As a person interested in math and numbers, I really found this task interesting.  I will try to use this tool in the final project if CCPD if we were needed to perform any experiment for data collection and we need to prove our hypothesis. 

I used to think that we were able to prove our hypothesis just by looking at the raw data of an experiment. However, how after learning how to use the hypothesis testing tool, I believe that this tool is a definite way to prove our hypothesis using numbers and calculations. I believe this tool will be a life-saver in the upcoming Capstone project in year 3 as experiments will be inevitable and we will need to prove our hypothesis as part of our assessment,

Design Of Experiments

 

Design Of Experiments

Hello, this week we learned about design of experiments (DOE) and its importance and how to apply it. We learned that DOE is a versatile data gathering and analysis technique that can be applied to a wide range of experiments. It allows for the manipulation of many input elements in order to determine their impact on a desired outcome. DOE can identify crucial interactions that might be missed when experimenting with one component at a time by altering several inputs at the same time.

I am tasked to perform DOE on case 1 on factors affecting the number of inedible “bullets” (unpopped kernels) remaining. I used both full and fractional factorial design to obtain the results.

Full Factorial Design

Table of Data:

Only the average is inputted as only the average was given in the case study.

Calculation of Mean:

Graph:

A: When the diameter of bowls increases from 10cm to 15cm, the mass of bullets increases from 1.43g to 1.48g.

B: when the microwaving time increases from 4 to 6 minutes, the mass of bullets decreases from 2.00g to 0.9g.

C: when the power increases from 75% to 100% the the mass of bullets decreases from 2.35g to 0.55g.

The graph shows the power line has the steepest gradient followed by the microwaving time line and the diameter line indicating that the power has the biggest impact on the mass of bullets, then followed by microwaving tine, and lastly the diameter.

Interactions Between Factors

For FULL factorial design: (A x B)

At LOW B, (runs 1 and 5) Average of low A=(3.1+0.7)/2=1.9

At LOW B, (runs 2 and 6) Average of high A=(3.5+0.7)/2=2.1

At LOW B, total effect of A=(2.1-1.9)= 0.2 (increase)

At HIGH B, (runs 3 and 7) Average of low A=(1.6+0.5)/2=1.05

At HIGH B, runs 4 and 8) Average of high A=(1.2+0.3)/2=0.75

At HIGH B, total effect of A=(0.75-1.05)=-0.3 (decrease)

The gradient of both lines are different, -B line is positive and +B line is negative. This shows that there are significant interaction between factors A and B.

For FULL factorial design: (A x C)

At LOW C, (runs 1 and 3) Average of low A=(3.1+1.6)/2=2.35

At LOW C, (runs 2 and 4) Average of high A= (3.5+1.2)/2=2.35 

At LOW C, total effect of A=(2.35-2.35)= 0 (no increase or decrease)

At HIGH C, (runs 5 and 7) Average of low A=(0.7+0.5)/2=0.6

At HIGH C, (runs 6 and 8) Average of high A=(0.7+0.3)/2=0.5

At HIGH C, total effect of A=(0.5-0.6)=-0.1 (decrease)

The gradients of both lines are only slightly different with very small margins. This indicates that there’s an interaction between A and B, but the interaction is very small. It could also be said that there is no interaction between factors A and B as the lines are almost parallel.

For FULL factorial design: (B x C)

At LOW C, (runs 1 and 2) Average of low B=(3.1+3.5)/2=3.2

At LOW C, (runs 3 and 4) Average of high B=(1.6+1.2)/2=1.4

At LOW C, total effect of B=(1.4-3.2)= -1.8 (decrease)

At HIGH C, (runs 5 and 6) Average of low B=(0.7+0.7)/2=0.7

At HIGH C, (runs 7 and 8) Average of high B=(0.5+0.3)/2=0.4

At HIGH C, total effect of B=(0.4-0.7)=-0.3 (decrease)

The gradients of both lines are negative and are different values. This shows that there are significant interaction between factors B and C.

From the fractional factorial design data, it seems that the strongest interaction is between BxC followed by AxB and finally AxC has the least interaction. 

Fractional Factorial Design

For the fractional factorial design, I decided to use the results from runs 2, 3, 5, 8. This is because all factors (both low and high levels) occur the same number of times. It is an orthogonal design and has good statistical properties.

Table of Data:

Only the average is inputted as only the average was given in the case study.

Calculation of Mean:

Graph:

A: When the diameter of bowls increases from 10cm to 15cm, the mass of bullets increases from 1.15g to 1.9g.

B: when the microwaving time increases from 4 to 6 minutes, the mass of bullets decreases from 2.10g to 0.95g.

C: when the power increases from 75% to 100% the the mass of bullets decreases from 2.55g to 0.5g.

The graph shows the power line has the steepest gradient followed by the microwaving time line and the diameter line indicating that the power has the biggest impact on the mass of bullets, then followed by microwaving time, and lastly the diameter. The ranking of strongest factors for the fractional factorial design is the same as the full factorial design which shows that the runs chosen for the fractional factorial design were valid. Therefore, the fractional factorial design is a more efficient way to conduct the experiment as it requires a lesser number of total experiments which means lesser time and resources are required for the experiment while still providing the correct results.

Link to Excel sheet for BOTH Full and Fractional Factorial Designs: https://drive.google.com/drive/folders/1Fvoryhn1d2HwTt75zmJWswlkN_5pPTWC?usp=sharing