Hypothesis Testing

 Hello everyone! 😁

For this entry, I will be going through Hypothesis Testing! 👀

This entry will consist of:

• What is hypothesis testing
• Applying hypothesis testing using an assigned task.

So, what is hypothesis testing?

It refers to a statistical hypothesis that is an assumption about a population parameter. This assumption may or may not be true. It also refers to the formal procedures used by experimenters or researchers to accept or reject statistical hypotheses. 

The ideal way to determine if a statistical hypothesis is true is by examining the entire population. However, since it is often impractical, researchers usually examine only a random sample from the population. If the sample data is not consistent with the statistical hypothesis, then the hypothesis is rejected. 

This would be the basic definition of what hypothesis testing is about. More info about it can be found here.

Now comes the assigned task, the main boss of this entry.

For this hypothesis testing task, every team member will be assigned a role from The Avengers. 

The roles are 

Iron Man	Jasmine
Thor	Hariz (me) ☺
Captain America	Tristan
Black Widow	Samantha
Hulk	Glenn

For Thor, I will be using Run #2 and Run #4 to determine the effect of projectile weight.

Refer to the rows highlighted in red for data for Runs #2 and #4. 

Factor A is Arm length
Factor B is Projectile weight

Factor C is Stop angle

The QUESTION	To determine the effect of Projectile Weight on the flying distance of the projectile
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 is collected using the factors below: Arm length = 33.3cm (HIGH) Projectile weight = 0.85 grams (LOW) and 2.03 grams (HIGH) Stop angle = 50 degrees (LOW)
Step 1: State the statistical Hypotheses:	State the null hypothesis (H0):   The projectile weight has no significant effect on the flying distance of the projectile   State the alternative hypothesis (H1):   The projectile weight has a significant effect on the flying distance of the projectile.
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 0.05 is used because 95% significance or rather an α of 0.05 is commonly used.
Step 3: Calculate the test statistic	State the mean and standard deviation of Run # 2: AVG = 198.4 Std. Dev = 3.49   State the mean and standard deviation of Run # 4: AVG = 146.9 Std. Dev = 0.86   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   As t=±65.33 lies within the rejected region, shaded in red, which means that the projectile weight does affect the flying distance of the projectile.Therefore, Ho is rejected and H1 is accepted. 😱
Conclusion that answer the initial question	As the null hypothesis (Ho) being rejected, the alternative hypothesis (H1) is thus accepted. Hence, the projectile weight will have significant effect on the flying distance of the projectile.
Compare your conclusion with the conclusion from the other team members.	I will be comparing my conclusion with Jasmine's and Glenn's conclusion, who are Iron Man and Hulk. All three of us are determining the effect of PROJECTILE WEIGHT on the flying distance of projectile.  Based on their results and conclusion, only Jasmine and I had rejected the null hypothesis(Ho) and accepted the alternative hypothesis(H1). Whereas Glenn actually accepted null hypothesis because his test statistic is within accepted range in the two-tailed curve. Note that Factor A is arm length, B is projectile weight and C is the stop angle of the catapult. Based on Jasmine's(Iron Man) data, both factor A and C are LOW. Based on Glenn's(Hulk) data, both Factor A and C are HIGH. While for me, Factor A is HIGH, whereas Factor C is LOW.  Moreover,  t value for Jasmine's(Iron Man) = ±7.43 t value for Glenn's(Hulk) = ±1.65 t value based on my workings = ±65.33
What inferences can you make from these comparisons?	Thus, I can infer that, if both Factor A and Factor C's value are both LOW, or if Factor A is HIGH, while Factor C is LOW, then the projectile weight will have a significant effect on the flying distance of the projectile. However, if Factor C is changed to HIGH, with Factor A being HIGH as well, then projectile weight will not have significant impact on the flying distance of the projectile.  Moreover, I can also infer that if Factor A is HIGH while Factor C is LOW, it's effect will create the LARGEST significance on the flying distance of projectile because the test statistic is the furthest away from the critical test statistic @97.5%. If both Factor A and C is HIGH, then it will result in the SMALLEST test statistic of ±1.65, this means that Factor C can create a large significance on the flying distance of the projectile because for factor A to be constant at HIGH, and Factor C changing from LOW to HIGH, the change in test statistic is >60, which is a large difference, and don't forget that if both factors are HIGH, then null hypothesis is actually accepted, meaning there is no significance in flying distance of projectile. However, If Factor A and C is LOW, then null hypothesis is still rejected, accepting alternative hypothesis, because the test statistic is in the rejected region. Based on the previous paragraph, because Factor C has significant difference, what if Factor A is set to LOW, while Factor C is set to HIGH, because the difference between my results and Glenn's results are significant(difference of >60 for test statistic), I would say that for Factor A being LOW while C being HIGH will result in acceptance of null hypothesis and rejects alternative hypothesis, because the test statistic for Jasmine's result is quite close to the critical test statistic as compared to mine.
Your learning reflection on this Hypothesis testing activity	To be honest, this topic was quite confusing at the start, but really thanks to the practice questions given to us on Brightspace, I slowly understood how hypothesis can be done and applied to almost any practical/experiment. I learned that if I want to find out the effects of ONE factor in an experiment, I have to carry out Hypothesis testing and if I want to find out the effects of ALL factors in the same experiment, then Design of Experiment(DOE) has to be used.  All in all, once I got the hang of it, it was quite simple and straightforward. I have never taken statistics before which is also why it was really unfamiliar to me, but with this experience, I actually look forward to more statistics hopefully in the near future(or after poly😆)

That's all for my 2nd last entry of this semester! See you soon 👹