Hypothesis testing

 HWALLO, welcome back to another blog of mine, this blog is relatively short because i will be showing how i am going to apply hypothesis testing to the previous experiment [DOE]. 

HYPOTHESIS TESTING

Before we begin applying hypothesis, What exactly is hypothesis testing even?

A statistical hypothesis is an assumption about a population parameter. This assumption may or may not be true so. Hypothesis testing then refers to the formal procedures used by experimenters or researches to accept or reject statistical hypothesis.

Although the ideal way to determine if a statistical hypothesis is true is by examining the entire population, it is often impractical. Thus a random sample is taken and compared to the statistical hypothesis, if they are not consistent, the hypothesis is rejected. 

DECISION ERRORS

There are some downsides when one uses sample data to estimate the properties of a population since the sample may not be representative of the population, which results in decision errors.

There are 2 types of errors:

Type 1 error: It occurs when the researcher rejects a null hypothesis when it is true. The probability of committing a Type 1 error is called the significance level (alpha) 

Type 2 error: It occurs when the researcher fails to reject a null hypothesis that is false. the probability of committing a Type 2 error is called beta

Let's Begin!

Each member in my group would take on a role and perform hypothesis testing on different runs and here is everyone's roles

Iron Man: Reinard

Thor: Clive (me)

Black Widow: Joelle

Hulk: Adyl

Table of Data: 

Since i am Thor, i will be doing hypothesis testing on runs #2 and #4

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 =  33cm Projectile weight = 0.89 grams and 2.01 grams Stop angle = 90 degree
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. n = 8 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 Run # 2: Mean = 107 Std. Dev. = 6.02   State the mean and standard deviation of Run #4: Mean = 111.2 Std. Dev = 11.34   Compute the value of the test statistic (t):
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 = ± 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   Therefore Ho is ACCEPTED.
Conclusion that answer the initial question	The projectile weight does not have a significant affect on the flying distance of the projectile
Compare your conclusion with the conclusion from the other team members.	Reinard and Adyl, who were also testing projectile weight against flying distance using other data runs.  Reinard accepted his Ho, Adyl rejected his Ho While the hypothesis testing i did had my Ho accepted.  Joelle, who was testing stop angle against flying distance, had her Ho rejected
What inferences can you make from these comparisons?	I think the reason why i had a different result was because there was an outlier data in run #4, This outlier data affected the average and standard deviation values thus affecting the final conclusion. Therefore i can conclude that i have encountered a type II error. Reinard could also have had a type II error because based on the practical, the projectile weight should have an effect on the flying distance. Adyl most likely did not have any errors as his Ho was rejected, therefor i can conclude that the two runs he used were accurately collected It is unknown for whether joelle's hypothesis testing was accurate or not because there was not enough members to do another hypothesis test on another set of data. However, according to the practical, Ho should be rejected.
Your learning reflection on this Hypothesis testing activity	when first learning about how to do hypothesis testing, i actually took quite a while to understand how to exactly do it. This is because i often get confused whether i should use one tail or two tailed tests. But after i was given some practice questions i realised that it was not so complicated after all, and what i learned from this was to take things slow and that everyone has their own learning pace.  From this activity, i also learnt that hypothesis testing can save a lot of time and provide answers with evidence. For example, when looking at the data for the catapult experiment, i initially thought that the projectile weight would have a significant effect on the flying distance. However i was proven wrong through hypothesis testing and this made me think of reasons why it was wrong. Could it be that the projectile weight difference was not big enough? or the data we have collected was not accurate? was there an error made? or was my hypothesis simply wrong?.  It made me question myself and reminded me that my 'logic' may not always align with reality. Therefore i would like to take this as a good learning experience as it taught me to be humble and always test my 'hypothesis' before skipping the steps and drawing a conclusion. I also hope to be able to apply this in future statistical experiments, for example my Final Year Project. I hope to be able to apply this concept and it could definitely come out to be helpful in drawing a conclusion.