Hypothesis testing

 In this lesson we use the statistical methodology of hypothesis testing to analyze the results of our Design of Experiment factorial, as a practical example of how to utilize it in our own future projects.

Each group member chooses one pair of runs from the fractional factorial and full factorial catapult experiment results; we then perform a difference of means test to prove or disprove a hypothesis.

The data of our experiment is as follows.

Full Factorial

Fractional Factorial

In an experiment, we wish to answer a question; to prove or disprove something. In a hypothetical scenario of being the manufacturer of these toy catapults, to ensure quality of their products they might wish to test whether two products have the same performance; and so they want to test the hypothesis of whether the projectile distance of the catapults is the same or different.

The structure of this methodology is to define a null statement to be accepted or rejected, and an alternative statement when the null is rejected. We then perform statistical analysis to ascertain whether the hypothesis is true or not.

The first step is the hypothesis statements which is to ascertain the performance of the catapults.

H0: No difference in distance launched by catapults between each other. µ₁=µ₂

H1: Difference in distance launched by catapults between each other. µ₁≠µ₂

I chose Black Widow so I will use run 8 of both catapults; the means, standard deviations and sample sizes of the groups I chose are below-

Catapult A: 

Catapult B:

Next is to calculate the test statistic. A difference in means between two groups has the following formulae:

So I just sub in the values to find sigma then 't'

The alternative statement has a not equal to sign which means this is a two-tailed test. I select the typical significance level of α=0.05.

The degrees of freedom is the sum of the sample sizes minus two, thus v=8+8-2=14

The probability level of this test is t_.975  

Thus the critical t would be ±2.145

Our test statistic of t=0.776 falls within the boundaries of the acceptance region that is ±2.145. Hence, we accept the null statement. From this hypothesis test, we can see that there is no difference in the distance of the projectiles launched by both catapults at 0.05 significance.

My groupmates of Pi Ti, Edmund and Andrew, picked Hawkeye, Iron Man and Captain America respectively. They all found differences between their groups. This difference in answers could be a result of a difference in significance levels or miscalculations, or because certain combinations of factors results in catapult makeup becoming insignificant. Just from a glance, one can see that the difference in means between some runs being up to 60cm wide, to a 20cm difference as well as a mere 2.5 cm difference. I have difficulty in providing a sufficient explanation for this discrepancy, and would suggest that further investigations into unaccounted factors of the catapult be conducted.

Reflection:

I take statistics for chemical process industry as an elective and as such am well familiar with the use of hypothesis testing. However, this is the first time I've used it to analyze data which I have personally obtained as opposed to those from questions or the internet. Thus, I think I have a slightly greater appreciation of the use of hypothesis testing as well as its multifactor and multigroup counterpart Analysis of Variance(ANOVA) because of this task, and will certainly find it useful in any future field I will join as well as my CAPSTONE project in the near future.