Statistical Testing of the Large Hadron Collider Presenter: Shu Min Group 5: Shu Min, Yan Ling, Yi Mou

Contents: Hypothesis testing (steps) Errors in Hypothesis Testing Background of the Large Hadron Collider (LHC) Hypothesis testing of LHC Conclusion

Hypothesis Testing 5 STEPS!

Hypothesis Testing Step 1: Hypothesis Step 2: Significance level Step 3: Test Statistic Step 4: p-Value Step 5: Conclusion

Step 1: Hypothesis Define H0 Define H1 Usually represents no effect Represent an effect of some kind H0 usually represents a currently observed scenario, while H1 usually suggests an alternative scenario.

Step 2: Significance Level Predetermined Denoted by α Probability of rejecting H0, given H0 is true. (Type I error) After setting the hypothesis, the significance level is usually predetermined by the statistician before the hypothesis testing is carried out. Denoted by alpha Alpha in this case, means the probability of rejecting the null hypothesis, given that the null hypothesis is true. This is a type I error, which I will be going through in the next section.

Step 3: Test Statistic Describes how far point estimate falls from the parameter value given in the null hypothesis Decide on a test statistic based on the hypothesis test that is being conducted. Calculate the value of test statistic and the critical value is determined.

Step 4: p-Value The probability of obtaining a result equal to or "more extreme" than what was actually observed. Step 4: p-value, which is the probability of obtaining a result equal to or more extreme than what was actually observed (double check)

Step 5: Conclusion Test statistic ≥ Critical value Small p-value (typically ≤ 0.05), Ho is rejected Test statistic ≤ Critical value Large p-value (typically > 0.05) , Ho is not rejected Test Statistic number is greater than critical value P value is be http://statistics.about.com/od/Inferential-Statistics/a/An-Example-Of-A-Hypothesis-Test.htm

Errors in hypothesis testing Type I: H0 is indeed true but it is rejected Type II: H0 is false (i.e. H1 is true) but it is not rejected https://onlinecourses.science.psu.edu/stat502/node/139

Example of Type I and II errors Ho= Person is innocent H1 = Person is guilty Ho the person is innocent, H1 the person is not innocent Type 1 error occurs when H0 is true but it is rejected Type 2 error occurs when H0 is not true, but it is not rejected

Large Hadron Collider (LHC) ‘Large’: Circular ring 27 km in circumference. It is buried 100 m underground 1 ‘Hadron’: It takes beams of protons (general classification: hadron) 2 ‘Collider’: Makes them collide 3 at the European Organisation for Nuclear Research (CERN) near Geneva, Switzerland.

Large Hadron Collider (LHC) http://news.oreilly.com/2008/06/large-hadron-collider-as-a-mas.html

Large Hadron Collider (LHC) Proton-proton collision at very high speeds Many other particles are formed ‘The Standard Model’ is a theory concerning the electromagnetic, weak, and strong nuclear interactions, as well as classifying all the subatomic particles known. http://abyss.uoregon.edu/~js/21st_century_science/lectures/lec16.html

Within the Large Hadron Collider Overview of Large Hadron Collider 2 groups of protons travelling at high speed towards each other Collision occurs Many particles formed

When they collide, many smaller objects are formed When they collide, many smaller objects are formed. These objects are representing the particles in the standard model

What’s more… Many extensions to the Standard Model have been proposed Supersymmetry (SUSY) This is a class of theory where for every known type of particle there exists a new partner particle, which should have a different angular momentum or “spin”. http://www.lhc-closer.es/taking_a_closer_look_at_lhc/0.supersymmetry

Hypothesis Testing of LHC Step 1 Hypothesis Step 2 Significance level Step 3 Test statistic Step 4 p-Value Step 5 Conclusion Ho: Standard Model H1: Another model exists NEW DISCOVERY! Significance level: α = 0.05 (general) Test statistic: unknown p-Value: unknown Rejecting the Standard Model with a sufficiently high significance level amounts to discovering something new The significance of the observed signal is often quantified by a p-value taken as the probability, assuming only background events are present.

Hypothesis Testing of LHC Common practice 5 s.d. effect as sufficient to announce a discovery Depend on many factors Proton-proton collision Detector http://www.investopedia.com/exam-guide/cfa-level-1/quantitative-methods/confidence-intervals.asp

Conclusion Some tests may be statistically significant, just by chance. Take into account the possibility of bias or confounding. Replication is always important to build a body of evidence. To support findings