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

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

3. Hypothesis Testing
5 STEPS!

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

5. 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.

6. 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.

7. 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.

8. 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)

9. 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

10. 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

11. 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

12. 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.

13. Large Hadron Collider (LHC)

14. 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.

15. 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

16. 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

17. 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”.

18. 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.

19. Hypothesis Testing of LHC
Common practice
5 s.d. effect as sufficient to announce a discovery
Depend on many factors
Proton-proton collision
Detector

20. 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