Nuclear Physics and Radiation Detectors

Nuclear Physics and Radiation Detectors


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Nuclear Physics and Radiation Detectors P4H 424 Course, Candlemas 2004 Nuclear Physics Lecture 1 Dr Ralf Kaiser Room 514, Department of Physics and Astronomy University of Glasgow P4H 424: Nuclear Physics Lecture 1 – p.1/21
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Lecture 7: Hypothesis
Testing and ANOVAGoals
• Overview of key elements of hypothesis testing
• Review of common one and two sample tests
• Introduction to ANOVAHypothesis Testing
• The intent of hypothesis testing is formally examine two
opposing conjectures (hypotheses), H and H0 A
• These two hypotheses are mutually exclusive and
exhaustive so that one is true to the exclusion of the
• We accumulate evidence - collect and analyze sample
information - for the purpose of determining which of
the two hypotheses is true and which of the two
hypotheses is falseThe Null and Alternative Hypothesis
The null hypothesis, H :0
• States the assumption (numerical) to be tested
• Begin with the assumption that the null hypothesis is TRUE
• Always contains the ‘=’ sign
The alternative hypothesis, H :a
• Is the opposite of the null hypothesis
• Challenges the status quo
• Never contains just the ‘=’ sign
• Is generally the hypothesis that is believed to be true by
the researcherOne and Two Sided Tests
• Hypothesis tests can be one or two sided (tailed)
• One tailed tests are directional:
H : µ - µ ≤ 00 1 2
H : µ - µ > 0A 1 2
• Two tailed tests are not directional:
H : µ - µ = 00 1 2
H : µ - µ ≠ 0A 1 2P-values
• Calculate a test statistic in the sample data that is
relevant to the hypothesis being tested
• After calculating a test statistic we convert this to a P-
value by comparing its value to distribution of test
statistic’s under the null hypothesis
• Measure of how likely the test statistic value is under
the null hypothesis
P-value ≤ α ⇒ Reject H at level α0
P-value > α ⇒ Do not reject H at level α0When To Reject H0
Level of significance, α: Specified before an experiment to define
rejection region
Rejection region: set of all test statistic values for which H will be0
Two SidedOne Sided
α = 0.05α = 0.05
Critical Value = -1.64 Critical Values = -1.96 and +1.96Some Notation
• In general, critical values for an α level test denoted as:
One sided test : X"
Two sided test : X"/2
where X depends on the distribution of the test statistic
• For example, if X ~ N(0,1):
One sided test : z (i.e., z = 1.64)" 0.05
Two sided test : z (i.e., z = z = ± 1.96)"/2 0.05 / 2 0.025
! Errors in Hypothesis Testing
Actual Situation “Truth”
H FalseH True 0 0 Decision
Do Not
Reject H0
Rejct H0Errors in Hypothesis Testing
Actual Situation “Truth”
H FalseH True 0 0 Decision
Incorrect DecisionDo Not Correct Decision
Reject H β1 - α0
Correct DecisionIncorrect Decision
Rejct H0 1 - βα