STAT-S 300 Lecture Notes - Lecture 22: Randomized Experiment, Conditional Probability, Null Hypothesis
Section 9.1 Notes- Significance Tests: The Basics 12-2-13
Significance test- formal procedure for comparing observed data with a claim (also called
hypothesis) whose truth we want to assess
oClaim is statement about parameter (population proportion or mean )
oExpress results of significance test in terms of probability that measures how well data
and claim agree
The Reasoning of Significance Tests
oTests ask if sample data gives good evidence against a claim
oAn outcome that would rarely happen if a claim were true is good evidence that the claim
is not true
Stating Hypotheses
oNull hypothesis (H0)- claim tested by statistical test, trying to find evidence against
Often called statement of “no difference”
Parameter = value
oAlternative hypothesis (Ha)- claim about the population that we are trying to find
evidence for
Hope or expect to be true instead of H0
One-sided alternative- states that parameter is larger than H0 value or states that
parameter is smaller than H0 value
Two-sided alternative- states that parameter is different from H0 value (could be
larger or smaller)
oHypotheses should express hopes or suspicions we have before seeing data- looking at
data and making fitting hypothesis is cheating (bias)
oAlways refer to population, not sample- be sure to state in terms of population
parameters, not statistics
oSymbols (# means the same number each time)
One-tailed
H0: = # or = #
Ha: > # or > # OR < # or < #
Two-tailed
H0: = # or = #
Ha: ≠ # or ≠ #
Interpreting P-Values
oP-value- probability, computed assuming H0 is true, that the statistic ( or ) would take a
value as extreme as or more extreme than what was observed by chance alone
The smaller the p-value, the stronger the evidence against H0 provided by the data
Probability that measures strength of evidence against null hypothesis
Conditional probability: P(statistic ≠ value | parameter = value)
oFailing to find evidence against H0 means only that data are consistent with H0, not that
we have clear evidence that H0 is true
Statistical Significance
oMake decision based on strength of evidence against H0 (and in favor of Ha)
Reject H0 if sample results too unlikely to have happened by chance assuming H0
is true
Fail to reject H0 otherwise- does not mean H0 is true
oNever accept H0 or use language implying that you believe H0 is true
find more resources at oneclass.com
find more resources at oneclass.com
Document Summary
The reasoning of significance tests: tests ask if sample data gives good evidence against a claim, an outcome that would rarely happen if a claim were true is good evidence that the claim is not true. Stating hypotheses: null hypothesis (h0)- claim tested by statistical test, trying to find evidence against. Parameter = value: alternative hypothesis (ha)- claim about the population that we are trying to find evidence for. Hope or expect to be true instead of h0. One-sided alternative- states that parameter is larger than h0 value or states that parameter is smaller than h0 value. Ha: > # or > # or < # or < # Interpreting p-values: p-value- probability, computed assuming h0 is true, that the statistic ( or ) would take a value as extreme as or more extreme than what was observed by chance alone. The smaller the p-value, the stronger the evidence against h0 provided by the data.
