24 terms

# Statistics 6.3 Using Significance Tests

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Why is statistical significance valued?
It points to an effect that is unlikely to occur simply by chance
What is the purpose of a test of significance?
To describe the degree of evidence provided by the sample against the null hypothesis
What describes the degree of evidence provided by the sample against the null hypothesis
P-value
How small a P-value is convincing evidence against the null hypothesis? It depends on: (2)
1. The plausibility of H₀
2. Consequences of rejecting H₀
Smaller the P
More convincing evidence
Larger the P
Less convincing evidence
APY 6.81
APY 6.81 (i)
APY 6.81 (ii)
APY 6.81 (iii)
APY 6.81 (iv)
APY 6.81 (v)
APY 6.81 interpretation
1. Find the z score
2. Find the P-value depending on the hypotheses
3. Check P-value > or < α
Statistically significant
An event occurred NOT by a chance
NOT statistically significant
An event occurred BY a chance
Statistically significant on H₀
Reject the null hypothesis
NOT statistically significant on H₀
Fail to reject the null hypothesis
What does the null hypothesis assume?
Assumes that any kind of difference or significance is due to chance.
P-value>α
NOT statistically significant
P-value>α WHY?
The probability that the point is extreme shows enough "strong-ness" to reject H₀
P-value<α
Statistically significant
P-value<α WHY?
The probability that the point is extreme shows NOT enough "strong-ness" to reject H₀
P-value and α
P-value measures the probability that the point is at the extreme value and α measures the "enough strong-ness" to reject H₀. If α is greater than P-value, we reject H₀.
Significance level α
The significance level α for a given hypothesis test is a value for which a P-value less than or equal to α is considered statistically significant.