Statistical Inference and Hypothesis Testing Exam 1 Flashcards
Alternate hypothesis (HA)
actual hypothesis
Null hypothesis (H0)
- Null hypothesis (H0):
- Conclusions are made in terms of rejecting or failing to reject the null hypothesis
Alpha
- Probability of a Type I error
- Reject the null when the null is true
- Conclude there is a difference when none exists
- False positive
- Confidence = 1-α
Beta
- Probability of a Type II error
- Fail to reject the null when the null is false
- Conclude there is no difference when one actually exists
- False negative
- Power = 1-β
Power
Probability of concluding there is a difference when one actually exists
a priori
alpha and beta are thresholds set by researchers before any data is collected; determined by literature or clinical relevance
p value
- Calculate p value by calculating the z score
- A z score has a corresponding p value
- p < 0.05 : H0 is rejected
- p > 0.05 : H0 fail to be rejected
Non-directional tests and examples
- two tailed, look in both directions
- Test of difference
- Test of equivalence
- Null is opposite of the type of test -> rejecting it would say that the type of test is true
Tests of difference
- Tests whether the difference between two quantities is 0
- H0 : X-Y = 0
Tests of equivalence
- Tests whether two quantities are within an acceptable range of each other
- H0 : |X-Y| ≥ Δ
Directional tests and examples
- one tailed, looks only in one direction
- Test of superiority
- Test of non-inferiority
Tests of superiority
- Tests whether one quantity is greater than or less than the other
- H0 : X-Y ≤ 0
- Rejecting the null says that one group is greater than (or less than) the other
Tests of non-inferiority
- Tests whether one quantity is no worse than a second quantity
- H0 : X-Y ≥ Δ
- Rejecting the null says the one group is noninferior to the other
How do you approach hypothesis testing?
- Convert the research question into appropriate null and alternate hypotheses
- Select the appropriate statistical test
- Select the desired significance level and the appropriate critical value for the statistical test
- Calculate the test statistic
- Compare the test statistic to the critical value and draw conclusions
How do you go about testing the null hypothesis?
- Temporarily assume H0 is true
- If data determines that H0 is extremely unlikely, this provides evidence against H0 and we reject H0
- If data determines that H0 is not extremely unlikely, this does not provide evidence against H0 and we fail to reject H0
statistical significance
when the null hypothesis is rejected after statistical analysis
clinical significance
relates to whether the findings are clinically or practically meaningful
Characteristics of hypothesis
- A declarative sentence
- Describes a relationship between two or more variables
- Testable by empirical means
- Provides an indirect method of statistical inference
What is a standard error?
Standard deviation of the population mean
