Exam 2 - Handout 6a - Inferential Stats Flashcards
Normal distribution
Symmetrical bell-shaped curve
Mean, median, and mode are equal
Standardized as the z-distribution with mean 0 and standard deviation 1
t-distribution
Similar to the z-distribution but with thicker tails
Used when the population standard deviation is unknown
Binomial distribution
Describes binary outcomes
Ex. Success/failure
Probability of success (p) and failure (q) sum 1 (p + q = 1)
Other distributions with specific applications in statistical tests
Chi-square
F
Poisson
Gamma
Central limit theorem
Mean of sample means = population mean
Standard deviation of sample means = standard error of the mean
As sample size increases, the distribution of sample means approaches a normal distribution
How are populations and samples represented
Population parameters are represented by Greek letters
Sample statistics are represented by latin letters
Point estimation
Estimating a single value for a population parameter
Interval estimation
Constructing a confidence interval to estimate a population parameter
How are confidence intervals calculated?
Point estimate ± (critical value) (standard error of the estimate)
Probabilistic confidence intervals
The interval contains the true population parameter w/ a certain level of confidence
Confidence interval range
Estimate be as high as the upper bound or as low as the lower bound
Importance of confidence intervals
Provide information about the precision of estimates
Can be used to conduct hypothesis tests
Null hypothesis (H0)
States the opposite of the null hypothesis
Alternative hypothesis (HA)
States the opposite of the null hypothesis
Type I error (α)
Rejecting the null hypothesis when it is true
Type II error (β)
Failing to reject the null hypothesis when it is false
Power
The probability of rejecting the null hypothesis when it is false (1 - β)
Types of hypothesis tests
Directional tests
Nondirectional tests
Directional tests
Test of superiority
Test of noninferiority
Test of superiority
Examines if one qty is greater than another
Test of noninferiority
Examines if one qty is no worse than another by a specified margin
Nondirectional tests
Test of difference
Test of equivalence
Test of difference
Examines if two quantities are different
Test of equivalence
Examines if two quantities are practically equivalent
Frequentist approach vs bayesian approaches
Frequentist approach:
- Views PARAMETERS as fixed and data as a variable
- Focuses on testing the null hypothesis
Bayesian approach:
- Views parameters as variable and data as fixed
- Incorporates prior knowledge and updates it with new evidence
Statistical significance
Refers to the results of a statistical analysis and whether the null hypothesis can be rejected
Clinical significance
Refers to the practical importance or relevance of the findings
