Exam 2 - Handout 6a - Inferential Stats

Question 1

Normal distribution

Answer 1

Symmetrical bell-shaped curve

Mean, median, and mode are equal

Standardized as the z-distribution with mean 0 and standard deviation 1

Question 2

t-distribution

Answer 2

Similar to the z-distribution but with thicker tails

Used when the population standard deviation is unknown

Question 3

Binomial distribution

Answer 3

Describes binary outcomes

Ex. Success/failure

Probability of success (p) and failure (q) sum 1 (p + q = 1)

Question 4

Other distributions with specific applications in statistical tests

Answer 4

Chi-square
F
Poisson
Gamma

Question 5

Central limit theorem

Answer 5

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

Question 6

How are populations and samples represented

Answer 6

Population parameters are represented by Greek letters

Sample statistics are represented by latin letters

Question 7

Point estimation

Answer 7

Estimating a single value for a population parameter

Question 8

Interval estimation

Answer 8

Constructing a confidence interval to estimate a population parameter

Question 9

How are confidence intervals calculated?

Answer 9

Point estimate ± (critical value) (standard error of the estimate)

Question 10

Probabilistic confidence intervals

Answer 10

The interval contains the true population parameter w/ a certain level of confidence

Question 11

Confidence interval range

Answer 11

Estimate be as high as the upper bound or as low as the lower bound

Question 12

Importance of confidence intervals

Answer 12

Provide information about the precision of estimates

Can be used to conduct hypothesis tests

Question 13

Null hypothesis (H0)

Answer 13

States the opposite of the null hypothesis

Question 14

Alternative hypothesis (HA)

Answer 14

States the opposite of the null hypothesis

Question 15

Type I error (α)

Answer 15

Rejecting the null hypothesis when it is true

Question 16

Type II error (β)

Answer 16

Failing to reject the null hypothesis when it is false

Question 17

Power

Answer 17

The probability of rejecting the null hypothesis when it is false (1 - β)

Question 18

Types of hypothesis tests

Answer 18

Directional tests
Nondirectional tests

Question 19

Directional tests

Answer 19

Test of superiority
Test of noninferiority

Question 20

Test of superiority

Answer 20

Examines if one qty is greater than another

Question 21

Test of noninferiority

Answer 21

Examines if one qty is no worse than another by a specified margin

Question 22

Nondirectional tests

Answer 22

Test of difference
Test of equivalence

Question 23

Test of difference

Answer 23

Examines if two quantities are different

Question 24

Test of equivalence

Answer 24

Examines if two quantities are practically equivalent

Question 25

Frequentist approach vs bayesian approaches

Answer 25

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

Question 26

Statistical significance

Answer 26

Refers to the results of a statistical analysis and whether the null hypothesis can be rejected

Question 27

Clinical significance

Answer 27

Refers to the practical importance or relevance of the findings