L18, L20, L22, L23- biostats lectures

Question 1

what is sampling distribution

Answer 1

where you take all data points (2) and pair them with themselves and each other to find a distribution of means => n^2 sample size with normal distribution curve
(mean stays the same, SD dec)

Question 2

what is the formula for standard error of the mean

Answer 2

SEM = σ / sqrt(n)

• measures variability in the mean
• decreases as sample size (n) increases

Question 3

Central Limit Theorem in terms of not normal population distribution

Answer 3

it yields a normal distribution- increases the sample size of the population

Question 4

calculation of degrees of freedom

Answer 4

df = n - 1

Question 5

define t-distribution

Answer 5

normal distribution with fatter tails (more extreme values included)
-as df increases (n - 1 inc), tails get smaller and t-values approach Z-values (n = infinity)

Question 6

define random sample

Answer 6

randomness means everyone has an equal probability of being included

Question 7

what does the Central Limit Theorem infer about a sample

Answer 7

allows us to infer population parameters (mean, SD) from a single sample of sufficient size

Question 8

describe when it is better to use standard error OR standard deviation

Answer 8

SEM- how well does the sample estimate the mean

SD- how widely scattered are the measurement in the population

Question 9

define the purpose of Confidence Interval

Answer 9

makes inferences about the true mean based on the mean and SD of the sample

Question 10

define null and alternative hyopthesis

Answer 10

null- nothing unusual is happening, no relationship between exposure/disease

alternative- something unusual is happening, exposure and disease are related

Question 11

what are the two ways to test a hypothesis

Answer 11

One-sided: alternative hypothesis specifies a direction (only better or only worse)

Two-sided: alternative hypothesis can go in either direction (either better or worse)

Question 12

CI = (1)

P = (2)

Answer 12

1- CI = 1 -α

2- P = 1 - β

Question 13

what is the Z value formula

Answer 13

Z = (X - µ) / (SD/sqrt(n))

Question 14

define type I and type II errors in terms of null hypothesis

Answer 14

Type I (α error/FP)- null hypothesis is true, study rejects Ho

Type II (β error/FN)- Ho is false, study supports Ho

Question 15

what situations are bad to have Type I errors

Answer 15

(false positives)

• Tx is expensive, difficult
• cost of false alarm is high
• no effective Tx

Question 16

what situations are bad to have Type II errors

Answer 16

(false negative)

• Tx is cheap, easy
• cost of false alarm is low
• Tx is only responsive in early stages

Question 17

Type I/α error can only occur if Ho is (T/F)

Type II/β error can only occur is Ho is (T/F)

Answer 17

1- (false positives), Ho is true

2- (false negatives), Ho is false

if one inc, the other dec

Question 18

inc β in will have what effect on α, σ, n, Δ

Answer 18

α- dec (type I error)
σ- inc (standard deviation)
n- dec (sample size)
Δ- dec (effect size)

Question 19

list the hypothesis test needed for the when the ind. and dep. variable are categorical

Answer 19

chi-squared test (contigency tables)

Question 20

list the hypothesis test needed for the when the ind. variable is categorical and the dep. variable is continuous

Answer 20

t-tests (2 groups)

ANOVA (3 or more groups)

Question 21

list the hypothesis test needed for the when the ind. and the dep. variable are continuous

Answer 21

correlation regression

Question 22

what are the assumptions of a chi-squared test

Answer 22

• categories are exclusive

- each category has an expected value of at least 5

Question 23

what is the calculation for Chi-squared test

Answer 23

(observed - expected)^2 / expected

Question 24

what is the formula for the degrees of freedom in a chi-squared test

Answer 24

df = (# columns - 1) * (# rows - 1)

Question 25

what is the assumption made in a t-test

Answer 25

• assumes sample population is normally distributed

- assumes variance of both samples are the same

Question 26

define both values used from a Pearson correlation

Answer 26

r = strength of association / correlation between variables

r^2 = variance or the percentage that the one variable explains the other

Question 27

list the r values and their associated correlation strengths

Answer 27

(note absolute value of r)
r < 0.4 --> weak corr.
0.4 < r < 0.6 --> mod. corr.
0.6 < r < 0.8 --> strong corr.
r > 0.8 --> very strong corr.

Question 28

list the assumptions of Pearson Correlation

Answer 28

• normality of variables (continuous normal distribution)
• linearity of associations (correlation strength doesn’t change with higher v lower variables)
• oval scatterplot (not triangle)

Question 29

what are some conditions that violate assumptions of Pearson Correlation

Answer 29

• extreme values
• multiple modes
• nonlinear / nonmonotone associations
• triangular scatterplot

Question 30

describe Spearman’s correlation, what is the disadvantage

Answer 30

• ranking correlations regardless of size differences, used when Pearson cannot be used
  (ex. extreme values, nonmonotonic data)
• less statistically powerful

Question 31

Spearman is the (1) correlation

Pearson is the (2) correlation

Answer 31

1- Safe

2- Powerful

Question 32

what is a correlation regression

Answer 32

there is a quantifiable correlation between the 2 variables

y = mx + b

Question 33

describe the linear association regression formula

Answer 33

y = α + βx

Question 34

what are residuals in linear regressions

Answer 34

• used for individual data points
• difference in actual value and predicted value
• y = α + βx + e (the residual)

Question 35

how do assumptions and power of a test relate

Answer 35

• more assumptions made –> the weaker the power (continuous stuff)
• less assumptions made –> the stronger the power (categorical stuff)

Question 36

list the 4 data types in order of increasing power

Answer 36

(in order of inc power and dec assumptions)

ratio < interval < ordinal < nominal

Question 37

what is the Odds formula in terms of probability

Answer 37

Odds = probability / (1 - probability)

Question 38

what is the Probability formula in terms of odds

Answer 38

Probability = odds / (1 + odds)

Question 39

describe Bayes Theorem

Answer 39

1) pretest probability –> odds ratio
2) PostTest Odds = PreTest Odds x LR
3) posttest odds –> probability
(only used if there is pretest knowledge that can be used)

Question 40

what are the 4 steps for identifying statistical errors in literature

Answer 40

1) were limits of design and statistical approach acknowledges
2) was appropriate data and statistical tools applied for hypothesis tested
3) were the assumptions of the approach violated
4) were the results interpreted correctly

Question 41

what are the assumptions of the residuals in a linear regression

Answer 41

• normally distributed
• uncorrelated with the outcome
• uncorrelated with each other