Hypothesis Testing and Statistical Interference EXAM 3

Question 1

What are the variables used in inferential statistics?

Answer 1

-Inferential means to make conclusions (decisions) based on evidence (data)

Variables: P-Value, Confidence Interval, alpha + beta error, Power

Question 2

Examples of tools to present descriptive statistics

Answer 2

Median, IQR, Box Plots

Question 3

What does the p-value represent under the curve?

Answer 3

Probability of one outcome under the curve Vs any other outcome under the curve

Question 4

How much % of the data can be determined with an SD of 1, 2, and 3?

Answer 4

1 SD: 68% of the data
1.96 SD: (approx. 2): 95% of the data
3 SD: 99% of the data

Question 5

QUESTION

Answer 5

Does the bell-shaped curve only contain data points of the mean? Could the data point also be a point estimate?

Can you tell what the CI is just by looking at the p-value? f.e. p=0.05 -> so CI is 95%?
p=0.02 -> so CI is 98%?

How is the SD different from the CI
-> Maybe the CI is only used when comparing the drug group with the placebo, to see if it crosses 0 or 1

Isn’t there always the possibility to commit a type 1 error, even with very small p-values

If I refuse a new drug because (f.e. due to p=0.07), and the drug actually works (type II error), how will I know that I’ve committed a type II error?

What happens if the p-value of a finding crosses the beta (f.e. beta is set to 0.1 (10%) and the finding has a p-value of 11%?

Question 6

What does the H0 state?

Answer 6

-The H0 states that the observed difference between the means is due to chance

Question 7

When can the H0 be rejected?

Answer 7

As the H0 states the differences are due to chance,
the findings have to be different to an extent that makes it allowable to reject the H0 even though there is a slim probability that is still due to chance (so the result of the experimental group has to be found in the tales)

-> it has to be different at least to a p-value of 5$

Question 8

What is the definition of the P-value?

Answer 8

The probability of finding an effect that is as big as the ones for the null

-> So not different (enough) from null (placebo)
->p=0.05 -> probability of 5% that the finding is due to chance, or not different from placebo

Question 9

What to look out for in p-values related to the validity of the research study!

Answer 9

The magnitude (strength) of the p only reflects the confidence to reject the null (so the certainty that the effect is different)

-it doesn’t tell how clinically significant the findings are

Question 10

What is a Type I and Type II error?

Answer 10

Type 1 (alpha) error: we claim a drug works but it actually doesn’t -> the findings were due to chance, and are not different from placebo -> NULL
FALSE POSITIVE

Type 2 (beta) error: we claim the drug does not work, but it actually works -> we falsely accepted the H0 (FALSE NEGATIVE)

Question 11

What are the clinical consequences of Type I and Type II errors?

Answer 11

Type I: the patient uses a drug, that is believed to work, but it doesn’t -> the patient is exposed to the risk of the disease w/o appropriate treatment, and to potential toxicities of the drug
-> The FDA requires multiple studies to prove its efficacy

Type II: the drug (f.e. w/ p=0.55) is abandoned, but it actually works

Question 12

When is it likely to commit a Type II error?

Possible Exam Question: Out of the p-values choose the one that is most likely associated with a Type II error

Answer 12

-With p-values slightly above 0.05

Question 13

Type II error

Answer 13

F.e.: the alpha is set to 0.05 and the beta is set to 0.2 -> the findings have a of p=0.1
we accept the H0 (refuse the drug)
->At this position we could have committed a type II error
->and we willingly accept the risk that we have committed a possible type II error

Question 14

What is the POWER of a study?

Answer 14

-The ability of a study to detect a difference when there TRULY is a difference
->so to NOT refuse the drug falsely (prevent Type II error)

1 - beta = POWER
100% - 20%(beta) = 80 % POWER

Question 15

When is it appropriate to assess the power of a study?

Answer 15

-Only when the P-value of a finding is bigger than 0.05

-if the p-value is 0.05 or less we have detected the difference already

Question 16

What is the minimum required POWER of a study?

Answer 16

Minimum beta = 20% -> so the minimum Power is 80%

Question 17

What are the factors affecting the statistical Power?

Answer 17

-Alpha error (significance criteria)
-Variance of the data
-Sample Size
-Effect Size

Question 18

How is the Alpha Error related to the statistical Power?

Answer 18

The lower (tight) the alpha the lower my statistical power (more likely I am to make a beta error)

Question 19

How is Variance related to the statistical Power?

Answer 19

If the Confidence intervals of the drug finding and the placebo overlap we can’t declare a difference -> bc there is the possibility the data point overlaps with a data point of the placebo

As the variance is reduced, the ability to detect a difference is enhanced -> POWER increased

Question 20

How is the Effect size related to the statistical Power?

Answer 20

The bigger the effect size, the easier it is to detect the difference from placebo -> the more POWER

Question 21

How is Power related to sample size?

Answer 21

The greater the sample size the greater the ability to pick up the TRUE difference

-greater sample size -> greater POWER
-> bc a great sample size shrinks the Confidence Interval and reduces the likelihood of crossing 0 or 1

Question 22

How is the Effect size related to sample size?

Answer 22

As the effect size rises, fewer patients are necessary to be enrolled for the study (low sample size needed)