Inferential Biostatistics

Question 1

what are the steps for hypothesis testing?

Answer 1

1. state the null and alternative hypotheses
2. select the alpha value (usually 0.05)
3. gather data and perform appropriate statistical tests generating a p value
4. accept or reject the null

Question 2

what is the null and alternative hypotheses for investigating whether a new drug improves symptoms of tension headache?

Answer 2

n: drug produces no change in headache symptoms compared to placebo
a: drug produces a significant change in headache symptoms compared to placebo

• -> must not say it makes symptoms better because you need to leave open possibility that it makes symptoms worse
• just say it produces a change or it does not

Question 3

what is the alpha level?

Answer 3

designates the level of uncertainty you’re willing to accept
- alpha=0.05… you’re willing to accept that 5 % of the time the test could be wrong, the results are generated by chance

Question 4

what is the p value?

Answer 4

the measure of significance obtained from statistical tests

-the probability that the difference between group means found in the research is due to chance alone

Question 5

describe a parametric test

Answer 5

• focused on population parameters
• requires a continuous variable (ex cholesterol levels)
• assumes a normal distribution
• generally more powerful than nonparametric

Question 6

what are examples of parametric tests

Answer 6

anova, t-test, paired t-test, confidence intervals

Question 7

what is the central limit theorem

Answer 7

creates a normal distribution by sampling the population and distributing the means of each sample

• states that for a sufficiently large sample size, the means will aways tend to be normal irrespective of the shape of the population from which the samples were drawn

Question 8

why are sampling distributions (central limit theorem) useful?

Answer 8

-allows parametric (ones that require normal distribution) tests to be done even if the underlying distribution is not normal so long as the sample size is large enough

Question 9

describe a non-parametric test

Answer 9

not focused on population parameters
can be applied to discrete variables
used for smaller samples
makes few assumptions about distribution
-used more frequently than parametric because they don’t need continuous data and don’t make assumptions about distribution

Question 10

what are examples of non-parametric test

Answer 10

chi-square

—also mann-whitney, fischer’s wilcoxon, etc (don’t need to know specifics)

Question 11

what does a paired t-test compare

Answer 11

compares means of a single group before/after an intervention

ex: pre/post testing to access of value of a workshop

Question 12

what does a t-test compare

Answer 12

compare means between two groups

ex: experimental drug group and placebo group

Question 13

what does an ANOVA compare?

Answer 13

compares means between more than one group

ex: birth weights in non, light, and heavy smokers

Question 14

what does a chi-square test do?

Answer 14

• non-parametric test
• used for testing hypothesis about nominal scale data
• test of proportions

ex: is there a significance difference in seat belt use between high school graduates and college graduates?
ex: is there a significant difference in growth of plants treated with water vs plants treated with grape solution?

Question 15

what is type I error?

Answer 15

false positives

-null is actually true but it was rejected

Question 16

what is type II error

Answer 16

false negatives

-null was actually accepted but alternative is true

Question 17

what is power?

Answer 17

estimate of the ability of a study to detect a false null hypothesis

• • the ability of a test to detect a difference if there is one
• • probability of avoiding a type II error, a false negative

Question 18

what does power depend on?

Answer 18

multiple aspects of a study design, but most importantly the sample size
-the larger the sample size, the greater the power

Question 19

how do you calculate power?

Answer 19

1-beta

beta=probability of making Type II error

Question 20

what is beta?

Answer 20

probability of making type II error

• for medical research, beta=0.2
• –> 20% chance of making a type II error, a false negative

Question 21

if beta=0.2, what is power of the study?

Answer 21

=1-0.2

power = 0.8
there is an 80% chance of avoiding type II error, 80% chance of avoiding false negatives

Question 22

what are the probabilities of type I and type II errors if alpha=0.05 an beta=0.2

Answer 22

type I - probability of making false positive is 5%
type I - probability of making false negative is 20%

power of this study is 0.8; 80% chance of avoiding false negatives

Question 23

what is a confidence interval?

Answer 23

gives measure of the precision of the study

-95% CI is the range of values within which we can be 95% certain that the actual population value lies

• also indicates whether a difference found in a study is statistically significant
• -> if the 95% CI does not include the value of equality, then the difference is significant at less than 0.05

-the narrower the CI, the more precise the estimate

Question 24

interpret:

a study finds the mean systolic blood pressure of 20-40 year old males to be 125 with a 95% CI of 120-130

Answer 24

we can be 95% certain that the actual population mean systolic blood pressure for 20-40 year old males lies between 120-130

Question 25

interpret:

a study demonstrates that penicillin cures strep throat in 90% of children, tetracyclin cures strep throat in 40% of childre. the difference in cure rates of strep throat using two different antibiotic regimens is 50% with a 95% CI (25%-75%)

Answer 25

we can be 95% certain that there is an actual difference between these two treatment regimen

since 0% is not included in the CI, we can be certain the difference between the antibiotic cure rates is significant at 0.05

Question 26

what determines the width of confidence intervals?

Answer 26

variability of the sample, size of the sample

Question 27

what is standard error of the mean?

Answer 27

• standard deviation of the means in the sampling distribution (generated by CLT)
• used in generating the t-test and confidence intervals

–> limited use as a descriptive statistic

Question 28

why is the SEM not a good descriptive statistic?

Answer 28

SD- measure of variability of the underlying population; ie, magnitude of SD depends primarily on the variability of the population

SEM - measure of the variability of the sampling distribution of means; ie, magnitude of SEM depends primarily on the sample size used in the CTL calculations

thus: SEM is always smaller than SD, and therefore is misleading
- usually only indicates a huge sample size, but often used in literature to make results look tighter