Inferential Biostatistics Flashcards
what are the steps for hypothesis testing?
- state the null and alternative hypotheses
- select the alpha value (usually 0.05)
- gather data and perform appropriate statistical tests generating a p value
- accept or reject the null
what is the null and alternative hypotheses for investigating whether a new drug improves symptoms of tension headache?
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
what is the alpha level?
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
what is the p value?
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
describe a parametric test
- focused on population parameters
- requires a continuous variable (ex cholesterol levels)
- assumes a normal distribution
- generally more powerful than nonparametric
what are examples of parametric tests
anova, t-test, paired t-test, confidence intervals
what is the central limit theorem
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
why are sampling distributions (central limit theorem) useful?
-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
describe a non-parametric test
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
what are examples of non-parametric test
chi-square
—also mann-whitney, fischer’s wilcoxon, etc (don’t need to know specifics)
what does a paired t-test compare
compares means of a single group before/after an intervention
ex: pre/post testing to access of value of a workshop
what does a t-test compare
compare means between two groups
ex: experimental drug group and placebo group
what does an ANOVA compare?
compares means between more than one group
ex: birth weights in non, light, and heavy smokers
what does a chi-square test do?
- 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?
what is type I error?
false positives
-null is actually true but it was rejected
what is type II error
false negatives
-null was actually accepted but alternative is true
what is power?
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
what does power depend on?
multiple aspects of a study design, but most importantly the sample size
-the larger the sample size, the greater the power
how do you calculate power?
1-beta
beta=probability of making Type II error
what is beta?
probability of making type II error
- for medical research, beta=0.2
- –> 20% chance of making a type II error, a false negative
if beta=0.2, what is power of the study?
=1-0.2
power = 0.8
there is an 80% chance of avoiding type II error, 80% chance of avoiding false negatives
what are the probabilities of type I and type II errors if alpha=0.05 an beta=0.2
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
what is a confidence interval?
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
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
we can be 95% certain that the actual population mean systolic blood pressure for 20-40 year old males lies between 120-130
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%)
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
what determines the width of confidence intervals?
variability of the sample, size of the sample
what is standard error of the mean?
- 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
why is the SEM not a good descriptive statistic?
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
