biostats module 2

sample distribution

a probability distribution for all values possible for an estimate

central limit theorem

1. sampling distribution will be less spread than the values in the population from which the sample is drawn

2. sampling distribution will be well modeled by a Gaussian (normal) distribution

3. spread of sampling distribution is related to spread of population values

4. bigger samples lead to smaller spread (more precision) in sampling distribution

standard error (SE)

standard deviation of the sampling distribution

measures accuracy or margin of error (how well you know the true population parameter)

standard error (SE)

= S / (n-1)^1/2

confidence interval

range of values calculated from a sample that is likely to contain the true value of the population parameter

an interval around the mean

CI = mean ± Z * SE

general equation for confidence interval if distribution is normal

1.00

z value for 68% confidence interval

1.96

z value for 95% confidence interval

2.58

z value for 99% confidence interval

narrow confidence intervals

more informative, but riskier

broad confidence intervals

indicates more confidence on the estimate

error bars

illustrate standard errors or confidence intervals

figure legends must be detailed and include the type of information these are displaying

uncertainty

error bars indicate ___ about the population parameter, NOT variability in the data

probability

the ___ of an event is the proportion of times the even would occur if we repeated a random trial repeatedly multiple times under the same conditions

probability theory

the foundation for statistical reasoning

used to connect sample estimates to population parameter

inferential statistics

make predictions and generalizations about the data

estimate parameters of the population based on sample

test if results are unusual or not

inductive reasoning

uses specific observations to arrive at a general conclusion

deductive reasoning

uses general observations to predict specific results

abductive reasoning

from incomplete observations to best prediction

testable

if you cannot logically test if something is true, the hypothesis is not ____

null hypothesis

default statement and generally assumes no statistical difference

alternative hypothesis

generally, the statement the researcher “hopes” is true — assumes samples are significantly different

two-sided

type of statistical hypothesis

does not matter is value is bigger or smaller than the average, as long as it is different from the mean, the alternative hypothesis is accepted

one-sided

type of statistical hypothesis

if a value is bigger than the average or if a value is smaller than the average but not at the same time, one or the other — if one or the other the null hypothesis can be rejected

test statistic

number you get when you use data to calculate

number calculated from the data that is used to evaluate how compatible the data are with the result expected under the null hypothesis

statistical significance

decision threshold to accept that a relationship between two variables is not caused by random chance

means we have evidence that the effect that we see in the sample also exists int he population

a probability of rejection of the null hypothesis

p-value

probability of obtaining data if the null hypothesis is true, NOT the probability that the null hypothesis is true

high p-value

if probability is high

H0 is likely true and the difference is due to chance

low p-value

probability is low

H0 is likely false and there is a statistically significant difference

higher

the lower the p-value, the __ the probability of difference between samples

significance level

alpha

the probability of rejecting the null hypothesis given the null hypothesis is true

defined by how much risk we’re willing to take

less than or equal to

if P is ___ alpha then there is sufficient evidence to reject H0 and accept HA

greater than

if P is ___ alpha there is insufficient evidence to reject H0

type i error

false positive

H0 is true in reality but rejected in study

type ii error

false negative

H0 is false in reality but not rejected in study

false positive

we reach the conclusion that something is true/exists when in fact it is/does not

false negative

we reach the conclusion that something is not true/doesn’t exist or work when it is/does

type i error

the alpha

probability is the significance level

type ii error

failing to reject a false null hypothesis

a study that has low probability of this type of error is said to have high power

power

probability a random sample will lead to rejection of a false null hypothesis

increased by increasing alpha or sample size

experimental unit

a subject or group of subjects that have been assigned an experimental treatment independently of other subjects or groups

control group

way to reduce bias

treatments should include at least two groups: one with treatment of interest and __

serves as baseline to compare the effect of the treatment against procedural effects

control group

unit that does not receive the treatment of interest; all other conditions are the same between this group and the treatment groups though

randomization

way to reduce bias

subjects should be randomly assigned to treatments to reduce bias introduced by confounding variables r

random assignment

randomly sorting sample participants into control and experimental groups

ensures no systematic differences between members in each group

allows you to conclude that outcomes can attributed to explanatory variable

blinding

way to reduce bias

concealing info from participants about which experimental unit received which treatment

single-blind experiments

only subjects are unaware of treatment

removes biases introduced by subjects (unconsciously) acting or feeling different depending on knowing their treatment

double-blind experiment

neither subjects nor researchers are aware of which subject has been assigned to each treatment

removes biases introduced by experimenters (unconsciously) acting or feeling difference depending on knowing the subjects’ treatment

sample size

increasing this does not reduce bias in a study

replication

way to reduce influence of sampling error

each treatment should include multiple independent experimental units (replicates)

pseudoreplication

when measurements are NOT independent from each other, but are analyzed as if they are

temporal pseudoreplication

take several measurements on same individual over time and treat data points as independent

spatial pseudoreplication

take several measurements around same location and treat data points as independent

taking several measurements will include precision — replica value should be average of all data points in an experimental unit

balanced design

way to reduce influence of sampling error

all treatments should have same sample size to reduce error and increase power

blocking

way to reduce influence of sampling error

reduce effect of unrelated variation (confounding variables) by dividing the experimental units into groups with similar characteristic and running separate experiments

matched pair design

way to reduce influence of sampling error

mainly used for observational studies

subjects are matched based on key variables, and then one is assigned to a treatment group and the other to a control group

meant to reduce the effect of unrelated variation but only about two treatments

extreme treatments

way to reduce influence of sampling error

including these in the design helps detect treatment effect

factorial design

evaluate possible interactions between variable — an interaction between two explanatory variables means the effect of one variable on the response variable depends on the state of a second variable

observational studies

these can still follow some principles of experimental design but the challenge is reducing biases from confounding variables when you cannot control for the elements

error

this will never be completely purged

precision

used when estimating sample size

having a narrow confidence interval

requires decision about how much uncertainty we can tolerate and the likely variability in the data

assumptions: measurements in both groups are normally distributed and have the same standard deviation

power

used when estimating sample size

probability of rejecting the null hypothesis is H0 is false

assumptions: populations are normally distributed with equal standard deviation and sample size is equal in both groups

effect size

part of power

measures the intensity of the relationship between two sets of variables or groups

0.8

conventional power value for estimating sample size for high power

experimental bias

larger sample sizes decrease the magnitude of SE, improve precision of parameter estimation, reduce risks of type ii error, but do NOT minimize effects of __ __

data dredging

carrying out of many statistical tests in same set of data in hope of finding at least one statistically significant result

increases chance of type i error

bonferroni correction

one solution to data dredging

corrects for multiple comparisons

alpha* = alpha / number of tests

parametric tests

if scale is metric (=numerical) and normally distributed

uses the mean value for central tendency

generally, the more powerful than non-parametric tests

non-parametric tests

if scale is not metric(=categorical), if true distribution is unknown, or if sample is too small to assume normal distribution

uses the median value for central tendency