Biostats final

What makes a good sample

precise (low sampling error)

accurate (unbiased)

random

What constitutes a random sample

independent (one doesn’t influence the others selection) and has equal chance of being selected

what makes a bad sample

sample of connivence - collection of individuals that happen to be available

population parameters

are consistent

sample estimates ____ with the sample

vary

2 ways to describe uncertainty

95% CI and Standard Deviation

Pseudoreplication

samples that are not independent but are treated like they are

How to change CI intervals with % change from 95 to 99

interval must widen

how increasing sample size effects CI interval at same %

narrower

Graphing 1 numerical

histogram

Graphing 1 categorical

bar graph

Graphing 2 categorical

mosaic or grouped bar graph

Graphing 1 categorical 1 numerical

box plot, violin plot, strip chart

Graphing 2 numerical

scatter plot

common problems with figures

do axes start at zero?

do axes titles have units?

are x-axis group names in a legend?

2 general statistics and examples

descriptive - characterizing aspects of a numerical data set (mean and sd)

inferential - evaluate strength of evidence about a hypothesis (t-value, F-ratio)

Type 1 error and how to decrease

false positive: rejecting Ho when it is actually true

decrease decision threshold

Type 2 error and how to decrease

false negative: fail to reject Ho when it is actually false

increase sample size = increased power

power

probability that a random sample results in the rejection of a false Ho

p value

probability of getting the data set if Ho is true

signal to noise ratios

t-value

F-ratio

r-value

1 sample t-test

comparing one value to another

proportions

when you have a number of successes/ sample number and want to test it to a known value

paired t-test

2 variables that are connected, test if they are different

2-sample t-test

2 variables not connected, see if they are different

paired, 2-sample, and ANOVA assumptions

random

normal distributions

2-sample and anova assumptions

variances of both populations are equal

correlation

describes linear assumptions between 2 numerical variables

correlation coefficient

quantifies linear association through

direction and

magnitiude/strength

why variables might be correlated

chance

a causes b

c may cause/influence a and b

a may lead to an increase in c which increases b

correlation missconception

association/correlation does not imply causation

point of linear regression

predict the value of one variable for another

difference between regression and correlation

regression does not treat the two variables equally

residuals

the difference between the actual value and the predicted value of the response variable

minimize these squared for best fit line

R²

variance in y (response variables) explained by x (explanatory variable)

predicting mean y for x

higher precision

use confidence intervals = bend towards the mean

predicting specific y for x

lower precision

use prediction intervals = run parallel to line of best fit

extrapolation

predicting y for x out of range

you don’t know if the trend continues

assumptions for correlation and regression

relationship between x and y is linear

frequency distributions are normal (no gaps, no outliers)

variance of x does not change with y (no funnel)

(each year is chosen at random for each x - regression)

three things to do when assumptions fail

ignore them

transform the data

non-parametric tests

non-parametric tests

ranks the data

Wilcox assumptions

both samples are random

both have same distribution shape

plots for addressing normal frequency

histgoram

qq plot

plots for addressing equal variance

equal IRQs

why normal distributions are important

the occur naturally in nature

symmetric about mean - bell shaped

fully described by mean and sd, mean = median = mode

95% of data are with in 2 sd of the mean

2 goals of experimental design

eliminate bias (increase accurate)

decrease sampling error (increase precision)

ways to eliminate bias

controls

random assignment of samples to treatments

blinding

random assignment can only happen for

experimental studies not observational

Placebo

special kind of control, the expectation to get better is powerful

independent recovery

people will get better inevitably cus they seek treatment when they don’t feel good so you need a control to compare too to see if the treatment actually works

goal of reducing sampling error

increase signal to noise ration

how to increase signal to noise ratio

increase sample size

decrease sd

4 ways to reduce sampling error

replication

balance

blocking

extreme treatments

balance

each group has equal number of samples

n1=n2 means smallest error so smallest noise

blocking

grouping of experimental unit with in each group

creates mini experiments in each block

accounts for variation between blocks

extreme treatments

stronger treatments can increase signal to noise ratio

threats to reproducible science

not biased - no controls, randomization, for blinding

low statistical power - small sample size

poor quality control (higher sampling error) -no replication, balance, block, or extremes

P-hacking - keep adding data till significance is seen

publication bias - only publishing significant results

harking - hypothesis testing after results are known

planning sample size and problems with that

want a sample size with sufficient power and precision

calculate sample size assuming 2 sample experiment comparing means with normal data sets and equal sd

n = 8 x (sd/margin of error)²

problem = can be hard to estimate the population sd and margin of error without literature or short trial experiment

focus on the beginning of the curve because that’s where you can add the most precision

frequentist stats

defines probability of some event in terms of relative frequency with which it tends to occur deductive

the true population looks like this so my sample should look like this

baysean stats

more subjective, defines probability as a measure of strength of your belief regarding true situation

inductive

my sample came out like this so the true population might be this

bayes theory for particular parameter

posterior = likelihood x prior

posterior

new probability given prior data and new data

likelihood

probability of data given parameter

prior

probability of parameter

2 factors that effect here posterior is on the graph

precision - posterior by skinniest curve

distance between prior and likelihood - further apart = more shifted posterior