biostat midterm 2

descriptive statistics

- arrange data (e.g. table, graph)
- characterize data (e.g. average, error)
characterizes the sample
summarizes, presents data

Inductive statistics

- generalization: → estimation
→ hypothesis testing
characterizes the statistical population (based on the sample)
interpret, analyze data

observation unit

he elements of a sample are known as sampling point, observation unit

sample

set of data collected

population

set of similar items or events which is of interest for some question or experiment, can be a group of existing objects

correct sampling method

define the population of interest
- decide sample size
- how many observation units are necessary to charaterize the population?
- representative sample size? (= representative of the scientific question!)
Sampling has to be unbiased (observation units can not be preferred)
Sampling is unbiased (objective) and representative if it contains random elements

sampling

Choosing part of the statistical population in order to characterize the population or
to predict characteristics of the population

sampling with replacement

one member of the popultion may be chosen more than once

sampling with no replacement

no member of the population can be choosen twice

sampling population

from finite population
from infinite population
sampling a finite population with replacement is the same as sampling from an infinite population

simple random sampling

- all members of the population have equal chance to be chosen
- sampling units are chosen independently
e.g. using random numbers

stratified sampling

- if there are sub-populations
- choosing from the sub-population should be random
(ex. sampling a group of students proportional to gender)

systematic sampling

select some starting point and then select every kth element in the population
(ex. choosing every 4th person at the supermarket)

qualitative variables

identifies (ex. id number), not all variables are numbers

quantitative variables

characterizes quantity (numbers), different ways to characterize them.

Nominal

example: country name, passport number
- text, identifying number
- has no numerical value, can not be added
- can not be ranked

Binomial

(special case of nominal)
- example: female/male, yes/no
- text or identifying number
- two possible values only
(participate in the Olympics (yes-no))

Ordinal

- example: grading, cloth sizing
- text or ranking number
- has value, can be ranked
(grades: E < D < C < B < A, T-shirt size: S < M <L <XL)

qualitative variables examples

Prevalence (frequency) can be given (e.g. 8 students are from Hungary, 5 from France)
Ordinal variable have cumulative frequency
(e.g. how many people wear L size? - frequency
how many people wear smaller than L size? - cumulative frequency)

Quantitative variables - interval scale

example: temperature in degree Celsius
- number in reference to an arbitrary zero
- possible to add, substract
- ratios can not be calculated (can not divide or multiply)

Quantitative variables - ratio scale / absolute scale

- example: mass in kilogram, number of people
- number in reference to an absolute zero
- possible to add, substract
- ratios can be calculated (possible to divide or multiply)

types of variables

qualitative (factors) : nominal, ordinal
quantitative (numeric or) random variables: discrete, continious, absolute, interval

presenting qualitative variables - one variable

factor (ordinal)
- frequency table
- bar graph

presenting qualitative variables - one variable

factor (nominal)
- frequency table
- bar graph

presenting quantitative variables

Bar graph
- simple (one variable)
- multiple (many variables)
- stacked (many variables)
Pie chart
Dots and/or lines
- two (or more) variables!

median

middle value

mean

the central value of a discrete set of numbers

modus

most repeated value, not all samples have medians

unimodial

a frequency distribution that has only one peak. Unimodality means that a single value in the distribution occurs more frequently than any other value.

range

x(max)-x(min)

interquartile region

q1-q3

lower and upper quartile

median of the upper / lower half of the data

Variance

sum of squared deviations from mean,
divided by the degrees of freedom

standard deviation

square root of variance

Normalization

make the maximum equal to a set value (usually =1)

Standardization

make the date set's mean =0 and SD =1

Estimation statistics

a data analysis framework that uses a combination of effect sizes,
confidence intervals, precision planning, and meta analysis to plan experiments, analyze
data and interpret results

point estimate

population statistics are approximated (estimated using sample statistics)
Example
population standard deviation (SD) ¬ sample standard deviation (SD)
population mean ¬ sample mean

standard error formula

SE = SD/√n sd= standard deviation

i

Gives the interval which contains the estimated parameter with given probability

Density function

describes the relative likelihood for a variable to take on a given value

Distribution function

describes the relative likelihood for a variable to be smaller than a given value