Biostatistics

population

entire set of measurement for a given parameter (N)

sample

subset of population, measurements actually made (n)

frequency distribution

an arrangement of data that indicates how often a particular score or observation occurred

measures of central tendency

mean, median, mode

population mean vs sample mean

pop - 𝜇

sample - 𝑋

mean equation

𝜇 = ∑𝑋/𝑁 - population

sample = X = ∑𝑋/n

∑𝑋 = raw scores (sum of all the data points)

N = population size

n = sample size

mean

- balance point

- average

- sum of all the data points divided by the number of points

- measure of central tendency

- sensitive to all raw data points

average distance from the mean

mean is the value that the sum of the differences between the mean and all other values is 0

- so avg difference is 0

mean of frequency distribution

measure of central tendency of the distribution but does not describe the entire distribution

mean is used when calculating what other measures?

standard deviation, coefficient of correlation, standard errors

asymmetrical distribution

a distribution of scores in which there is not an exact correspondence in arrangement on the opposite sides of the middle line

median

the middle score in a distribution; half the scores are above it and half are below it

- divides the distribution in half

- not sensitive to every data point

what is a better measure for an asymmetrical distribution?

median

mode

the most frequently occurring score(s) in a distribution

- greatest frequency

- easiest to compute

standard deviation

measure of the variability of the distribution

- square root of deviation

- measure of the average deviation from the mean

population - 𝜎 (sigma)

sample - S

average deviation

An alternative measure of variation that, like the standard deviation, indicates the average difference between the scores in a distribution and the mean of the distribution.

variance

standard deviation squared

standard deviation in excel

uses n-1, due to the central limit theorem

interquartile rage

middle 50% of the data (the box)

Q3-Q1

distributions are split into

4 equal areas or quartiles

- 25%

q1

25th percentile

q2

up to 50%, median, divides into half

q3

75th percentile

q4

maximum value, 100th percentile

range

maximum raw value - minimum raw value

percentiles

indicate the distance of a score from 0

- 100 equal parts (1% each)

box and whisker plot

A graph that displays the highest and lowest quarters of data as whiskers, the middle two quarters of the data as a box, and the median

max and min values on box and whisker plot

do NOT include outliers

outlier

value greater than Q3 + 1.5x IQR

or

value less than Q1 - 1.5x IQR

mean measure of variability

standard deviation

median measure of variability

interquartile range

mode measure of variability

range

probability experiment

a chance process that leads to well-defined results called outcomes

outcome

the result of a single trial in a probability experiment

sample space

the set of all possible outcomes of a probability experiment

probability equation

P(E)= (Number of outcomes E) / (Total number of outcomes in sample space S)

E = event

probability of any event E is a number between?

0 and 1

the sum of all probabilities of all the outcomes in a sample space is

1

If an event cannot occur (i.e. is not a member of the sample space), its probability is?

0 → P(E) = 0

If an event is certain, its probability is?

1 → P(E) = 1

Two events are mutually exclusive events if they?

cannot occur at the same time.

probability of mutually exclusive events

P(A or B) = P(A) + P(B)

Two events are not mutually exclusive events if they can?

occur at the same time.

probability of non-mutually exclusive events

P(A or B) = P(A) + P(B) - P(A and B)

Two events A and B are independent events if the fact that?

A occurs does not affect the probability of B occurring

probability of independent events

P(A and B) = P(A) x P(B)

relative risk

probability of disease in exposed group/ probability of disease in unexposed group (controls)

odds in favor of an event with a probability p is

p/1-p

if p is 1/2, the odds are?

1:1 odds in favor

if p = 2/3 then the odds are

2:1 odds in favor

odds ratio (OR)

odds of disease in exposed group/odds of disease in unexposed group

Odds ratio is often a better?

statistical parameter

odds ratio: 2 x 2 table

a is number of exposed who developed disease

b is number of exposure who did not develop disease

c is number of control who developed disease

d is number control who did not develop disease

odds of disease in exposed group

((a/a) + b) / (1-(a/(a+b))) = a/b

odds of disease in unexposed group

((c/c) + d) / (1-(c)/(c+d)) = c/d

odds ratio in a case control study is a?

cross product

= ad/bc the cross product

variable

Any characteristic that can be measured

discrete variable

can assume only a finite or countable number of outcomes

continuous variable

can take on any value within a specified interval

sum of all probabilities must equal?

1

binomial distribution

- There must be a fixed number of trials

- Each trial can have only two outcomes

- The outcomes of each trial must be independent of each other

- The probability of success must remain the same for each trial

a binomial distribution can be used to describe?

Can be used to describe:

1. Number of siblings who inherit a certain genetic trait

2. Number of patients who experience adverse reaction to drug

3. Quanta release (or not release) from synaptic cleft

binomial distribution formula

P(X)= n!/((n− X)!X!)p^xq^(n-x)

P(x) is the probability of X successes in n trials

X is the number of successes for n trials

n is the number of trials

p is the probability of success

q is the probability of failure

Excel binomial formula

+binom.dist(x,n,p,true/false)

true - looking for success probability

false - looking for exactly x success

Poisson Distribution is useful when?

n is large and p is small

Poisson Distribution conditions

1. The random variable X is the number of occurrences of an event over some interval. The interval can be for example: time, length, area, volume, etc...

2. The occurrences occur randomly

3. The occurrences are independent of one another

4. The average number of occurrences over an interval is known.

Poisson Distribution can be used to model

• number of particles emitted from radioactive material

• number of bacterial colonies growing on a Petri dish

• number of motor vehicle accidents per year

• number of plants growing per acre

• number of nucleotide based substitutions in a gene over a period of time• number of offspring

• number of Koala per square mile in Australia

poisson distribution formula

P(X )= (e^-λ)(λ^x)/x!

P - probability of X occurrences in interval for a variable

λ - the mean number of occurrences per unit

normal/gaussian distribution is a function described by what two variables?

u: mean

o: standard deviation

normal/gaussian distribution with a different mean and the same SD

same width

normal/gaussian distribution with a different SD and the same mean

different widths

z score

a measure of how many standard deviations you are away from the norm (average or mean)

- quantitative comparison of different normal distributions

= (value - mean)/standard deviation

In statistics it is often useful to be able to calculate the ____ under a normal distribution

area