biostats

categorical data

• ordinal

• not ordinal

what is not ordinal data

data you canNOT sort

• blood type

• geo location

• sex

• colors

what is ordinal data

data you CAN sort

• numbers

• dates

• size

• time

what is quantitative data

• discrete

• continuous

what is discrete data

can list all possible values (finite)

• # of eggs

• colonies in agar

• people in a room

what is continuous data

you cannot count/list all possible values (this largely depends on how accurate data is)

• age

• repeating numbers (pi)

• truly accurate weights/heights

in a histogram do the bars touch

yes

represents continuity

in a bar plot do the bars touch

no

what kind of data does a histogram represent

continuous data only

what are the types of distributions

• symmetrical

• long tail

• skewed right

• skewed left

• exponential

• bimodal (2 modes)

• uniform

• u shaped

what is “Y”

random variable

what is “y”

value of random variable

what is “n”

sample size

what is “yi”

value of y in the ith place in sample

what is a minimun

lowest number in sample

max

largest number in sample

mode

most common # in sample

median

middle # in sample after data had been ordered from lowest to highest

mean

average

range

max - min

avg absolute deivation

how far away is data from average

variance

how spread out data is from each other

standard deviation

how spread out data is compared to mean

when do you use median over mean

when a sample had MAJOR outliers

• income in Seattle WA: mean=1.2 mill median=500 thousand

• bill gates income skews data so mean is no longer accurate

what are the steps to making a box plot

1. find median

2. find Q1 and Q1

   • split data into 2 parts at median.. find median of those 2 parts

3. get IQR=(Q3-Q1)

4. find 1.5x IQR

5. Find upper fence (if data above this=outlier)

   • Q3 + 1.5xIQR

6. find lower fence (if data below this=outlier)

   • Q1 - 1.5xIQR

μ

pop mean

σ

pop standard deviation

p

population

ȳ

sample mean

• estimates μ

s

sample standard devation

• estimates σ

p̂

sample population

• estimates p

random sampling

everyone has equal chance of being picked

systematic sampling

measure values in set increments

• every 20th person

stratified sampling

sample proportional to data

opperuntisitic sampling

sample everything as you come across it

• can be biased

what is basic probability

number of time event can occur / number of possible outcomes

number of time you WANT event to occur / number of time event CAN occur

what is the range a prob can be

0-1

what does P{E} mean

probability of event E

what can do you if 2 probabilities are independent

• Pr (H and roll 6)

multiply them

does conditionally prob change outcomes. if so, how?

yes

states a condition that must happen

what can you use the binomial coefficient for

finding how many different ways tings can be arranged

what can the binomial distribution formula be used for

finding prob of an event

what are the binomial distributions parameters

sample size

probability

what makes a distribution

all possible outcomes add to one

parameters determine shape

what are the parameters of the normal distrubtion

standard deviation (pop)

pop mean

what is the central limit theorem (CLT)

calc prob using normal distribution no matter original distribution

why do we use the normal distrbution

many things in bio are approx normal

what do we need to make the standard normal curve

z

what examples of continuous data distributions

T distrib

chi square

normal

what are discrete data distrib

binomial

poisson

unifrom

what do you need in order to calc the poisson distrib

pop mean

how is ȳ typically distrubted

normal distrib

what do you do if you don’t know the pop standard deviation

use sample standard deviation

what is SEȳ

standard error for ȳ

noise

Variation in the data we are interested in

Statistics

a value calculated or derived from the data

does a bar plot represent continuous data?

no— its discrete data

show by not touching bars

how would you find Pr(z>-2.0)

a) 1- Pr(z>-2.0)

b) Pr(z< 2.0).. look up 2 rather than -2

Know when statistics might be appropriate (or inappropriate). Be able to give an example of each.

appropriate: analyze medical data

inappropriate: to lie using false/unspecific stats

• 90% effective with no parameters

Be able to give an example of an application of statistics

weather forecasting

testing drug effectiveness

election polling

What is a record ( = observational unit = case)?

individual entity or subject that data is collected on

Why do we use n - 1 in the denominator for the variance (and standard deviation)? Why not just n?

provides a more accurate estimate of the population variance by correcting for the bias introduced when using the sample mean to estimate the population mean

• samples tend to be closer to the center than pop data

• add extra room to var to account for this error

What is the difference between a sample and a population?

sample = section of pop

pop= whole

When is sampling better than trying to measure everything?

more efficient/cost effective and just as accurate

Why is it so important to define a population precisely?

students at gmu is very different than student at gmu taking biostats

• defined pop helps narrow targeted group

• minimize risk bias

Why do we sometimes have to be careful with studies done in zoos or labs?

limited sampled size can lead to errors

Know the difference between estimates and parameters

parameter: specific characteristic of an entire population

estimate: calc based on sample to approx true pop parameter

What does the ^ (hat) symbol mean?

estimated value

How would you do random sampling?

1. define your population

2. determine your desired sample size

3. assign a unique number to each member of the population

4. use a random number generator or lottery to select the individuals that will be included in your sample

Are the random numbers generated by a computer truly random? Why, or why not?)

no. random number are given based on algorithm

What is the effect of sample size?

larger than sample = more precise and higher confidence

Why is probability important to statistics?

can determine the the probability of getting this result by chance.

If this probability is low, we say the experiment had an effect on the outcome

what is a distribution

function that shows how values are spread out across a range of possible values

How does the shape of a binomial distribution depend on n and p?

• p = 0.5: Symmetrical distribution regardless of n. 

• p < 0.5: Skewed right. 

• p > 0.5: Skewed left. 

• Large n: Even when p is not exactly 0.5, the distribution tends to appear more symmetrical due to the "central limit theorem" effect. 

• Small n: The skewness caused by p value is more pronounced

How does the shape of a normal distribution depend on μ and σ

μ:

• increases= entire curve shifts to the right

• decreases= curve shifts to the left

σ

• larger= creates a wider, flatter curve

• smaller= narrower, steeper curve

How does area relate to probability (for a continuous distribution)?

area under a curve = prob{e}

How do you use the normal distribution? What table do you use

z score table

What is reverse lookup?

looking up the z area and finding the z score from that

What is the mean (μ) of a binomial distribution? What is the standard deviation (σ)?

μ= np

σ= sqrt[np(1-p)]

What is the mean (μ) of a normal distribution? What is the standard deviation (σ

mean=0

standard deviation= 1