Biostatistics - Descriptive Stat

7/23/2019 Biostatistics - Descriptive Stat

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Biostatistics

Descriptive statistics

Dr. N Shiukashvili



What is biostatistics??? Almost everyday several news portals inform as similar information:

A new treatment for HIV disease works better than current therapies

High blood pressure is demonstrated to be associated with heart

disease

A study suggests that a certain pollutant may be harmful to

humans

Such results are the work of multidisciplinary teams of researchers, including•hysicians•public and environmental health specialists•BIOSTATISTICIANS

!iostatisticians play essential roles in•designing the studies•analy"ing the data•creating new methods for addressing these problems#



Descriptive Statistics$lass A

I%s of &' Student

&()

&&*

&)+

&(

&'&

+

+

&(-

&.(

&&

'/

&&(

$lass !

I%s of &' Students

&)/

&-)

&'&

&('

-

&&&+(

&(

'

+/

&)(

&(*

&(

Which Group is Smarter?



Descriptive Statistics

0hich group is smarter now1

$lass A22Average I% $lass !22Average I%

&&(#*. &&(#)'

They’re roughly the sae!

0ith a summary descriptive statistic, it is much easier to answer our 3uestion#

Descriptive statistics merely describe, organi"e, or summari"e data4 they refer only

to the actual data available#

5or e6amples: mean blood pressure of a group of patients

success rate of a surgical procedure#



Descriptive Statistics

opulation Sample

A population is a set of measurements, for e6ample 2 the I% of the whole

university students 7 taken as a whole#

5ew of those measurements evaluated separately from the rest of the

population make up a sample#



!iostatistics is also used in modeling and hypothesi"ing#

8iven a set of data, scientists combine biostatistics and probability theory in order to

determine the likelihood of diseases to hit populations, drugs to cure those diseases,

and people9s reaction to those drugs#

In this way, biostatistics promises to be as good at predicting the future as it is at

analy"ing the past#

A physician say that a patient has a *(*( chance of surviving a certain

operation#

A physician may say that she is * percent certain that a patient has a particular

disease#

What ea"s #robability???

As these e6amples suggest, most people e6press probabilities in terms of

percentages#

robability



#robability

we measure the probability $ p) of the occurrence of some event by a number

between "ero and one as the event either occurs or "ot

( 2 &;he event less likely to occur is closer to the number &4

0hereas the event more likely to occur is closer to the number (#

An event that cannot occur has a probability of "ero, and an event that is certain to

occur has a probability of one



#robabilityA%%itio" rule;wo events are called to be dependent if they <= affect one another

If there are . cards, what is the probability of after random taking to have heart card1

)* >

0hat is the probability to get red card1

)*?)*@ *(>

;he a%%itio" rule of probability states that

If events A and ! are mutually e6clusive, then the probability of any one of several

particular events occurring is e3ual to the sum of their individual probabilities,

mutually exclusive - they cannot both happen



#robability&ultiplicatio" rule

;wo events are called to be independent if they do =; affect one another

A method for finding the probability that both of two events occur together#

A 2 blue eyes

! 2 high I%

If the probability for a newborn

girl to have blue eyes is )*>,

and high I% &>

what is the probability that the

newborn blue eyed girl has highI%1

If we take probability range from 0-1

0.25 B (.01 @ .0025 (0.25!



Bi"oial Distributio"

Cepresentation of descriptive statistics data:

=rgani"e <ata ;ables

8raphs

Summari"e <ata $entral ;endency Variation



Bi"oial Distributio";he binomial distribution is a probability distribution#

It has discrete values# It counts the number of successes in yesDno2typee6periments#

;here are two parameters:•the number of times an e6periment is done EnF•the probability of a success EpF#

G6ample:

;ossing a coin &( times, and counting the number of face2ups# En@&(, p@&D)F



Bi"oial Distributio"

if coins will be tossed twice the four possible outcomes are:



5re3uency <istributions

ou are a researcher and conducting study about arterial tension in normal population#

ou have a data of *(( person#

0hats the ne6t step1

=rgani"ing the data from the highest to the lowest in order, recording the

fre3uency E ƒ' (ith (hich each score occurs.

0hat will be the fre3uency of -(D.( mm Hg1

)OW

0hat will be the fre3uency of )-(D)(( mm Hg1

)OW

0hat will be the fre3uency of &&(D/( mm Hg1

*I+*

Arterial tension

o p u l a t i o

n

(

) ( (

* ( (



,re-ue"cy Distributio"

8rouped fre3uency



,re-ue"cy Distributio"

/)ATI0/ ,/12/NC3 DISTIB2TIONS

It transforms data, which shows the percentage of all the elements that fall withineach class interval#

If &+ person from *( had same data, relative fre3uency will be '- E&+D*( B &((F



Noral Distributio"

If we take the same e6ample: arterial tension in normal population

gathered from *(( person#

8raphically it will be represented like this

Arterial te"sio"

# o p u l a t i o "

4

5 4 4

6 4 4

called:•syetrical7•bell8shape%

•+aussia" %istributio"



No"8Noral Distributio"<istribution is not always symmetrical# ;here are Asymmetric fre3uency distributions

called ske(e% distributions#

by the location of the tail of the curve distribution can be:•#ositively Eor rightF ske(e% distributions•"egatively Eor le9tF ske(e% distributions E!ecause the long JtailJ is on the negative side of the

peakF

#ositive ske( 2 have a relatively

large number of low scores and a

small number of very high scores4

Negative ske( 2 have a relatively

large number of high scores and a

small number of low scores#



No"8Noral Distributio";here is also another non2normal distribution called Bio%al %istributio"

G6: 8ood pasteur9s syndrome: A very rare diseases with bimodal age distribution)(2'( years and -(2/( years#



&easures o9 Ce"tral Te"%e"cy0hat is Jcentral tendency,J and why do we want to know it1

Imagine this situation:ou have a *2point 3ui" in !ehavioral science#

e6t day your score is written to be J'D*J E-(>F

How do you react1

Are you happy with your score of ' or disappointed1

How do you decide1

0hat additional information you will need for final feeling1

What other stu%e"ts got???Are you like ost stu%e"ts???

Kight be your -(> is the highest in groupL# =r lowestL



&easures o9 Ce"tral Te"%e"cy$omparing individual scores to a distribution of scores is fundamental to statistics#

0hich of the three datasets would make you happiest1

<ataset ! is a depressing outcome even though your score is no different than

the one in <ataset A#

;he problem is that the other four students had higher grades, so if we will

make graph your mark will be below the ce"ter o9 the %istributio"#



&easures o9 Ce"tral Te"%e"cyKeasures of central tendency are:•Kean

•Kedian•Kode

&/AN;he JmeanJ same as MKathematical averageJ is the number where you add up all

the numbers and then divide by the number of numbers#

;his is the age at which some disease affects teenagers:

:;7 :<7 :;7 :=7 :;7 :>7 :=7 5:7 :;

;he mean age for this disease onset will be:

E&' ? &+ ? &' ? &. ? &' ? &- ? &. ? )& ? &'F N @ :6



&easures o9 Ce"tral Te"%e"cy&/AN<uring normal distribution will be directly in the middle

egative skewed distribution most negative directionositive skewed distribution most positive direction



&easures o9 Ce"tral Te"%e"cy&/DIAN;he JmedianJ is the JmiddleJ value in the list of numbers#

;o find the median, your numbers have to be listed in numerical order

;his is the age at which some disease affects teenagers:

:;7 :<7 :;7 :=7 :;7 :>7 :=7 5:7 :;

Cewrite in a numerical order

:;7 :;7 :;7 :;7 :=7 :=7 :>7 :<7 5:

So the median is &.#

&OD/;he mode is the number that is repeated more often than any other# If no

number is repeated, then there is no mode for the list#

:;7 :;7 :;7 :;7 :=7 :=7 :>7 :<7 5:

so in above numbers &' is the mode#



&easures o9 0ariable;here are two normal distributions EA and !F with the identical means, modes, and

medians

<espite these similarities, these two distributions are obviously different4

Keans that only central tendency alone is not enoughOOO

;he scores forming distribution A are clearly more scattered than are those

forming distribution !#

;hey differ in terms of their variability



&easures o9 0ariable

If these ) graphs depict the drug effect, which drug will be more efficient111

atient number

! l o o d g l u c o s e

l e v e l

drug ! is the better, as fewer patients

on this distribution have very high or

very low glucose levels

;here are three important measures of variability:•a"ge•0aria"ce•Sta"%ar% %eviatio"#




AN+/

Is the difference between the highest and the lowest scores in the distribution#

:;7 :;7 :;7 :;7 :=7 :=7 :>7 :<7 5:

;he largest value in the list is )&, and the smallest is &'

so the range is )& &' @ <#




0AIANC/

;he variance measures how far each number in the set is from the mean#

ou and your friends have Pust measured the heights of your dogs Ein

millimetersF:

;he heights Eat the shouldersF are: -((mm, ./(mm, &/(mm, .'(mm and'((mm#

Kean EaverageF height is ;=




Now we calculate each dog's difference from the Mean:




So, the Variance is 21,704.

To calculate the Variance, take each difference, square it, andthen average the result:

Variance e3ual to "ero indicates that all values within a set of numbers are

identical4

A large variance indicates that numbers in the set are far from the mean and each

other, while a small variance indicates the opposite#

Has a limited use




Sta"%ar% Deviatio"

It is Pust the s3uare root of Variance, so:

Standard <eviation: @ 5:74= :=.;5... @ :=

So, using the Standard <eviation we have a JstandardJ way of knowing what is

normal, and what is e6tra large or e6tra small#

Cottweilers are tall %ogs# And <achshunds are a bit short ###

but %o"t tell the!



&easures o9 0ariableSamples can be very uniform with the data all collected around the mean or they

can be spread out a long way from the mean#

Standard deviation measures it#

><868 rule






What is biostatistics??? According to statistics every -th on the earth is $hinese

How many are you here111

0ho of you is $hinese111

Do NOT take statistics TOO seriously



Thanks For Attention

Dr. Nino Shiukashvili

Documents

Biostatistics - Descriptive Stat