Statistical Methods Lecture Summary

, LECTURE I 27110



Statistics : science of data ,
study of collecting ,
organising analysing
, ,




interpreting and
presenting data

( population)
gain
and/or objects
Used to information about
group a
of
predictions
to make decisions and




has to be
choose subset
e
good sample sample population
of pop .




collect

data 7
^
✓ Collect data
analysis
✓
sample and draw
data conclusions


census



statistical study
:




I .

prepare
context
.




-


source :
now was the data collected ?


sampling method : how were the participants chosen
-




2 .

Analyse
Graph data
-




Explore data
'




Apply statistical methods further investigate data
-
-




3 .
conclude




statistical and critical
thinking
.




common flaws

I Bad method
.


sampling
different sample →
different data . :
different conclusions

sample should be representative and unbiased

representative :
same characteristics as population
unbiased : no systematic difference with population


2 O data
starting misleading presentation
→
.
Not y-axis from of



3 correlation causation
. does not
imply

, collecting sample Data

Different sampling methods

voluntary response sample :
subjects decide themselves to be included
-




in sample ( biased)

Random sample : each member of population has equal probability
-




of

being selected can biased)

simple random sample each sample of size has equal
-


: n


( unbiased
probability of being chosen .

very representative and ,
but hard

to do with a large population)
systematic sampling after starting point select
every th member
-

:
, K -




'



stratified sampling : divide population into
subgroups such that


subjects within groups have same characteristics ,
then draw a


sump ie random sample from each
group
cluster divide population into clusters randomly select
'




sampling :
,
then

some of these clusters ( can lead to biased data)

convenience
sampling easily available results C biased ) C pilots)
-



: ok for




important concepts
variable :
varying quantity
in cause and effect studies :

(dependent) variable
Response representing effect to
study
-


:
the

( independent) variable effect
Explanatory
:
possibly causing that
'




variables
confounding mixing influence of several explanatory
-


: on


response



Different types of study
Observational
study : characteristics of subjects are observed ; subjects
are not modified
Retrospective ( case control) data from the past
-
-
:




sectional data point in time
-



cross -
:
from one


prospective (
longitudinal) data are to be collected
-

:




Experiment : some subject treatment
sometimes control and treatment single blind ( participant doesn't
-




group : -




know) or double -
blind ( participant + researcher don't know)

To measure placebo effect or experimenter effect
'




data
Types of :




parameter : numerical measurement
describing a population 's

characteristic . Notation :
typically ooeek symbols e -



g .

µ ,
o .




Statistic : numerical measurement
describing a sample 's characteristic .




Notation small letters s
e.g x
: .
.
,

, Qualitative (
categorical) names easels represent counts or
:
or


measurements

Quantitative Cneumericae) : numbers represent counts or measurements
-

Discrete the set of possible values is countable Ce number of
g
: -
.




siblings)
continuous the set possible is Ce weight)
-




of values uncountable
g
: -
.




Level of measurement of data determines which statistical methods are


applicable
Qualitative data
-


:




Nominal names
categories ( no
ordering)
-


:
,
labels ,




ordinal
categories with
ordering differences (e.g grades)
-

:
. no -




-



Quantitative data :


'


Interval :
ordering possible and meaningful differences (
e.g . YOB)

Ratio &
ordering possible and
meaningful differences natural
starting
-
:




point ( e.g .
marathon times)




summarising and Graphing Data

choose most question
summary suitable for research

Often interested in data distribution
A
good summary shows :



characteristics data distribution
-




of

location . spread .
range , extremes , accumulations ,
gaps ,
symmetry .
.
.




Depending on context and
goal :



-

are data sampled from a certain distribution ?


Aoe different needed for further analysis ?
'




groups
are there influences other variables ?
of
-




is there dependence between variables ?
-




Summarise →
describe find structure in data distribution :




Graphical :
tables graphs other
figures
-



. .




Descriptive
-




Qualitative describe location and dispersion Ivar lotion
-




shape
-


: .




-



Quantitative : numerical summaries of location lvariation


Graphical summaries :


'




Frequency distribution :
count occeerances

-

cumulative frequencies and relative cumulative) frequencies
-



Bar chart cumulative bar chart and Pareto bar chart
,



circle
diagram
-




Histogram ( can only be used for quantitative data)
-




series plot visualize
Time time varying quantity
-
: -