Biostat lec01 basicconcepts

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Biostatistics School of Biotechnology International University

Slide 1

Basic Concepts ofStatistics

Dang Quoc Tuan, Ph.D

School of Biotechnology

International University

Lecture 1


Slide 2

Statistics

What is Statistics?

Why Statistics?

- Statistic vs. Statistics?

How to learn Statistics?

- Common sense vs. mathematical expertise

- Almost all fields of study benefit from theapplication of statistical methods


Slide 3Goals of the lecture:To introduce fundamental concepts and definitions in Statistics:

- Statistic vs. Statistics

- Descriptive and inferential statistics

- Population vs. sample

- Parameter vs. statistic

- Variable, random variable, random number

- Data, types of data

- Observation, event, measurement

- Experiment, treatment, replication

- Sampling, types of sampling, sampling errorBiostatistics School of Biotechnology International University

Slide 4

Biostatistics

Statistics is the collection, processing, interpretation

and presentation of numerical information.

Biostatistics is the application of statistics to questions

about living systems.

Biostatistics is an umbrella term that encompasses statistical

research in several subject matter areas. These areas include

pharmacology, medicine, biology, genetics, biotechnology, food

technology and public health.


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Slide 5Biostatistics

Statistics is critical in analyzing patterns of genomic variationwithin populations, and in relating this variation to diseasestates or other phenotypes

- Genomes differ from the reference copy(single nucleotide polymorphisms, structural variants)

- Gene mapping by linkage and association methods

Statistics supports analyses to determine the functionof genes/transcripts/proteins


Slide 6

Introduction to Statistics

1. Population and Data

2. Types of Data

3. Critical Thinking

4. Design of Experiments


Slide 7Overview

A common goal of surveys and other data

collecting tools is to collect data from a smaller

part of a larger group so we can learn

something about the larger group.

In this section we will look at some of ways to

describe data.


Slide 8Overview

Statistics

Two Meanings Specific numbers

Method of analysis

Field of study

Method of analysis(a way of thinking)


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Slide 9Overview

Specific numbernumerical measurement determined by aset of data

Example:

- 23% of people polled believed that there are too manypolls.

- Average age of Vietnamese men in 2000 is 68.

- Price index in December increased by 1% compared tothat in November


Slide 10

Statistics=method of analysis

a collection of methods for planning experiments,

obtaining data, and then organizing, summarizing,

presenting, analyzing, interpreting, and drawing

conclusions based on the data.

= drawing of inferences (generalization) about the

large groups (population) on the basis of

observations made on smaller ones (sample)

Definitions


Slide 11

Definitions

Populationthe complete collection of all elements(scores, people, measurements, and so on)to be studied.

The collection is complete in the sense thatit includes all individual items or unitswhich are the subject of investigation.

Unit = an individual of the population


Slide 12

Census

the collection of data from every member of thepopulation

Samplea sub-collection of elements drawn from a

population

Sample sizenumber of units in the sample (or % of units fromthe population)

Definitions


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Slide 13

Variable

Characteristics of a population which differ from unit to

unit

Data

Observations on the variable (such as measurements,

degrees, orders, properties, outcome, results) that havebeen measured and collected

Definitions


Slide 14

Population: All 1st year students in the School

of Biotechnology

Unit: a student

Variable: score in a math final exam

Observation (data): points of the score (60, 71,

95 , etc..)

Sample: a group of 30 student

Sample size: 30

Example:


Slide 15Random sampling and randomnumbers

Sample data must be collected in anappropriate way, such as through aprocess of random selection

(each unit in a population must have anequal chance of being drawn)

If sample data are not collected in anappropriate way, the data may beso completely useless, information

may not be properly extrapolated to thepopulation


Slide 16Random sampling and randomnumbers

Random number

Select units to be measured by referenceto random number

The way to avoid bias

Random number table (in any statisticalbook)

Computer: MINITAB, Excel, SAS,StatGraphic, SPSS, etc.

Calculator (some versions)


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Slide 17Random Sampling

selection so that each has anequal chance of being selected

In Excel: RANDBETWEEN (a, b)


Slide 18

Table of random numbers


Slide 19Descriptive and inferentialstatistics

Descriptive Statistics

summarize or describe the important

characteristics of a known set of

population data

Inferential Statistics

use sample data to make inferences (orgeneralizations) about a population


Slide 20

Types of Data

Processing Data


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Slide 21

Parametera numerical measurement describingsome characteristic of a population

population

parameter

Definitions


Slide 22Definitions

Statistica numerical measurement describingsome characteristic of a sample

sample

statistic

XS


Slide 23Definitions

Quantitative data

Numbers representing counts or measurements

Example: weights, lengths, ages, pressure,temperature


Slide 24Definitions

Qualitative (or categorical orattribute) data

can be separated into different categories

that are distinguished by some non-numericcharacteristics.

Example: genders (male/female),

colors (blue, red, )

marital status

levels of satisfaction


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Slide 25Working with

Quantitative DataQuantitative data:- Measure of quantity- Can compare one to others (more orless)- Can calculate an average

Quantitative data can furtherbe distinguished betweendiscrete and continuous types


Slide 26

Discrete

data result when the number of possiblevalues is either a finite number or acountable number of possible values

0, 1, 2, 3, . . .

Example: The number of eggs that hens lay

Definitions


Slide 27

Continuous(numerical) data result from infinitely many possiblevalues that correspond to some continuous scalethat covers a range of values without gaps,interruptions, or jumps

Definitions

2 3

Example: The amount of milk that a cow produces;e.g. 2.343115 gallons per day


Slide 28

Levels of Measurement

Another way to classify data is touse levels of measurement. Fourof these levels are discussed inthe following slides


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Slide 29

Example: - Survey responses: yes, no, undecided

- Marital status: single, married, divorced,

widows

Definitions nominal level of measurement

characterized by data that consist of names, labels, or

categories only. The data cannot be arranged in an

ordering scheme (such as low to high)


Slide 30

ordinal level of measurement

involves data that may be arranged in some order, but differences

between data values either cannot be determined or are meaningless. It

is used to indicate rank order, but nothing more

Definitions

Examples: Course grades A, B, C, D, or F

Score given to answer such as how often you use a bus service?:

- very often: 5

- Often: 4- Occasionally: 3

- Rarely: 2

- Never: 1

It gives a bit more information than nominal, but still cant calculate the average


Slide 31

interval level of measurement

like the ordinal level, with the additional property that the

difference between any two data values is meaningful.

However, there is no natural zero starting point (where

none of the quantity is present).

- The interval can be added or subtracted but not divided (the

ratio makes no sense)

Date is a very widely used interval scale.

Example: - Years 1000, 2000, 1776, and 1492

- Temperature: 5oC, 10oC, 20oC

- 1st , 5th, 10th day in a month

Definitions


Slide 32

ratio level of measurement

the interval level modified to include the natural zero

starting point (where zero indicates that none of the

quantity is present). For values at this level, differences

and ratios are meaningful. It incorporate the properties ofthe interval, ordinal and nominal levels

Example:

- Prices of college textbooks ($0 represents no cost)

- Measurement of mass and length

Definitions


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Slide 33Summary -Levels of Measurement

Nominal - categories only

Ordinal - categories with some order

Interval - differences but no naturalstarting point

Ratio - differences and a natural startingpoint


Slide 34Summary -Levels of Measurement

Nominal

Data

Qualitative Quantitative

Ordinal Interval Ratio


Slide 35

Recap

Basic definitions and terms describing data

Parameters versus statistics

Types of data (quantitative and qualitative)

Levels of measurement

In the previous sections we have looked at:


Slide 36

Critical Thinking


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Slide 37

Success in StatisticsSuccess in the introductory statistics

course typically requires more commonsense than mathematical expertise

This section is designed to illustrate

how common sense is used when wethink critically about data and statistics


Slide 38

Limitations of Statistics:

-Not to proof anything, just to show

the chance of occurring of some

event

-May lead to some misuse


Slide 39

self-selected survey

(or voluntary response sample)

one in which the respondents themselves decide whether to be

included

In this case, valid conclusions can be made only about the

specific group of people who agree to participate.

Abuses (or misuses) of Statistics

Bad Samples


Slide 40

Abuses of Statistics

Loaded Questions

Misleading Graphs

Bad Samples

Small Samples


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Slide 41

Bachelor High School

Degree Diploma

Figure. Salaries of People with Bachelors Degrees and with High

School Diplomas

$40,000

30,000

25,000

20,000

$40,500

$24,400

35,000

$40,000

20,000

10,000

0

$40,500

$24,40030,000

Bachelor High School

Degree Diploma

(a) (b)


Slide 42

We should analyze thenumerical information givenin the graph instead of beingmislead by its general shape

Misleading Graphs


Slide 43

Bad Samples

Small Samples

Misleading Graphs

Pictographs

Distorted PercentagesLoaded Questions

Order of Questions

Refusals

Correlation & Causality

Self Interest Study

Precise Numbers

Partial Pictures

Deliberate Distortions

Misuses of Statistics


Slide 44

Design of Experiments


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Slide 49

Sample Sizeuse a sample size that is large enough to seethe true nature of any effects and obtain thatsample using an appropriate method, such as

one based on randomness

Sample Size


Slide 50

Random Samplemembers of the population are selected insuch a way that each individual member hasan equal chance of being selected

Definitions

Simple Random Sample (of size

n

)subjects selected in such a way that every

possible sample of the same size n has the

same chance of being chosen


Slide 51

Randomnesswhy randomness is important in statistics?

Random sample = representativesample-The best way to get a representative sample =choose a proportion of a population at random

-Every possible experimental unit having equalchance of being selected, without bias

Random sample


Slide 52

Random Sampling - selection so thateach has an equal chance of being selected


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Slide 53

Systematic Sampling - Select somestarting point and then select every k-th element inthe population


Slide 54Stratified Samplingsubdivide the population into at

least two different subgroups that share the samecharacteristics, then draw a sample from each

subgroup (or stratum)


Slide 55

Cluster Sampling - divide the populationinto sections (or clusters); randomly select some ofthose clusters; choose allmembers from selectedclusters


Slide 56Major Points

If sample data are not collected in anappropriate way, the data may be socompletely useless.

Randomness typically plays a criticalrole in determining which data tocollect.


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Slide 57

Random

Systematic

Stratified

Cluster

Methods of Sampling


Slide 58

Sampling Error

the difference between a sample result and the truepopulation result; such an error results from chancesample fluctuations

Nonsampling Errorsample data that are incorrectly collected, recorded,or analyzed (such as by selecting a biased sample,using a defective instrument, or copying the data

incorrectly)

Definitions

Precision vs. Accuracy?


Slide 59

Recap

In this section we have looked at:

Types of studies and experiments

Controlling the effects of variables

(replication and sample size)

Randomization

Types of sampling

Sampling errors


Slide 60

HOMEWORK

Chernick: Introductory Biostatistics for theHealth Sciences

2.1; 2.2; 2.8; 2.14

3.1

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Biostat lec01 basicconcepts