statistics the theory and methods lecture[1]

8/14/2019 Statistics the Theory and Methods Lecture[1]

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Master of Water and Environmental Science

Course Title

Statistical Methods in water and Environmental

Science.

Dr. Mohammed Abudaya


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Course OutlineCatalog description:

Using of advanced Statistical methods in evaluation andinterpretation of water and environmental data in: graphicalpresentation, data sources and accuracy. It also includes an

interpretation of probability theory, probability distributions, mean,median, standard deviation, variance, normal distribution and

binomial distribution. Other topics will be covered such as; validityof questionnaire, sampling distributions, central limit theory,hypothesis testing, analysis of variance, correlation, regression

analysis and forecasting. It will cover advance statistical methodsin evaluation and interpretation of Environmental data, expectation

and its applications, sampling distributions and statistical inference,two sample problems, non-parametric tests, analysis of discretedata, linear regression, multiple regression, analysis of variance

(ANOVA).


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Required Text Books/other materials

(1) Choosing and Using Statistics. A Biologist's Guide, 2ned. Calvin Dytham (Blackwell Publishing 2003).

(2) SPSS software


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Recommended Text Books.

(3)Statistical For Environmental Science and Management. 2nded. Bryan F.J.Manly (Taylor & Francis Group 2009).

(4) Using Statistical Methods for Water Quality Management,

Issues, Problems and Solutions. 1st ed. Graham B. McBride (AJohn Wiley & Sons, Ltd. 2005).

(5) Environmental Statistics, Methods and Applications. 1st ed.Vic Barnett (A John Wiley & Sons, Ltd. 2007).

. .0 . (6).1997 . .


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Statistical Methods in water and Environmental Science

COURSE.

Units of study (without details):Unit I Statistics, Variables and DistributionUnit II Hypothesis testing, sampling and experimental designUnit III Descriptive and Presentational Techniques

Unit IV Tests to Look at DifferencesUnit V Tests to Look at RelationshipsUnit VI Applications of SPSS

Evaluation of student learning:

30% Mid Exam20% Case Studies40% Final Exam10% Class Participation


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Chapter 1: Introduction

What are Statistics?

Methods for organizing, summarizing, presenting, &interpreting information (data)

Statistics bring chaos to order condense large

amounts of information into smaller understandable unitsVocabulary & symbols for communicating about data

How to make judgments (about data) under uncertainty

(1)How do you know which tool to use? (2)What do you want to know?(3)What type of data do you have?


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is [the theory and method of analyzingis [the theory and method of analyzingquantitative data obtained from samplesquantitative data obtained from samples

of observations in order to study andof observations in order to study and

compare sources of variation ofcompare sources of variation ofphenomena, to help make decisions tophenomena, to help make decisions toaccept or reject hypothesized relationsaccept or reject hypothesized relations

between phenomena, and to aid in]between phenomena, and to aid in]making [reliable] inferences frommaking [reliable] inferences fromempirical observations"empirical observations"

(Kerlinger, 1986, p. 175(Kerlinger, 1986, p. 175)])]

Statistics Definition


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Limitations of Statistics

Statistics is used from the mooring bedStatistics is used from the mooring bedtea to the bed at night, howtea to the bed at night, how????????

Statistics methods are best applicable to quantitative data.Statistics methods are best applicable to quantitative data.

Statistics decisions are subject to certain degree of error.Statistics decisions are subject to certain degree of error.

Statistics statements are true on an average i.e. true for a groupStatistics statements are true on an average i.e. true for a groupof individuals and may not be true for an individuals.of individuals and may not be true for an individuals.


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Branches of Statistics

1.Descriptive Statistics

Tools for summarizing, organizing & simplifying data

Tables & Graphs Measures of Central Tendency Measures of Variability

Examples:

Average rainfall in Gaza last yearConcentration of Nitrate in ground waterPercentage of seniors in this class


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2. Inferential Statistics

Data from sample used to draw inferences about a

population

Tools for generalizing beyond actual observationsGeneralize from a sample to apopulation

Population

The entire collection of events of interest E.g., collection of people you want to understand

Doesnt necessarily mean big but often is


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Sample

Subset of events selected from a populationIntended to represent the population

Why not just collect data from the whole population?

Sometimes impractical, often impossible!

If we cannot measure everyone in the population, does thatmean we cannot study populations or make anyconclusions about them?

NO!Data from a sample can tell us something about a

population


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Sample will not be identical to the populationSample will not be identical to the population

So, generalizations will have some errorSo, generalizations will have some error

Generalizations will depend on how well the sampleGeneralizations will depend on how well the samplerepresentsrepresents the population.the population.Representative sampleRepresentative sample = Sample whose characteristics are= Sample whose characteristics are

similar to populationsimilar to populationRandom samplingRandom sampling= each event in the population has= each event in the population has

equal chance of being selected for sampleequal chance of being selected for sample

RS increases chances that sample will beRS increases chances that sample will be representativerepresentative

rather thanrather than biasedbiased

example:example:

Sample of 10 students from our classSample of 10 students from our classSelect students at random vs. select first rowSelect students at random vs. select first row

Random sampling doesRandom sampling does notnot guaranteeguarantee no bias!no bias!


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Sampling

PopulationPopulation is an aggregate of individualsis an aggregate of individuals.. Population or the size of the populationPopulation or the size of the populationchanges with the objective of the studychanges with the objective of the study..

SampleSample is a fraction of the populationis a fraction of the population

chosen by some sampling procedurechosen by some sampling procedure..

It is not always possible to study theIt is not always possible to study the

total population, because of (costs,total population, because of (costs,

time, requirements...etctime, requirements...etc..


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Methods of Sampling

1.Simple Random Sampling:

An equal chance of selection is assigned to each unitAn equal chance of selection is assigned to each unitof the populationof the population..

Samples less thanSamples less than 3030Samples aboveSamples above 3030Table of random numbersTable of random numbers

Example 1Example 1: Selection of drinking water wells: Selection of drinking water wells..

Example 2Example 2: Selection samples from an agricultural: Selection samples from an agricultural

field ???population and ??? samplefield ???population and ??? sample..


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Methods of Sampling

2.Stratified Random Sampling:

Dividing the population into L classes or StrataDividing the population into L classes or Strata..Strata are formed on the basis ofStrata are formed on the basis of

Homogeneity or similaritiesHomogeneity or similarities..N=N1+N2+N3.+NLN=N1+N2+N3.+NL

Example 1Example 1: Population = 1000, Sample = 20: Population = 1000, Sample = 20,,

Strata1 = 400, Strata2 = 300, Strata3 = 200, Strata4 = 100Strata1 = 400, Strata2 = 300, Strata3 = 200, Strata4 = 100,,Answer: Number of samplesAnswer: Number of samples

Strata 1= (400/1000x20=8Strata 1= (400/1000x20=8

Strata 2= (300/1000x20=6Strata 2= (300/1000x20=6

Strata 3= (200/1000x20=4Strata 3= (200/1000x20=4

Strata 4= (100/1000x20=2Strata 4= (100/1000x20=2

20


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Methods of Sampling

3.Systematic Sampling:

Divide the population units intoDivide the population units into nn groups eachgroups eachcontaining an equal number of units saycontaining an equal number of units say kk

Example 1: Selection of 5 drinking water wells fromExample 1: Selection of 5 drinking water wells from5050..

50/550/5==1010

Choose a random number let say 7Choose a random number let say 777,,1717,,2727,,3737,,4747


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Methods of Sampling

4.Cluster Sampling:

The smallest units into which the population can beThe smallest units into which the population can becalled the elements of the population, and groups ofcalled the elements of the population, and groups of

element are called the clusterselement are called the clusters..


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Chapter 2: Basic concepts

WHAT ARE DATA?

Collection of information, comprised of 2 parts(1)Individuals (also called cases or observations)

(2)Variables

Individuals are ANY OBJECTS described by data

Do NOT have to be peopleVariables are characteristics recorded on/from the individuals

A variable is something that varieshas at least 2 values

Something that changes over time ORSomething that varies across individuals


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Types of Data

Categorical (qualitative): records which group or category

an individual/observation belongs in; it classifies; doesntmake sense to perform arithmetic on this type of variableE.g., gender (Female or Male)

Quantitative: a true numerical value; it indicates anamount; often obtained from a measuring instrument; itmakes sense to perform arithmetic on these types ofvariables

E.g., Weight in pounds

Other examples?????


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Pick out the individuals and variables in these

examples:

1. 100 business executives were asked their age

2. 6 water wells measured the dissolved oxygen

3. 8 farmers obtained the weight of 25 pigs

4. 4 technicians measured the sound quality of 10 stereos


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Variables can be divided into:

1.Discrete (discontinuous:

(a Indivisible units

(b Restricted to whole numbers(c Can be counted

e.g. # of children in a family

# of houses in a neighborhood


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Continuous:

(a)Unlimited number of possible values

(b) Infinite number of values can fall b/n any 2 observedvalues(c) No gaps between unitse.g. time taken to solve a problem, height or weight

Variables can be measured on four different types ofscales:

1. Nominal:

(a) Consists of a set of categories or labels(b) The score does NOT indicate an amount(c) The score is arbitrary(d) e.g. Sea Level: 1=Low, 2=Medium, 3=High(c) e.g. land use or soil classifications


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2.Ordinal (Rank:

(a) Score indicates rank order along some continuum

(b) It is a relative score, not an absolute scoreMight have the highest score on the exam, but we still

dont know how well you did

(c) There is NOT an equal distance between scores

e.g. Finish 1st ,2nd , or 3rd in a race; could be a difference of2seconds b/n 1st & 2nd but a difference of 10 minutes

b/n 2nd & 3rd.

e.g. Plants from six pots could be ranked in health orderby simple observation and assigned values from 1 to 6.


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Research and Gathering Data

Science attempts to discover order in the universe

Science searches for relationships between & amongvariables

Two general methods of research: Correlation (non-experimental) Experimental

Begin with an hypothesis, a hunch/guess/belief about howvariables might be related or influence each other:

Meditation can reduce stress


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1.Correlational Research

Measure variables as they occur naturally

Questionnaires, interviews, observational or archival research

Test hypotheses about association between 2 or more variablesTheory may be causal, but conclusions cannot be

Example:

Survey 100 people

Measure how often (if ever) they meditateMeasure their level of life stressLook at association between meditation and stress

Can we draw a causal inference?


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2.Experimental Research:

Manipulate one variable; examine its effect on an outcomevariableIndependent Variable Dependent Variable

Goal is to draw causal inferences

Cause Effect

The IV presumed to cause changes in DV

IV DV


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Any questionAny questionNext Lecture 12/11/2009Next Lecture 12/11/2009

statistics the theory and methods lecture[1]

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