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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