Introduction to StatisticsIntroduction to Statistics

Engr. DrEngr. Dr. Attaullah Shah . Attaullah Shah

Some quotes about Statistics A statistical analysis, properly conducted, is a delicate dissection of A statistical analysis, properly conducted, is a delicate dissection of

uncertainties, a surgery of suppositions.  ~M.J. Moroneyuncertainties, a surgery of suppositions.  ~M.J. Moroney

Do not put your faith in what statistics say until you have carefully Do not put your faith in what statistics say until you have carefully considered what they do not say.  ~William W. Watt.considered what they do not say.  ~William W. Watt.

Statistics may be defined as "a body of methods for making wise decisions Statistics may be defined as "a body of methods for making wise decisions in the face of uncertainty."  ~W.A. Wallisin the face of uncertainty."  ~W.A. Wallis

The theory of probabilities is at bottom nothing but common sense reduced The theory of probabilities is at bottom nothing but common sense reduced to calculus.  ~Laplace. to calculus.  ~Laplace.

Statistics can be made to prove anything - even the truth. -UnknownStatistics can be made to prove anything - even the truth. -Unknown

Definition of Statistics: The science of producing unreliable facts from Definition of Statistics: The science of producing unreliable facts from reliable figures. reliable figures. Evan Evan EsarEsar

What is Statistics Derived from the Latin for “state” - governmental data collection and Derived from the Latin for “state” - governmental data collection and

analysis analysis Study of data branch of mathematics dealing with numerical facts i.e. Study of data branch of mathematics dealing with numerical facts i.e.

data.data. The science of StatecraftThe science of Statecraft concerning the collection and use of data by concerning the collection and use of data by

State.State. The mathematical science of making decisions and drawing The mathematical science of making decisions and drawing

conclusions from data in situations of uncertainty. conclusions from data in situations of uncertainty.

StatisticsStatistics is the science of the collection, organization, and is the science of the collection, organization, and interpretation of data interpretation of data

Statistics is the science of data. This involves collecting, Statistics is the science of data. This involves collecting, classifying, summarizing, organizing, analyzing, and interpreting classifying, summarizing, organizing, analyzing, and interpreting numerical information.numerical information.

Must not be confused with word “ Statistic” referring to quantity such Must not be confused with word “ Statistic” referring to quantity such median, mean etc. median, mean etc.

..

Types of Statistical Applications

Descriptive Statistics: Descriptive Statistics: Inferential Statistics.Inferential Statistics.

Descriptive Statistics

Is the science of describing data to facilitate Is the science of describing data to facilitate its understanding.its understanding.

It uses both numerical and graphical methods.It uses both numerical and graphical methods. Goal is to recognize trends, summarize data, Goal is to recognize trends, summarize data,

and to present information in a and to present information in a comprehensive way.comprehensive way.

Examples: Mean, Mode, Variance, Standard Examples: Mean, Mode, Variance, Standard Deviation etc. Deviation etc.

Inferential Statistics Is the science of drawing conclusions from data.Is the science of drawing conclusions from data. It utilizes a sample data to make inferences to a It utilizes a sample data to make inferences to a

larger population.larger population. Inference refers to estimates, decisions, and Inference refers to estimates, decisions, and

predictions about the population.predictions about the population. Examples: testing of hypothesis, Regression Examples: testing of hypothesis, Regression

analysis, correlation, prediction, estimation etc. analysis, correlation, prediction, estimation etc.

Key Terms Population: a set of units that we are Population: a set of units that we are

interested in studying.interested in studying. Variable: a characteristic of an individual Variable: a characteristic of an individual

population unit.population unit. Sample: a subset of the units of a Sample: a subset of the units of a

population.population. Statistical inference: estimate, or prediction Statistical inference: estimate, or prediction

of the population based on information of the population based on information contained in the sample.contained in the sample.

Population

Sample

City

500 households

Four Elements of Descriptive Statistics

1. The population or sample of interest1. The population or sample of interest 2. One or more variables to be investigated2. One or more variables to be investigated 3. Tables, graphics, or numerical summary 3. Tables, graphics, or numerical summary

toolstools 4. Identification of patterns in data4. Identification of patterns in data

Five Elements of Inferential Statistics

1. The population of interest1. The population of interest

2. One or more variables to be investigated2. One or more variables to be investigated

3. The sample of population units3. The sample of population units

4. The inference about the population based 4. The inference about the population based on information contained in the sampleon information contained in the sample

5. A measure of reliability for the inference5. A measure of reliability for the inference

Descriptive analysis – data distributionDescriptive analysis – data distribution

Inferential analysis – hypothesis testingInferential analysis – hypothesis testing

Differences analysis – hypothesis testingDifferences analysis – hypothesis testing

Association analysis – correlation Association analysis – correlation

Predictive analysis – regression Predictive analysis – regression

Five Different Types of Statistical Five Different Types of Statistical AnalysisAnalysis

Environmental Statistics Environmental statisticsEnvironmental statistics is the application of statistical is the application of statistical

methods to environmental science. methods to environmental science.

It covers procedures for dealing with questions concerning both It covers procedures for dealing with questions concerning both the natural environment in its un-disturbed state and the the natural environment in its un-disturbed state and the interaction of humanity with the environment. interaction of humanity with the environment.

Thus weather, climate, air and water quality are included, as are Thus weather, climate, air and water quality are included, as are studies of plant and animal populations.studies of plant and animal populations.

All types of study involve sampling over time and space, and it All types of study involve sampling over time and space, and it is important that sampling designs be cost effective, reliable, is important that sampling designs be cost effective, reliable, consistent, easily manageable and , if necessary, that they can consistent, easily manageable and , if necessary, that they can be justified in a court of law.be justified in a court of law.

Three major situations of interest for us: Three major situations of interest for us: Baseline studies to document the present state of an Baseline studies to document the present state of an

environment to provide background in case of unknown environment to provide background in case of unknown changes in the futurechanges in the future; ;

What can be the potential changes in the Ambient Air What can be the potential changes in the Ambient Air Quality (AAQ) due to new cement factory in an area. Quality (AAQ) due to new cement factory in an area.

What is the present distribution of heavy metal in the surface What is the present distribution of heavy metal in the surface water of Islamabad? ( If any) water of Islamabad? ( If any)

Targeted studies to describe the likely impact of changes Targeted studies to describe the likely impact of changes being planned or of accidental occurrencesbeing planned or of accidental occurrences; ;

To predict the impact of pollen concentration on the health To predict the impact of pollen concentration on the health of asthmatic patients in Islamabad. of asthmatic patients in Islamabad.

The impact on human health due accidental toxic releases The impact on human health due accidental toxic releases from fertilizer factory. from fertilizer factory.

Regular monitoring to attempt to detect changes in the Regular monitoring to attempt to detect changes in the environment. environment.

Data collection and monitoring & evaluation of air pollution Data collection and monitoring & evaluation of air pollution due to construction activities and its comparison with due to construction activities and its comparison with NEQS.NEQS.

To assess the widespread concern about acid rains, regional survey of To assess the widespread concern about acid rains, regional survey of small lakes were carried out for pH, sulfate concentration, nitrate small lakes were carried out for pH, sulfate concentration, nitrate concentration, and calcium concentration at each sampled lakes.concentration, and calcium concentration at each sampled lakes.

The main questions of interest are: The main questions of interest are: Is there any evidence of trends or abrupt changes in the values for Is there any evidence of trends or abrupt changes in the values for

one or more of the four measured chemistry variables?one or more of the four measured chemistry variables? If trends or changes exist, are they related for the four variables, If trends or changes exist, are they related for the four variables,

and are they of the type that can be expected to result from acid and are they of the type that can be expected to result from acid precipitation?precipitation?

Is there evidence of spatial correlation such that measurements on lakes that are in close proximity tend to be similar?

Is there evidence of time correlation such that the measurements on a lake tend to be similar if they are close in time?

We may use the correlation and Time Series analysis for such We may use the correlation and Time Series analysis for such study. study.

Case Study: Acid Rain in Norway

EXAMPLE: Pollution at an oil refinery

Environmental Protection Agency (EPA) has accused Environmental Protection Agency (EPA) has accused Shell Oil Company of violation environmental Shell Oil Company of violation environmental regulations at its refinery located in Huston during the regulations at its refinery located in Huston during the year 2001. The regulations state that the average year 2001. The regulations state that the average petroleum leaked into the ground at the refinery must petroleum leaked into the ground at the refinery must not exceed 100 gallons per day during any calendar not exceed 100 gallons per day during any calendar year. Fine for violating the regulations is $1,000,000.year. Fine for violating the regulations is $1,000,000.

EPA regulators visited the refinery on eight days in EPA regulators visited the refinery on eight days in December, 2001 and measured the petroleum leaked December, 2001 and measured the petroleum leaked in gallons as 110,96,104,101,87,99,116,108.in gallons as 110,96,104,101,87,99,116,108.

EXAMPLE: Pollution at an oil refinery

The Six Step Inference Process:The Six Step Inference Process: Question: Does average leakage exceed 100 gallons Question: Does average leakage exceed 100 gallons

per day?per day? Population: Every single day of that year 2001.Population: Every single day of that year 2001. Sample: Measurements on those 8 days in December.Sample: Measurements on those 8 days in December. Variable: Leakage in gallons.Variable: Leakage in gallons. Summary: Average leakage=102.625 gallon/day.Summary: Average leakage=102.625 gallon/day. Inference: The average leakage for the year Inference: The average leakage for the year

2001exceeds 100 gallons. The company should be 2001exceeds 100 gallons. The company should be fined.fined.

EXAMPLE: Pollution at an oil refinery

Follow-up questions:Follow-up questions:

Is the sample representative of the population?Is the sample representative of the population? What argument might Shell use to contend that the What argument might Shell use to contend that the

EPA's conclusions are unreliable?EPA's conclusions are unreliable? What could EPA administrators do to improve the What could EPA administrators do to improve the

statistical techniques?statistical techniques?

Evolution of environment statistics Compared to economic and social statistics a Compared to economic and social statistics a

relatively new fieldrelatively new field Frameworks and standards are evolving Frameworks and standards are evolving

developing nationally and internationallydeveloping nationally and internationally Have build up knowledge and can more clearly Have build up knowledge and can more clearly

define information needsdefine information needs The field is maturing and some hard monitoring The field is maturing and some hard monitoring

and measurement issues are being addressedand measurement issues are being addressed

Course outline:

ItemItem Lectures Lectures

1.1. The role of Statistics in Environmental ScienceThe role of Statistics in Environmental Science

( Chapter-1) ( Chapter-1)

22

2. Some basic Statistical Methods (Appendix-1)2. Some basic Statistical Methods (Appendix-1) 33

3. Environmental Sampling ( Chapter 2) 3. Environmental Sampling ( Chapter 2) 77

4. Models for Data ( Chapter 3) 4. Models for Data ( Chapter 3) 44

5. Drawing Conclusions from Data ( Chapter 4) 5. Drawing Conclusions from Data ( Chapter 4) 66

6. Environmental Monitoring ( Chapter 5) 6. Environmental Monitoring ( Chapter 5) 55

7. Time Series Analysis ( chapter 8) 7. Time Series Analysis ( chapter 8) 55

Total Total 3232

Recommended Book:

Statistics for Environmental Science and Statistics for Environmental Science and ManagementManagement Bryan F.J. ManlyBryan F.J. Manly

The Role of Statistics in Critical Thinking

H.G. Wells wrote: Statistical thinking will H.G. Wells wrote: Statistical thinking will one day become as important in society as one day become as important in society as as the ability to read and write as the ability to read and write

Why?Why? How related to critical thinking?How related to critical thinking? How important for society? How important for society? Find article!Find article!

Exercise 1 ( Case study Exxon Valdez oil spill)

Despite the large amounts of money spent on them, the studies on the effects of the Exxon Valdez oil spill on the coastal habitat of Alaska all failed to produce simple, easily understood estimates of these effects.

What happened was that the oil spill took everyone by surprise, and none of the groups involved (state and federal agencies and Exxon) apparently was able to quickly produce a good sampling design and start collecting data. Instead, it seems that there were many committee meetings, but very little actually done while the short Alaskan summer was disappearing.

With the benefit of hindsight, what do you think would have been a good approach to use for estimating the effects of the oil spill?

This question is not asking for technical details—just a broad suggestion for how a study might have been designed.