S.S. RAWAT

Statistical decision making theory,

Introduction

1) STATISTICS MAY BE CALLED THE SCIENCE OF COUNTING2) STATISTICS MAY RIGHTLY BE CALLED THE SCIENCE OF AVERAGE3) STATISTICS MAY BE DEFINED AS THE SCIENCE OF COLLECTION,

PRESENTATION , ANALYSIS AND INTERPRETATION OF NUMERICAL DATA

4) STATISTICS IS METHOD OF DECISION MAKING IN FACE OF UNCERTAINLY ON THE BASIS OF NUMERICAL DATA AND CALCULATED RISKS.

5) STATISTICS IS THE SCIENCE OF ESTIMATES AND PROBABILITY

Meaning of statistics

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Is statistics a science or an art or both ?

“STATISTICS IS BOTH A SCIENCE AND AN ART OF HANDLING

AGGREGATE OF FACTS-OBSERVATION ,RECORDING ,

CLASSIFYING AND OTHERWISE SYSTEMATICALLY TREATING THEM .”

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Function’s of statistics

a) Comparison. b)Formulation and testing of hypotheses c) Prediction d) Formulation of suitable policies. e) Preciseness and definiteness.

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LIMITATIIONS OF STATISTICS

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1) STATISTICS DOES NOT DEAL WITH INDIVIDUAL FIGURES.

2) STATISTICS DOES NOT STUDY QUALITATIVE DATA.3) STATISTICAL LAWS ARE NOT EXACT.4) STATISTICS CAN BE MISUSED5) STATISTICAL INTERPRETATIONS REQUIRE A HIGH

DEGREE OF SKILL AND UNDERSTANDING OF THE SUBJECT

Limitation of statistics

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• ANALYSTS MUST OFTEN MAKE DECISIONS ABOUT SOME CONDITION IN THE REAL

WORLD.

Statistical Decision Making

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• CASE :-

•Assume that you have finished your MA in policy studies and have been hired as the environmental affairs officer for the city of Dheradun.

• You must make the following assessment:

• Does the water supply in Dheradun comply with safe drinking water standards?

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Hypothesis Testing

We can decide the facility is In Compliance.

or

We can decide the facility is in Violation.(not in compliance)

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If we decide:

The facility is in compliance – and it is.

or

We decide the facility is in violation – and it is.

Then we are fine. We have made a correct decision

But sometimes…

No, make that often…

we’re not correct.

We make mistakes.

Statistics gives us some rules to reduce the likelihood of making these mistakes

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Example of a statistical test

• In order to test the facilities water we will collect several bottles of water at different times.

• We take this sample…

• (Do not be confused by the chemistry. Each bottle of water is a sample to the chemist, while all of the separate bottles of water are the sample to the statistician.)

• And we calculate the average amount of the pollutant – e.g. lead.

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The average of the samples is thus

Our hypothesis is thus

ppb (the standard for lead)

Because we will say that the standard actually refers to a population distribution with a mean

equal to the standard, we can restate this is conventional statistical terms

For info on EPA standards

Hypotheses

• The hypothesis is:

•The facility is in violation.

• Sometimes referred to as “The alternate hypothesis.”

• The null hypothesis is:

•The facility is in compliance.

• In this instance, you want to be able to reject the alternate hypothesis, or more properly, fail to reject the null hypothesis.

Hypothesis?pothesis?