Probability in SamplingProbability in Sampling

Key ConceptsKey Concepts

Statistical terms in samplingStatistical terms in sampling Sampling errorSampling error The sampling distributionThe sampling distribution

Statistical Terms in SamplingStatistical Terms in Sampling

VariableVariable

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Statistical Terms in SamplingStatistical Terms in Sampling

VariableVariableSelf-esteemSelf-esteem

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Statistical Terms in SamplingStatistical Terms in Sampling

VariableVariable

StatisticStatistic

Self-esteemSelf-esteem

11 22 33 44 55

Statistical Terms in SamplingStatistical Terms in Sampling

VariableVariable

StatisticStatistic

Self-esteemSelf-esteem

Average = 3.72Average = 3.72SampleSample

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Statistical Terms in SamplingStatistical Terms in Sampling

VariableVariable

StatisticStatistic

ParameterParameter

Self-esteemSelf-esteem

Average = 3.72Average = 3.72SampleSample

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Statistical Terms in SamplingStatistical Terms in Sampling

VariableVariable

StatisticStatistic

ParameterParameter

Self-esteemSelf-esteem

Average = 3.72Average = 3.72

Average = 3.75Average = 3.75

SampleSample

PopulationPopulation

Sampling ErrorSampling Error

4.54.03.53.0

150

100

50

0

Self-esteemSelf-esteem

Freq

uenc

yFr

eque

ncy

The population has The population has a mean of 3.75.a mean of 3.75.

Sampling ErrorSampling Error

4.54.03.53.0

150

100

50

0

Self-esteemSelf-esteem

Freq

uenc

yFr

eque

ncy

The population has The population has a mean of 3.75...a mean of 3.75...

...and a ...and a standard standard

error of .25.error of .25.

Sampling ErrorSampling Error

4.54.03.53.0

150

100

50

0

Self-esteemSelf-esteem

FFFr

eque

ncy

Freq

uenc

yThe population has The population has

a mean of 3.75...a mean of 3.75...

...and a ...and a standard standard

error of .25.error of .25.

This means that...This means that...

Sampling ErrorSampling Error

4.54.03.53.0

150

100

50

0

Self-esteemSelf-esteem

Freq

uenc

yFr

eque

ncy

The population has The population has a mean of 3.75...a mean of 3.75...

...and a ...and a standard standard

error of .25.error of .25.

This means that...This means that...about 64% of cases fall between 3.5 - 4.0.about 64% of cases fall between 3.5 - 4.0.

Sampling ErrorSampling Error

4.54.03.53.0

150

100

50

0

Self-esteemSelf-esteem

Freq

uenc

yFr

eque

ncy

The population has The population has a mean of 3.75...a mean of 3.75...

...and a ...and a standard standard

error of .25.error of .25.

This means...This means...About 64% of cases fall between 3.5 - 4.0.About 64% of cases fall between 3.5 - 4.0.

About 95% of cases fall between 3.25 - 4.25.About 95% of cases fall between 3.25 - 4.25.

Sampling ErrorSampling Error

4.54.03.53.0

150

100

50

0

Self esteemSelf esteem

Freq

uenc

yFr

eque

ncy

The population has The population has a mean of 3.75...a mean of 3.75...

...and a ...and a standard standard

error of .25.error of .25.

This meansThis meansAbout 64% of cases fall between 3.5 - 4.0.About 64% of cases fall between 3.5 - 4.0.

About 95% of cases fall between 3.25 - 4.25.About 95% of cases fall between 3.25 - 4.25.about 99% of cases fall between 3.0 - 4.5about 99% of cases fall between 3.0 - 4.5

Sampling ErrorSampling Error

The standard error is called the The standard error is called the sampling error.sampling error.

4.54.03.53.0

150

100

50

0

The sample of 1000 The sample of 1000 has a mean of 3.74 has a mean of 3.74

and a standard error and a standard error of .0074.of .0074.

Self-esteemSelf-esteem

Freq

uenc

yFr

eque

ncy

Sampling ErrorSampling Error

The sampling error shows that the odds are .95 that The sampling error shows that the odds are .95 that the population mean is 3.74 the population mean is 3.74 ++ 2(.0074). 2(.0074).

4.54.03.53.0

150

100

50

0

Self-esteemSelf-esteem

Freq

uenc

yFr

eque

ncy

The sample of 1000 The sample of 1000 has a mean of 3.74 has a mean of 3.74

and a standard error and a standard error of .0074.of .0074.

Sampling ErrorSampling Error

4.54.03.53.0

150

100

50

0

Self-esteemSelf-esteem

Freq

uenc

yFr

eque

ncy

The sampling error shows that the odds are .95 that The sampling error shows that the odds are .95 that the population mean is 3.74 the population mean is 3.74 ++ 2(.0074). 2(.0074).

The sample of 1000 The sample of 1000 has a mean of 3.74 has a mean of 3.74

and a standard error and a standard error of .0074.of .0074.

Confidence levelConfidence level

Sampling ErrorSampling Error

4.54.03.53.0

150

100

50

0

Self-esteemSelf-esteem

Freq

uenc

yFr

eque

ncy

The sampling error shows that the odds are .95 that The sampling error shows that the odds are .95 that the population mean is 3.74 the population mean is 3.74 ++ 2(.0074). 2(.0074).

The sample of 1000 The sample of 1000 has a mean of 3.74 has a mean of 3.74

and a standard error and a standard error of .0074.of .0074.

Confidence intervalConfidence interval

The Sampling DistributionThe Sampling Distribution

SampleSample SampleSample SampleSample

The Sampling DistributionThe Sampling Distribution

SampleSample

4.44.24.03.83.63.43.23.0

5

0

5

0

SampleSample

4.44.24.03.83.63.43.23.0

5

0

5

0

SampleSample

4.44.24.03.83.63.43.23.0

5

0

5

0

The Sampling DistributionThe Sampling Distribution

SampleSample

4.44.24.03.83.63.43.23.0

5

0

5

0

SampleSample

4.44.24.03.83.63.43.23.0

5

0

5

0

SampleSample

4.44.24.03.83.63.43.23.0

5

0

5

0

AverageAverage AverageAverage AverageAverage

The Sampling DistributionThe Sampling Distribution

AverageAverage AverageAverage AverageAverage

4.44.24.03.83.63.43.23.0

15

10

5

0

The sampling The sampling distribution...distribution...

...is the distribution ...is the distribution of a statistic across of a statistic across an infinite number an infinite number

of samples.of samples.

SampleSample

4.44.24.03.83.63.43.23.0

5

0

5

0

SampleSample

4.44.24.03.83.63.43.23.0

5

0

5

0

SampleSample

4.44.24.03.83.63.43.23.0

5

0

5

0