From Samples to Populations

STAT 20: Introduction to Probability and Statistics

Adapted by Gaston Sanchez

Vocabulary

Terms

  • Sample
  • Population
  • Statistic
  • Parameter

Populations and Samples

Interested in

Often we want to know something about the population:

  • Proportion of female fish (out of all fish)

  • Proportion of male fish (out of all fish)

  • Average weight (of all fish)

  • Average number of fins (of all fish)

We call these Parameters

Typical limitations

But we don’t have access to all of its individuals

  • Hard to observe population

  • Not enough time

  • Not enough money

  • Not enough resources

  • ETC

From the sample …

We can catch some fish and calculate:

  • Proportion of female fish (in sample)

  • Proportion of male fish (in sample)

  • Average weight (in sample)

  • Average number of fins (in sample)

We call these Statistics

Estimation Idea

Estimation (Generalization) Idea

To help you remember


Estimation

Estimating Parameters

Estimate parameters:

  • population mean
  • population proportion


BTW:

  • We never estimate statistics
  • Watch out for estimation errors

Sampling (in practice)

Sampling: Sources of Error

Sources of Error: Bias and Variance

Types of Bias

  • Selection Bias: When not all units in the population are equally likely to be selected for the sample.

  • Measurement Bias: When your process of measuring a variable systematically misses the target in one direction.

    • when questions are confusingly worded or leading,
    • when respondents may not be comfortable answering honestly.
  • Non-response Bias: When certain units originally selected for the sample fail to provide data

Solution (ideal): Simple Random Sample (SRS)

Types of Variation

  • Sampling Variability: the variability from one sample to the next


  • Measurement Variability: When we take multiple measurements on the same object and we get variations in measurements from one sample to the next.

Sampling Distribution

What is a Sampling Distribution?

Sampling Distribution is the distribution of a statistic upon repeated sampling.


No longer are we considering the (usually unknowable) distribution of the population or the observed distribution of the data


Usually the sampling distribution is a hypothetical thing: what would our statistic have looked like if we had taken a different sample of data?

Demo

Worksheet

35:00

Lab-4: Elections

35:00