Introduction to Inferential Statistics: Sampling and Sampling Distribution, Slides of Statistics for Psychologists

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Chapter 6 Introduction to

Inferential Statistics

Sampling and the

Sampling Distribution

Outline

• The logic and terminology of inferential

statistics

• Random sampling
• The sampling distribution

Logic And Terminology (cont.)

•                                                              
• Solution :

We choose a sample --

a carefully chosen

subset of the

population – and use

information gathered

from the cases in the

sample to generalize to

the population.

Basic Logic And Terminology

• Statistics are

mathematical

characteristics of

samples.

• Parameters are

mathematical

characteristics of

populations.

• Statistics are used to

estimate parameters.

PARAMETER

STATISTIC

Random Sampling Techniques

• Simple Random Sampling (SRS)
• Systematic Random Sampling
• Stratified Random Sampling
• Cluster Sampling

Suppose we select a random sample of 500 from a university student body and find that 74% of our sample has worked during the semester….

• Population = All 20,000 students.
• Sample = The 500 students selected and

interviewed.

• Statistic =74% (% of sample that held a job

during the semester).

• Parameter = % of all students in the

population who held a job.

The Sampling Distribution

• Every application of inferential statistics involves 3 different distributions.
• Information from the sample is linked to the population via the sampling distribution.

Population

Sampling Distribution

Sample

The Sampling Distribution: Properties

1. Normal in shape.

2. Has a mean equal to the population mean.

x

3. Has a standard deviation (standard error)

equal to the population standard deviation

divided by the square root of N.

x

= σ/√N

Central Limit Theorem

• For any trait or variable, even those that are not normally distributed in the population, as sample size grows larger, the sampling distribution of sample means will become normal in shape.
• The importance of the Central Limit Theorem is that it removes the constraint of normality in the population.

The Sampling Distribution

• The Sampling Distribution is normal so we can

use Appendix A to find areas.

• We do not know the value of the population

mean (μ) but the mean of the S.D. is the same

value as μ.

• We do not know the value of the pop. Stnd.

Dev. (σ) but the Stnd. Dev. of the S.D. is equal

to σ divided by the square root of N.