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Introduction To inferential statistics, Lecture notes of Statistics

American University in CairoStatistics

inferential statistics,statistics,introduction to inferential statistics,statistics (field of study),statistical inference,descriptive statistics,introduction,statistics for bba,statistics for mba,statistics for bcom,statistical tests,statistical significance,point and interval estimates,education,inference,experimental group,correlation,quantitative variable,hypothesis testing,population,mathematics,control group,margin of error

Typology: Lecture notes

2022/2023

Available from 04/02/2023

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Lecture (chapter 6):
Introduction to inferential
statistics: Sampling and the
sampling distribution
Ernesto F. L. Amaral
February 12–14, 2018
Advanced Methods of Social Research (SOCI 420)
Source: Healey, Joseph F. 2015. ”Statistics: A Tool for Social Research.” Stamford: Cengage
Learning. 10th edition. Chapter 6 (pp. 144–159).
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Lecture (chapter 6):

Introduction to inferential

statistics: Sampling and the

sampling distribution

Ernesto F. L. Amaral

February 12–14, 2018 Advanced Methods of Social Research (SOCI 420) Source: Healey, Joseph F. 2015. ”Statistics: A Tool for Social Research.” Stamford: Cengage Learning. 10th edition. Chapter 6 (pp. 144–159).

Chapter learning objectives

  • Explain the purpose of inferential statistics in terms of generalizing from a sample to a population
  • Define and explain the basic techniques of random sampling
  • Explain and define these key terms: population, sample, parameter, statistic, representative, EPSEM sampling techniques
  • Differentiate between the sampling distribution, the sample, and the population
  • Explain the two theorems presented 2

Basic logic and terminology

  • Statistics are mathematical characteristics of samples
  • Parameters are mathematical characteristics of populations
  • Statistics are used to estimate parameters 4 Statistic Parameter

Samples

  • Must be representative of the population
    • Representative: The sample has the same characteristics as the population
  • How can we ensure samples are representative? - Samples drawn according to the rule of EPSEM ( e qual p robability of s election m ethod) - If every case in the population has the same chance of being selected, the sample is likely to be representative 5

Source: Babbie 2001, p.184. 7

Nonprobability sampling

EPSEM sampling techniques

  1. Simple random sampling
  2. Systematic sampling
  3. Stratified sampling
  4. Cluster sampling 8

Example

  • You want to know what percent of students at a large university work during the semester
  • Draw a sample of 500 from a list of all students (N=20,000)
  • Assume the list is available from the Registrar
  • How can you draw names so every student has the same chance of being selected? 10

Example

  • Each student has a unique, 6 digit ID number that ranges from 000001 to 999999
  • Use a table of random numbers or a computer program to select 500 ID numbers with 6 digits each
  • Each time a randomly selected 6 digit number matches the ID of a student, that student is selected for the sample
  • Continue until 500 names are selected 11

Example

  • Disregard duplicate numbers
  • Ignore cases in which no student ID matches the randomly selected number
  • After questioning each of these 500 students, you find that 368 (74%) work during the semester 13

Applying logic and terminology

  • In the previous example:
  • Population: All 20,000 students
  • Sample: 500 students selected and interviewed
  • Statistic: 74 % (percentage of sample that held a job during the semester)
  • Parameter: Percentage of all students in the population who held a job 14

2. Systematic sampling

  • Useful for large populations
  • Randomly select the first case then select every k th case
  • Sampling interval
    • Distance between elements selected in the sample
    • Population size divided by sample size
  • Sampling ratio
    • Proportion of selected elements in the population
    • Sample size divided by population size
  • Can be problematic if the list of cases is not truly random or demonstrates some patterning Source: Babbie 2001, p.197–198. 16

Example

  • If a list contained 10,000 elements and we want a sample of 1,
  • Sampling interval
    • Population size / sample size = 10,000 / 1,000 = 10
    • We would select every 10th element for our sample
  • Sampling ratio
    • Sample size / population size = 1,000 / 10,000 = 1/
    • Proportion of selected elements in population
  • Select the first element at random Source: Babbie 2001, p.197–198. 17

Example

  • If you want a sample of 1,000 students
    • That would be representative to the population of students by sex and GPA
  • You need to know the population composition
    • E.g., women with a 4.0 average compose 15 percent of the student population
  • Your sample should follow that composition
    • In a sample of 1,000 students, you would select 150 women with a 4.0 average 19

Stratified, systematic sample

Source: Babbie 2001, p.202. 20