Page 1: Introduction

Instructor Information

• Psychological Statistics

• Instructor: Jade G. Villanueva, CSPE, RPm

Page 2: Definition of Psychological Statistics

Overview

• Psychological Statistics encompasses:

  • The art and science of collecting data

  • Presenting data in various forms

  • Analyzing data for interpretation

  • Utilization in psychological reports and materials

Page 3: Descriptive vs. Inferential Statistics

Key Differences

• Descriptive Statistics:

  • Collection and presentation of data.

• Inferential Statistics:

  • Interpretation and usage of data derived from descriptive statistics.

Page 4: Types of Measurement

Data Classification

• Continuous Data:

  • Measures that allow varying degrees of precision.

• Non-Continuous (Discrete) Data:

  • Measured in whole units.

Page 5: Measurement of Scales

Four Types of Scales (according to Stevens)

1. Nominal Scales:

   • Measures of identity, e.g., classifications like gender or religion.

2. Ordinal Scales:

   • Used for ranking, provides relational information about size or preference.

3. Interval Scales:

   • Reflect numerical differences, e.g., test scores and temperature readings.

4. Ratio Scales:

   • Highest type of scale, measures such as length and weight.

Page 6: Statistical Symbols

Symbol Definitions

• ∑: sum of

• f: frequencies

• F: cumulative frequencies

• n: sample size

• N: population size

• i: interval

• X: independent variable

• Y: dependent variable

• µ: population mean

Page 7: Sample and Population

Definitions

• Population:

  • Total number of objects under investigation.

• Sample:

  • Representative subset from the population.

Sampling

• Obtaining a sample is referred to as sampling, especially when the population is large.

Page 8: Categories of Sampling

Types of Sampling

• Probability Sampling:

  • Random selection leading to strong statistical inference.

• Non-Probability Sampling:

  • Non-random selection based on convenience or criteria, easier data collection but less reliability.

Page 9: Probability Sampling Techniques - Simple Random Sampling

Overview

• Every member of the population has an equal chance of selection.

• Example: Select 1000 employees randomly by assigning numbers and using a random generator.

Page 10: Probability Sampling Techniques - Systematic Sampling

Description

• Similar to simple random, but involves regular intervals in selection.

• Example: Start at a random point and select every 10th person from an ordered list of employees.

Page 11: Probability Sampling Techniques - Stratified Sampling

Methodology

• Population is divided into subgroups (strata) for adequate representation.

• Example: Stratifying by gender to ensure valid representation when sampling.

Page 12: Probability Sampling Techniques - Cluster Sampling

Explanation

• Random selection of entire subgroups rather than individuals.

• Example: Randomly choosing company offices for data collection.

Page 13: Probability Sampling Techniques - Area Sampling

Technique

• Areas divided into smaller units for sampling when full population frame is unavailable.

• Example: Using city maps to randomly sample blocks.

Page 14: Probability Sampling Techniques - Multi-Stage Sampling

Approach

• Used when clusters are still too large, can yield further sub-sampling.

• Example: Randomly selecting individuals from previously chosen clusters.

Page 15: Non-Probability Sampling Techniques - Judgment Sampling

Explanation

• Researcher selects a sample based on expertise to fit the research needs.

• Example: Selecting students with diverse needs to explore their experiences.

Page 16: Non-Probability Sampling Techniques - Convenience Sampling

Description

• Samples of readily available individuals, risky for bias.

• Example: Surveying classmates post-lessons, potentially unrepresentative.

Page 17: Non-Probability Sampling Techniques - Quota Sampling

Definition

• Non-random selection to meet specific quotas from targeted groups.

• Example: Dividing consumers by dietary preferences to gauge interest levels, ensuring diverse representation.

Page 18: Non-Probability Sampling Techniques - Panel Sampling

Overview

• Random selection of a panel for repeated surveys over time.

• Example: Monitoring vaccine participants over several assessments.

Page 19: Non-Probability Sampling Techniques - Snowball Sampling

Method

• Used for hard-to-access populations, relying on participants to recruit others.

• Example: Researching homelessness by gaining access through networks among the homeless.

Page 20: Sample Size Calculation

Common Calculation Method

• Slovin's Formula:

  • Used for determining sample size, factoring in margin of error.

  • Common margin of error in social science: 1% to 10% (90%-99% accuracy).

Page 21: Example 1 - Sample Size Calculation (Population = 2500)

Calculation Steps

• At 95% accuracy, margin of error is 5% (0.05).

• Formula Execution:

  • n = 2500 / (1 + 2500(0.05)^2)

Page 22: Example 1 - Continued Calculation

Results

• Continue calculations to find:

  • n = 2500 / (1 + 6.25)

  • Final size: n = 345 sampled.

Page 23: Example 2 - Sample Size Calculation (Population = 200)

Calculation Steps

• At 97% accuracy, margin of error is 3% (0.03).

• Formula Execution:

  • n = 200 / (1 + 200(0.03)^2)

Page 24: Example 2 - Continued Calculation

Results

• Following through leads to:

  • n = 200 / (1.18)

  • Final size: n = 169 sampled.

Page 25: Exercise 1

Task

• Find the sample size if the population is 9550 at 96% accuracy.

Page 26: Exercise 2

Task

• Find the sample size if the population is 11550 using a 0.07 margin of error.