PSY 002: Introduction to Psychological Statistics

Introduction to Statistics

• Statistics refers to a set of mathematical procedures for organizing, summarizing, and interpreting information.
• It is a branch of mathematics that deals with the collection, organization, and interpretation of data.

Purpose of Statistics in Research

• Organize and summarize information to see what happened to the research study.
• Communicate the results to others.
• Answer general questions that initiated the research by determining exactly what conclusions are justified based on the results obtained.

Population and Samples

• Population: The set of all individuals of interest in a particular study, denoted by N.
• Sample: A set of individual selected from a population, usually intended to represent the population in a research study, denoted by n.
• Relationship between a population and a sample: a sample is a subset of the population.

Parameters and Statistics

• Parameter: A numerical value that describes a population, obtained from the population.
• Statistic: A numerical value that describes a sample, an estimate of a parameter, obtained from a sample.

Variables and Data

• Variable: A characteristic or condition that changes or has different values for different individuals.
• Data: Measurements or observations, facts or set of information or observation under study.
• Classification of variables:
  • Discrete Variables: consists of separate, indivisible categories.
  • Continuous Variables: has an infinite number of possible values that fall between any two observed values.
• Classification of data:
  • Metric Data: data obtained by measurement.
  • Enumeration Data: data obtained by counting.
  • Categorical Data: data which can be classified into groups or categories of responses.

Scales of Measurement

• Nominal Scale: consists of a set of categories that have different names, used for identification purposes.
• Ordinal Scale: consists of a set of categories that are organized in an ordered sequence, used to rank observations.
• Interval Scale: has an arbitrary zero point, used to specify the amount of difference.
• Ratio Scale: anchored by a zero point that is not arbitrary, used to specify the amount of difference.

Statistical Notations

• Descriptive Statistics: used to summarize, organize, and simplify data.
• Inferential Statistics: used to make generalizations about a population from a sample.

Sampling Error

• Sampling Error: the discrepancy between a sample statistic and the corresponding population parameter.

• Margin of Error: the maximum likely size of the sampling error when the sampling is random.### Sampling Techniques

• Bias in sampling can occur due to various reasons, such as: • Bias in choosing samples • Typographical errors or wording used in questionnaires • Undesirable answers in surveys or polls • Low response rates

Probability Sampling

• Definition: A sampling technique where each member or element of the population has an equal chance of being selected as a member of the sample.
• Assumptions: • The researcher has a complete list of the members of the population. • The selection of members of the sample is not predetermined.
• Characteristics: • Sampling without bias • Every member of the population has an equal opportunity to be part of the sample
• Techniques: • Simple Random Sampling (SRS) • Systematic Sampling • Stratified Sampling • Cluster Sampling • Multi-Stage Sampling

Simple Random Sampling (SRS)

• Definition: A technique of drawing a sample where each element of the population has an equal chance of being taken into the sample.
• Characteristics: • The most basic form of probability sampling • Unbiased • Saves time and resources
• Example: Lottery, Table of Random Digits

Systematic Sampling

• Definition: A technique of choosing an element for every k elements of a population.
• Characteristics: • Easy to implement • Time-efficient • Requires a starting point and sample size
• Example: Choosing every 10th individual from a population of 5000

Stratified Sampling

• Definition: A technique of dividing a population into groups (strata) and sampling is done in each stratum.
• Characteristics: • Ensures representation of the entire population • Can be used for both equal and proportional allocation
• Example: Dividing a population of 1000 families into high, average, and low socio-economic status groups

Cluster Sampling

• Definition: A technique of taking a sample from groups, and all the elements in those groups are chosen.
• Characteristics: • Identifies clusters based on demographic parameters • Simple and cost-effective
• Example: Dividing the US into states (clusters) to evaluate the number of immigrants

Multi-Stage Sampling

• Definition: A sampling technique in various stages until the desired sampling units are obtained.
• Characteristics: • Used for large-scale studies • Allows for flexibility in sample selection

Non-Probability Sampling

• Definition: A sampling technique where members of the sample are drawn from the population based on the judgment of the researcher.
• Characteristics: • Lacks objectivity • Results are relatively biased • Not suitable for making inferences about a population
• Techniques: • Convenience Sampling • Purposive Sampling • Snowball Sampling • Quota Sampling

Convenience Sampling

• Definition: A technique of selecting samples based on ease of access to subjects.
• Characteristics: • Used for pilot studies or exploratory research • Limited to no prior information available • Time-efficient and cost-effective

Purposive Sampling

• Definition: A technique of choosing sampling units from a given population with specific characteristics.
• Characteristics: • Used for studying specific populations or groups • Selection is based on the researcher's discretion

Snowball Sampling

• Definition: A technique of tracking a few categories to interview and derive results.
• Characteristics: • Used for difficult-to-reach populations • Used for sensitive topics

Quota Sampling

• Definition: A technique of setting a sample size based on the nature of the data needed.
• Characteristics: • Used for rapid collection of samples • Selection is based on pre-set standards

Determining Sample Size

• Formula: n = 1 / (1 + Nα^2)
• Where: • n = sample size • N = population size • α = level of significance (allowable error)
• Example: Calculating the minimum sample size for a survey of 5000 students with an error of at most 5%.### Psychological Statistics

Scales of Measurement

• Nominal scale: used to label or categorize data, e.g. religion, civil status, address
• Ordinal scale: used to rank data, e.g. IQ scores, size of a T-shirt
• Interval scale: used to measure data with equal intervals, e.g. speed of a car, temperature
• Ratio scale: used to measure data with a true zero point, e.g. land area, salary of workers

Descriptive vs. Inferential Statistics

• Descriptive statistics: used to describe and summarize existing data, e.g. computing the average grade of students, counting furniture in a school
• Inferential statistics: used to make predictions or inferences about a larger population based on a sample, e.g. predicting future sales, investigating the relationship between mental age and chronological age

Sample Size

• Errors in sample size: 1% error, 2.5% error, 5% error, 7.5% error, 10% error
• Formula for determining sample size: depends on population size and desired error margin

Presentation of Data

• Frequency distribution table: a table that displays the frequency of each value or range of values in a dataset
  • Types: simple, complete, relative, cumulative, cumulative percentage
• Graphs: used to visualize data
  • Types: bar chart, histogram, frequency polygon, pie chart, ogive