Statistics in Psychology

• Key concepts include data types, data statements, relationships/associations, samples and populations, distributions of scores, and measures of central tendency (e.g., mean).

Why Study Statistics in Psychology?

• Psychology relies on empirical data, using observations and measurements.
• Measurements are systematic, not casual.
• Data is collected from many individuals.
• Systematic data collection involves assigning scores or categorizing behavior and organizing data into measurement sets for analysis.
• Essential for making sense of large datasets.
• Aiding in summarizing information for clarity and sharing.

Public & Structured Analysis

• Data is summarized and shared using established methods.
• Conclusions must follow agreed principles and systems.

Identifying Behavior Patterns & Predictions

• Observations often compare two behaviors to uncover relationships between behaviors.
• Enables predictions and hypothesis testing about human behavior.

Making Sense of Data

• Ketchup preference study found vanilla-flavored ketchup more popular among both bottle-fed (20/30) and breast-fed (30/103) infants.
• Study correlated testosterone levels and violent behavior in prison inmates, also considering punishment duration.

Key Definitions

• Variable: Property with varying values.
• Score: Individual's value for a variable.
• Measurement Data: Numerical scores.
• Categorical Variable: Data not on a numeric scale.
• Population: Complete set of scores of interest.
• Sample: Subset of the population.
• Parameter: Number summarizing a population.
• Statistic: Number summarizing a sample.

Types of Data

• Measurement Data: Numerical values (e.g., test scores).
• Categorical Data: Count data/frequency (e.g., number of students).

Types of Data Statements

• Frequency Statements: How often scores occur.
• Association Statements: Relationships between two variables.

Statistical Activities

• Descriptive Statistics: Summarizes samples using graphs and statistics.
• Inferential Statistics: Draws conclusions about a population from a sample.

Core Statistical Concepts

• Summarizing: Representing data effectively.
• Standardization: Making comparisons across different datasets.
• Sampling Variability: Understanding fluctuations in sample data.
• Statistical Inference: Predictions based on sample data.

Research Studies & Key Concepts in Data Analysis

• Researchers conducted a public taste test with regular and vanilla-flavored ketchup.
• Participants indicated their infant feeding method (bottle-fed or breastfed).
• Hypothesis: Bottle-fed infants (vanilla-flavored formula) may prefer vanilla ketchup.
• Data representation used dark diamonds for vanilla ketchup preference and light diamonds for regular.
• Groups were divided into bottle-fed and breastfed.
• Bottle-fed individuals: 20 out of 30 preferred vanilla ketchup (66.7%), while breastfed: 30 out of 103 (29.1%).
• A higher percentage of bottle-fed individuals preferred vanilla ketchup.

Study 2: Testosterone & Prison Inmate Behaviour

• Examined the relationship between saliva testosterone which may influence levels and violent behavior, which can be measured by punishment days per infraction in 15 prison inmates.
• A scatter plot displayed the data to identify patterns.
• Higher testosterone levels correlated with a longer punishment, shown by a positive correlation.

Key Concepts in Research & Statistics

• Variables can take different values.
• Saliva testosterone concentration and number of days of punishment per infraction are examples of measurement variables.
• Infant feeding method and ketchup preference are examples of categorical variables.
• A score is a specific value for a variable.
• "Bottle-fed" is a score for the feeding method variable.

Types of Data

• Measurement data: Ordered numerical values like testosterone levels and punishment days.
• Categorical data: Non-numerical categories like bottle-fed vs. breastfed.

Populations & Samples

• Population: The full set of scores of interest.
• Sample: A subset of scores used for study.
• Prison inmate study used sample of 15, aiming to understand a larger population.

Parameters & Statistics

• Statistic: Summary of a sample (e.g., "66.7% preferred vanilla ketchup").
• Parameter: Summary of a population.

Key Takeaways

• Research studies analyze categorical or measurement-based variables.
• Data is often from samples, but conclusions aim at understanding the larger population.
• Statistical summaries help make sense of data.
• Scatter plots can identify relationships between variables.

Video 03

• Measurement Data: Scores on a numeric scale (e.g., Saliva testosterone scores in the prison study).
• Categorical Data: Numerical count of items in categories (e.g., Number of people preferring vanilla ketchup).

Types of Data Statements

• Frequency Statements: Example is "How many people preferred vanilla ketchup?", expressed as percentages.
• Association/Relationship Statements: Relationships between two variables. Example "Is there a link between infancy feeding method and ketchup preference?" - Uses scatter plots for measurement data, and associations help in predicting one category based on another.

Types of Statistical Activity

• Summarizing key data points, graphically or numerically.
• Drawing conclusions about a population based on a sample, to make general conclusions beyond the study group.

Key Concepts

• Summarizing Data: Meaningful summaries of raw data.
• Standardization: Defining high versus low scores and strong versus weak relationships between variables.
• Sampling Variability (Sampling Error): Different samples yield slightly different results.
• Statistical Inference: Making general conclusions using sample data.

Statistical Inference - Sample Size and Effect Size

• Small sample: unreliable conclusions.
• Large sample: more reliable conclusions.
• Large difference is strong evidence.
• Small difference is weak evidence.

Key Takeaways

• Measurement and categorical data are used.
• Descriptive and inferential statistics are used to interpret research findings.
• Summarizing, standardization, sampling variability, and inference are essential.
• Larger sample sizes and bigger differences provide more reliable conclusions.

Score/Numerical Measurement

• Definition: Assigning a numerical value.
• These numerical measurements are called scores.
• Numbers quantify the variable, indicating higher or lower values.

Nominal/Categorical/Category Measurement

• Definition: Deciding to which category a variable belongs.
• Qualitative measure
• No numbers are involved and are described in words

Measurement Scales - Frequency

• A count of how often something occurs in data.
• Numbers can be frequencies or scores, and careful distinction avoids confusion.

Four Measurement Scales

• Nominal Categorization: Places cases into named categories.
• Ordinal (or Rank) Measurement: Orders scores from smallest to largest.
• Interval Measurement: Intervals between numbers are equal.
• Ratio Measurement: Is like interval measurement, but with an absolute zero point.

Key Points

• Clarity of Thinking: Identify numerical scores vs. categories.
• Avoid Assumptions: Numbers could be frequencies.
• Statistical Understanding: Precision in understanding terms is crucial.

Scales of Measurement

• Nominal Categories: Puts variables into categories, and do not correspond to numerical values.
• Ordinal Measurement or Ranks: Scores ordered from smallest to largest, implying only rank order (e.g. 1st, 2nd).
• Interval Measurement: Magnitude indicated by score differences, based on interval.
• Ratio Measurement: Allows meaningful ratio calculations and has a meaningful zero.

Characteristics of Different Scales of Measurement

• It is hard to separate how it applies to data in practice
• It is difficult to distinguish between ordinal, interval, scales of measurement
• Psychological scores do not have directly observable physical basis and cant decide if they consist of intervals or have an absolute zero.
• The most convincing examples come from the physical world and not psychology itself.

Measurement Controversy in Psychology

• Longtime problem causing great controversy.
• Current usage of statistics in psychology largely ignores the distinctions.
• Some psychologists prefer to regard some data as rankable, lacking qualities that are of interval/ratio data so it can cause issues in adopting statistical methods.

Use of Measurement Scales in SPSS

• Nominal and ordinal terms are used as described above for categorizing variables
• SPSS combines interval and ratio levels under the name 'scale'

Systematic Empiricism

• Definition: Structured approach to data.
• Relevance: Ensure reliable and valid observations, and to distinguish psychological science.

Replication of Findings

• Repeating a study to confirm its results
• Relevance: Helps establish reliability, and building knowledge in psychology.

Replicability of Methods

• Procedures used in a study are detailed.
• Relevance: Allows other scientists to transparency to verify results.

Publicly Verifiable Knowledge

• Scientific findings are accessible to others for verification, by Publishing research in peer-reviewed journals and sharing data and methodologies.
• Relevance: Allows scientific community to build on findings.

Testable Theories

• Definition: Hypotheses/models that empirically testable.
• Relevance: Theories must be testable to and being scientific.

Variables - Tables and Diagrams

• Raw Data: Unprocessed information, and structuring data communicates characteristics.
• Importance of Clarity: Must be clear and concise.

Box 3.1 Focus on: Multiple Responses

• Avoid Multiple Responses: Complicates data analysis.
• Dummy Coding: Handles multiple responses by creating variables, and coding the presence or absence of each response

Choosing Tables and Diagrams

• Apply descriptive statistics and techniques for understanding trends, patterns, and irregularities.
• Quantitative researchers should spend the same time with familiarizing themselves with data as quantitative researcher do
• Descriptive statistics help in understanding anticipation of problems.
• Use tables and diagrams to find new connections with the data.
• Determine if data is scores or categories, the charts or tables must be correctly labeled, avoid multiple responses in the data,
• Make sure diagrams that are chosen are clear, and combine the less frequent categories if needed.

Tables and Diagrams for Nominal Data

• Frequency Tables: Show frequencies in each category.
• Broaden categories to help with trends, and also help keep categories low if the sample set is small.
• Pie Diagrams: Has slices expressing each category and make sure to avoid confusion.
• Bar Charts: Represent the size of each category and should be easy to read and understandable.

Choosing Tables and Diagrams (Continued)

• Bar Charts should avoid overcrowding, and use the right amount of categories
• Ensure the vertical axis is labeled correctly with percentage or amounts with the bars being equal width.

Numerical Score Data

• When dealing with a lot of scores, the data should be grouped in ranges.

Handling Numerous Scores

• Use bands and cutoffs to help organize the data and keep in mind to label correctly for effective communication within the chart.

Errors to Avoid

• Always use titles and labels for the analysis's with clear descriptions.
• Only focus on the data that is for a single variabe.

Computer Analysis

• Computer Analysis: Name variable, labels, and what measure is being worked with through analysis.
• Data View: Enter value category for each case within study if needed.
• Charts: Move chart type into box for effect communication to analysis.

Notes on Distributions and Frequency Data

• Goal is to describe and summarize these scores to understand how they vary.
• Frequency Distribution a organize data to understand these scores better and can be shown within graphs, figures, and charts.

Histograms

• Is a graphical representation where it will break down the scores within their groups.

Distribution Of Scores

• Can be shown through Tables or Graphs to help understand that data in a better more detailed way.
• Data can differ with groupings of bins if broken down to individual details
• The major features of a distribution always remain Consistent within data no matter the group.

Number of Major Peaks

• Bimodal and Uni-modal distributions have single major peaks within the group.

Symmetry and Skewness

• Symmetrical Distribution is when the center is drawn that both sides are similar to each other.
• Skewed Distribution both negatively and positively effect the direction within each distribution.