Psychological Statistics Notes

Introduction to Psychological Statistics

Importance of Statistics

• Statistics serves as a link between a research idea and usable conclusions.
• Without statistics, interpreting massive amounts of information in data would be impossible.
• Statistics helps us think critically about numbers, their resources, and the procedures used to generate them.
• Examples:
  • “4 out of 5 dentists recommend Sensodyne.”
  • “More than 80% of dentists recommend Colgate.”
  • “Condoms are effective 94% of the time.”
  • “There is an 80% chance that in a room full of 30 people, at least two people will share the same birthday.”

Basic Concepts

• Statistics Definition:
  • General field of mathematics involving numerical facts and figures.
  • Relies heavily on how numbers are chosen and interpreted, not just calculations.
  • A range of techniques and procedures for analyzing, interpreting, displaying, and making decisions based on data.

Types of Statistics

1. Descriptive Statistics
   • Describe, summarize, and organize data in a meaningful manner.
2. Inferential Statistics
   • Make inferences from the sample and generalize them to the population.

Population and Sample

• Population: The entire set of individuals of interest in a particular study.
• Sample: A set of individuals selected from a population, intended to represent the population in a research study.

Parameters and Statistics

• Parameter: A value (usually numerical) that describes a population; derived from measurements of individuals in the population.
• Statistic: A value (usually numerical) that describes a sample; derived from measurements of individuals in the sample.

Variables and Measurement

• Constructs: Internal attributes or characteristics that cannot be directly observed but are useful for describing and explaining behavior.
• Operational Definition:
  • Identifies a measurement procedure (a set of operations) for measuring an external behavior.
  • Uses the resulting measurements as a definition and a measurement of a hypothetical construct.
  • Describes a set of operations for measuring a construct.
  • Defines the construct in terms of the resulting measurements.
• Examples of Constructs and Operational Definitions:
  • Construct: Online post-purchase guilt
    • Operational Definition: Degree of feeling remorse and shame after the internet shopping passion of consumer fades.
  • Construct: Perceived usefulness
    • Operational Definition: The degree to which a person believes that using a system would be free of effort.
  • Construct: Perceived compatibility
    • Operational Definition: The degree to which an innovation is perceived as being consistent with the existing values, needs, and past experiences.
• Variable: A characteristic or condition that changes or has different values for different individuals.
  • Example: Grade 10 students’ level of stress, anxiety, and their physical health during the 1st quarter of the academic year. Stress, anxiety, and physical health are the variables.

Independent and Dependent Variables

• Independent Variable: The variable that is manipulated to observe its effect.
• Dependent Variable: The outcome or response that is measured.
• Examples:
  • Study: Can blueberries slow down aging? 19-month-old rats were fed a standard diet or a diet supplemented with blueberry, strawberry, or spinach powder. Memory and motor skills were tested after 8 weeks. Blueberry supplementation showed the most notable improvement.
    • Independent Variable: Type of diet supplementation (blueberry, strawberry, spinach).
    • Dependent Variable: Memory and motor skills.
  • Study: How bright should brake lights be? An automobile manufacturer wants to know how bright brake lights should be to minimize the time required for a driver to realize the car in front is stopping.
    • Independent Variable: Brightness of brake lights.
    • Dependent Variable: Reaction time of the driver.
  • Study: Does beta-carotene protect against cancer? 39,000 women were given beta-carotene supplements or a placebo.
    • Independent Variable: Beta-carotene supplement or placebo.
    • Dependent Variable: Cancer rates.

Quantitative and Qualitative Variables

• Qualitative Variables: Values do not imply a numerical ordering; also known as categorical variables.
• Quantitative Variables: Variables that are measured in terms of numbers.

Discrete and Continuous Variables

• Discrete Variable: Consists of separate, indivisible categories; no values can exist between two neighboring categories.
  • Examples: Children in a family, number of students, gender, occupation.
• Continuous Variable: An infinite number of possible values exist between any two observed values; divisible into an infinite number of fractional parts.
  • Examples: Height, weight, time.
• Real Limits: The boundaries of intervals for scores represented on a continuous number line.
  • The real limit separating two adjacent scores is located exactly halfway between the scores.
    • Upper Real Limit: Top of the interval.
    • Lower Real Limit: Bottom of the interval.

Scales of Measurement

• Measuring the Dependent Variable (DV) to observe changes.
• Each variable is measured differently depending on its type.
• The measurement scale helps determine the statistics used to evaluate the data.
• Goal: Identify the type of measurement scale and understand its proper use and interpretation.
• Three important properties:
  1. Magnitude: Property of "moreness"; a higher score refers to more of something.
  2. Equal Intervals: Scale units along the scale are equal to one another.
  3. Absolute Zero: The scale has a true zero point, below which no value exists.

Types of Scales

• Nominal Scale:
  • Definition: Set of categories that have different names.
  • Examples: Gender, origin of country, marital status.
• Ordinal Scale:
  • Definition: Set of categories organized in an ordered sequence.
  • Examples: Car racing, drink size, sizes of clothes, socioeconomic status, education level.
• Interval Scale:
  • Definition: Consists of ordered categories that are all intervals of exactly the same size; zero does not indicate a total absence of the variable being measured.
  • Examples: Celsius and Fahrenheit.
• Ratio Scale:
  • Definition: An interval scale with the additional feature of an absolute zero.
  • Examples: Heartbeat, Kelvin, number of intimate relationships.

Properties of Scales

Numerical Operations and Descriptive Statistics

Sampling Error

• The naturally occurring discrepancy or error that exists between a sample statistic and the corresponding population parameter.

Statistical Notation

• $\sum$: Summation
• $\mu$: Population mean
• $\sigma$: Population standard deviation
• $X$: Score
• $M$: Sample mean
• $s$: Sample standard deviation
• $N$: Number of scores in a population
• $n$: Number of scores in a sample

Order of Mathematical Operations

1. Calculations within parentheses.
2. Squaring.
3. Multiplying and/or dividing (from left to right).
4. Summation.
5. Addition and/or subtraction.

Research Strategies

• A general approach to research determined by the type of question the study hopes to answer.

Types of Research Strategies

1. Descriptive Research Strategy
   • Focuses on individual variables and produces a description of individual variables as they exist within a specific group.
   • Data is a list of scores obtained by measuring each individual in the group being studied.
   • Example: On average, students at the local college spend 12.5 hours studying outside of class each week and get 7.2 hours of sleep each night.
2. Correlational Research Strategy
   • Examines the relationship between variables by measuring two (or more) variables for each participant.
   • Only attempts to describe the relationships – not trying to explain the relationship.
   • Correlation does not imply causation.
   • Example: There is a relationship between Facebook time and academic performance for college students, but we don’t know why.
   • Types of Correlations:
     • Linear: Data points form a straight-line pattern.
     • Curvilinear: Consistent, predictable relationship but the pattern is a curved line.
     • Positive: Both variables move in the same direction.
     • Negative: Each variable moves in different directions.
3. Experimental Research Strategy
   • Intended to answer cause-and-effect questions about relationships between two variables.
   • Creates two treatment conditions by changing the level of one variable then measures a second variable for the participant in each condition.
     • Manipulation
     • Control: Use random assignment or matching to control other variables and ensure equivalent groups or environments, respectively.
   • Example: Increasing the amount of exercise causes a decrease in cholesterol levels.
4. Quasi-Experimental Research Strategy
   • Attempts to answer cause-and-effect questions about the relationship between two variables but cannot produce an unambiguous explanation.
   • Uses some of the rigor and control that exists in experiments.
   • Quasi-experimental studies always contain a flaw that prevents the research from obtaining an absolute cause-and-effect answer.
   • Example: The treatment may cause a reduction in smoking behavior, but the reduced smoking may be caused by something else.
5. Non-Experimental Research Strategy
   • Intended to demonstrate a relationship between variables but does not attempt to explain the relationship and does not use rigor and control.
   • Example: There is a relationship between gender and verbal ability. Girls tend to have higher verbal skills than boys, but we don’t know why.

Research Designs

• A general plan for implementing a research strategy.
• Specifies whether the study will involve groups or individual participants, will make comparisons within a group or between groups, or how many variables will be included in the study.

Types of Validity

External Validity

• Refers to the extent to which we can generalize the results of a research study to people, settings, times, measures, and characteristics other than those used in that study.
• There is a threat to external validity when any characteristic of a study limits the ability to generalize the results from a research study.
• Three different kinds of generalizations:
  • Generalization from a sample to the general population.
  • Generalization from one research study to another.
  • Generalization from a research study to a real-world situation.
• Threats to External Validity:
  • Generalizing Across Participants or Species:
    1. Selection bias
    2. College bias
    3. Volunteer bias
    4. Participant characteristics
    5. Cross-species generalization
  • Generalizing Across Features of a Study:
    1. Novelty effect
    2. Multiple treatment interference
    3. Experimenter characteristics
  • Generalizing Across Features of the Measures:
    1. Sensitization
    2. Generality across response measures
    3. Time measurement

Internal Validity

• Refers to the production of a single, unambiguous explanation for the relationship between two variables.
• There is a threat to internal validity when the existence of any factor allows for an alternative explanation.
• Threats to Internal Validity:
  1. Extraneous Variable
  2. Environmental Variables
  3. Participant Variables
  4. Time-related Variables

Introduction to SPSS

• SPSS stands for “Statistical Package for the Social Sciences”.
• Software used for data analysis in research.
  1. Processing questionnaires
  2. Reporting in tables and graphs
  3. Analyzing: means, chi-square, correlation, regression, etc.
• SPSS comes into picture after data has been collected.
• Important factors to consider before data entry into SPSS:
  1. Question response formats:
     • Close-ended
       • Example: How is your satisfaction with the customer service of the staff of Jollibee? [ ] Excellent [ ] Good [ ] Bad [ ] Very Bad
     • Open-ended with numerical response
       • Example: What is your average expenditure in the café on a weekly basis? [PHP ___ per week]
     • Open-ended with text response
       • Example: I would like to have the assortment extended with the following products: ____
     • Multiple response questions
  2. Scale characteristics
  3. Levels of measurement
• SPSS has two tabs:
  • Data View
  • Variable View
• 'Data View' is where the numbers are inputted (e.g., survey responses).
• Each row represents a respondent's answers to a survey.
• Each column contains all the answers to a particular question by all respondents.
• 'Variable View' is where you see behind the data i.e., where you tell SPSS what the numbers represent.
• In 'Variable View' this is what the data looks like. Think of this part as putting a key to your graph, a way of telling people what the numbers represent.
• Each variable can be named. No spaces or special characters are allowed (just keep it to simple one word names).
• SPSS can deal with words as well as numbers, but the 'Type' of data should mostly be numeric. Data made up of words is called 'String' data
• This is where you can give your variable a meaningful label. This will be the label that appears in tables and graphs.
• The 'value' tab is where you turn your numbers into meaningful values. E.g., 1 = Female, 2 = Male