Research Methods and Statistics Summary PDF

Pierce's Four Paths of Establishing Knowledge (Ranked from weakest to strongest) 1.​ Method of Tenacity ○​ Holding onto familiar beliefs because they bring comfort and peace of mind. 2.​ Method of Authority ○​ Accepting something as true because an authority f...

Pierce's Four Paths of Establishing Knowledge (Ranked from weakest to strongest) 1.​ Method of Tenacity ○​ Holding onto familiar beliefs because they bring comfort and peace of mind. 2.​ Method of Authority ○​ Accepting something as true because an authority figure says so. 3.​ A Priori Method ○​ Relying on logical reasoning without direct observation. 4.​ Scientific Method ○​ The most reliable method, using systematic observation, experimentation, and data analysis. Dialectics in Research (Contrasting Research Approaches) Basic vs. Applied Research ​ Basic Research: Expands knowledge, tests theories. ​ Applied Research: Solves real-world problems, informs decisions. Lab vs. Field Research ​ Lab Research: Controlled settings, better precision. ​ Field Research: Real-world settings, more realistic findings. Inductive vs. Deductive Reasoning ​ Deductive (Top-Down): 1.​ Start with a hypothesis 2.​ Collect data 3.​ See if data supports or rejects hypothesis ​ Inductive (Bottom-Up): 1.​ Start with data collection 2.​ Identify patterns 3.​ Formulate a conclusion (which can later be tested deductively) Qualitative vs. Quantitative Research Qualitative Research (Exploratory, In-Depth) ​ Open-ended questions ​ In-depth interviews ​ Focus groups ​ Helps generate background information ​ Useful in problem formation ​ Seeks input from individuals (e.g., consumers) Quantitative Research (Statistical, Measurable) ​ Best for generalizing results  ​ Identifies differences between groups ​ Statistical analysis ​ Data collection methods: ○​ Observations ○​ Surveys ○​ Experiments Measurement & Conceptualization What is Measurement? ​ Links abstract concepts to real-world observations. ​ Follows rules for assigning numbers to represent attributes. Ways to Measure a Concept (Example: Reading) ​ Self-report (e.g., survey asking how often someone reads) ​ Observation (e.g., tracking time spent reading) ​ Existing Data (e.g., using library records, secondary data) Concepts in Research ​ A generalized idea about a class of objects, attributes, or processes. ​ Examples of Advertising-Related Concepts: ○​ Advertising efficacy ○​ Brand equity ○​ Product use ○​ Brand loyalty Conceptual Definition vs. Operational Definition ​ Conceptual Definition: ○​ A verbal explanation of a concept. ○​ Defines what it is and what it is not. ○​ Example: "Attitude" in advertising research means a person's evaluative judgment of a product, ad, or brand. ​ Operational Definition: ○​ Specifies how we measure the concept. ○​ Ensures the concept is observable and testable. ○​ Example: Measuring "attitude" through survey responses on a Likert scale (1 = very unfavorable, 5 = very favorable). Operationalism ​ Ensures scientific concepts are grounded in observable, measurable events. ​ Eliminates subjectivity (feelings, intuitions). ​ Allows others to replicate the measurement process. Steps to Develop an Operational Definition 1.​ Specify the concept of interest 2.​ Identify different aspects of the concept's meaning 3.​ Explicitly state observable indicators  4.​ Select the best method(s) of measurement Conceptualization vs. Operationalization ​ Conceptualization: Defining a variable (e.g., what does "intelligence" mean?). ​ Operationalization: How you measure the variable (e.g., IQ test scores). ​ Example: ○​ Conceptualizing "Age": Age is the number of years a person has lived. ○​ Operationalizing "Age": Asking "How old are you?" in a survey with a textbox entry or number range. Descriptive Statistics Descriptive statistics summarize data. A. Measures of Central Tendency (Find the "center" of data) ​ Mean: The average. ​ Median: The middle score. ​ Mode: The most frequent score. ​ Application: Income distributions often have a positive skew, meaning the median is a better measure than the mean. B. Measures of Variability (Spread of data) ​ Range: Maximum score - Minimum score. ​ Standard Deviation (SD): How much scores vary from the mean. ​ Variance: The squared differences from the mean. ​ Z-Score: How many standard deviations a score is from the mean. ○​ Formula: Z = (X - μ) / σ ○​ Interpretation: Helps compare scores across different distributions. C. Frequency Distributions ​ Used to visualize data distribution. ​ Types: ○​ Frequency polygons (e.g., tracking sardine sizes over 16 seasons). ○​ Histograms (used to check skewness). ○​ Normal distribution curves. Probability Distributions ​ Normal Distribution: Bell-shaped curve where the mean = median = mode. ​ Skewed Distributions: ○​ Positive Skew: Tail on the right (e.g., income data). ○​ Negative Skew: Tail on the left. Measures of Dispersion (Spread) ​ Deviation Scores: Differences between each observation and the mean.  ​ Mean Squared Deviation: Squaring each deviation and averaging. ​ Formulas: ○​ Population Mean (μ): ΣX / N ○​ Sample Mean (X̄): ΣX / n ○​ Variance (σ² or s²): Σ(X - X̄)² / (n-1) Ethical Considerations in Research ​ Ensuring validity & reliability of data. ​ Avoiding misleading correlations (e.g., spurious relationships). ​ Reporting results transparently. Study Set: Research Methods, Measurement & Ethics Conceptualization vs. Operationalization ​ Conceptualization: Defining a variable (e.g., "Age is the number of years a person has lived"). ​ Operationalization: Measuring a variable in a study (e.g., "How old are you?" with a textbox entry for numerical input). Descriptive Statistics ​ Mean: The average value. ​ Median: The middle score when data is ordered. ​ Mode: The most frequently occurring value. Variability (Spread of Data) ​ Range: Max score - Min score (Difference between highest & lowest values). ​ Standard Deviation (SD): Measures how much scores vary from each other. ​ Z-Score: Shows how far a single score is from the mean in standard deviation units. Normal Distribution & Standardization ​ Normal Distribution (Bell Curve) ○​ Most values fall within ±3 SDs. ○​ IQ scores are an example of normally distributed data. ​ Standardized Normal Distribution: ○​ Mean = 0, SD = 1. ○​ Used to compare different distributions. Ethics in Research ​ Deontological Ethics: ○​ Actions are inherently right or wrong. ○​ Rights Principle: ​ Universality (applies to everyone). ​ Reversibility (Golden Rule: treat others as you’d want to be treated). ○​ Justice Principle:  ​ Distributive: Fair allocation. ​ Retributive: Punishment should fit the wrongdoing. ​ Compensatory: Harm should be restored (e.g., insurance). ​ Teleological Ethics (Utilitarianism): ○​ Focuses on the greatest good for the greatest number. ○​ Ethical evaluation is based on consequences. ○​ Key questions: ​ What are the harms and benefits? ​ What’s the least harm I can do? Research Ethics Guidelines ​ Respect for Persons: Informed consent & protection of vulnerable individuals. ​ Beneficence: "Do no harm" while maximizing research benefits. ​ Justice: Fair distribution of benefits and burdens. Other Considerations: ​ Voluntary participation ​ No harm to participants ​ Anonymity & confidentiality ​ Informed consent ​ Minimizing deception Levels of Measurement 1.​ Nominal: Categories (e.g., gender, race) – Only mode can be calculated. 2.​ Ordinal: Ranked order (e.g., satisfaction ratings) – Median & mode. 3.​ Interval: Equal intervals, no true zero (e.g., temperature) – Mean, median, mode. 4.​ Ratio: Absolute zero exists (e.g., weight, income) – Allows full statistical analysis. 💡 Rule: Always collect data at the highest level possible for better analysis. Study Set: Research Methods & Ethics Statistics & Variability ​ Variance: Measures how far each number in a dataset is from the mean (squared units). ​ Standard Deviation (SD): Square root of variance; measures average deviation from the mean. ​ Sample Variance Formula: S2=∑(X−Xˉ)2n−1S^2 = \frac{\sum (X - \bar{X})^2}{n-1}S2=n−1∑(X−Xˉ)2 ​ Sample Standard Deviation Formula: S=∑(X−Xˉ)2n−1S = \sqrt{\frac{\sum (X - \bar{X})^2}{n-1}}S=n−1∑(X−Xˉ)2 Normal Distribution ​ Bell Curve: Most values fall within ±3 SDs. ​ Standardized Normal Distribution: ○​ Mean = 0, SD = 1 ○​ Symmetrical & continuous  ○​ Total area under curve = 1.0 ​ Z-Scores: Standardized values calculated as Z=X−μσZ = \frac{X - \mu}{\sigma}Z=σX−μ ​ Why Standardization Matters: ○​ Makes different scores comparable. ○​ Helps determine probabilities in a normal distribution. ○​ Useful for central limit theorem applications. Ethics in Research ​ Ethics: Principles guiding right vs. wrong in research. ​ Deontology (Duty-Based Ethics): ○​ Actions are inherently right or wrong. ○​ Rights Principle: ​ Universality: If an action is right for one, it should be right for all. ​ Reversibility: Golden rule – treat others as you’d like to be treated. ○​ Justice Principle: ​ Distributive: Fair allocation of resources. ​ Retributive: Punishment should fit the wrongdoing. ​ Compensatory: Those harmed should be restored. ​ Teleology (Consequence-Based Ethics): ○​ Utilitarianism: Maximizing good for the greatest number. ○​ Questions to consider: ​ What are the harms and benefits? ​ How can harm be minimized? Code of Ethics in Research 1.​ Respect for Persons: ○​ Informed consent ○​ Protection of vulnerable individuals 2.​ Beneficence: ○​ Minimize harm ○​ Maximize benefits 3.​ Justice: ○​ Fair distribution of research benefits and burdens Other Ethical Issues: ​ Voluntary participation ​ No harm to participants ​ Anonymity & confidentiality ​ Informed consent ​ Minimized deception Research Process ​ Research Question: A question guiding the study. ​ Hypothesis: A predictive statement tested through research.  ​ Scientific Method: Research is necessary to verify or refute beliefs. Levels of Measurement 1.​ Nominal: Labels/categories (e.g., gender, race) – Mode only. 2.​ Ordinal: Ordered categories (e.g., rankings) – Median & mode. 3.​ Interval: Equal intervals, but no true zero (e.g., temperature) – Mean, median, mode. 4.​ Ratio: True zero exists (e.g., weight, income) – Full range of statistical operations.