Psychology/Study Notes/Research Methods & Statistics

Research Methods & Statistics

Essential research methodology and statistical analysis for psychological research, including experimental design, data collection, and interpretation of results.

1. The Scientific Method 2. Research Designs 3. Sampling Methods 4. Data Collection Methods

5. Variables & Measurement 6. Descriptive Statistics 7. Inferential Statistics 8. Research Ethics

1. The Scientific Method

Steps of the Scientific Method

1
Identify Problem/Question
Observe phenomenon, review literature
2
Form Hypothesis
Testable prediction about relationship between variables
3
Design Research
Choose methodology, select participants
4
Collect Data
Implement study, gather information
5
Analyze Data
Apply statistical techniques
6
Draw Conclusions
Interpret results, accept/reject hypothesis
7
Report Findings
Publish, share with scientific community

Types of Hypotheses

Null Hypothesis (H₀)

States there is NO relationship or difference between variables.

"There is no significant difference in test scores between the two groups."

Alternative Hypothesis (H₁ or Ha)

States there IS a relationship or difference.

"Students who study more will have higher test scores."

Directional Hypothesis

Predicts specific direction of effect (one-tailed).

"Group A will score higher than Group B."

Non-directional Hypothesis

Predicts difference without direction (two-tailed).

"There will be a difference between Group A and Group B."

Characteristics of Good Research

Empirical

Based on observation

Systematic

Organized method

Objective

Unbiased

Replicable

Can be repeated

2. Research Designs

Experimental Research

Gold standard for establishing cause-and-effect relationships. Researcher manipulates independent variable and measures effect on dependent variable.

Requirements

• Manipulation of IV
• Random assignment
• Control group
• Control of extraneous variables

Strengths

• Establishes causation
• High internal validity
• Controlled conditions

Limitations

• Artificial setting
• Ethical constraints
• May lack generalizability

Quasi-Experimental Research

Similar to experiments but lacks random assignment. Uses pre-existing groups. Cannot definitively establish causation.

Example: Comparing depression levels between naturally formed groups (e.g., students who chose morning vs. evening classes)

Non-Experimental Research

Correlational Research

Measures relationship between two or more variables without manipulation. Cannot establish causation - only association.

Correlation coefficient (r): Ranges from -1.00 to +1.00

• Positive (+): Variables increase together
• Negative (-): One increases, other decreases
• 0: No relationship

⚠️ Correlation ≠ Causation

Descriptive Research

Describes characteristics of a population or phenomenon.

• Case study: In-depth study of one individual/group
• Survey: Questionnaires, interviews
• Naturalistic observation: Observe in natural setting
• Archival research: Use existing records/data

Experimental Designs Comparison

Design	Description	Strength	Weakness
Between-Subjects	Different participants in each condition	No order effects	Need more participants
Within-Subjects	Same participants in all conditions	Fewer participants needed	Order/practice effects
Mixed Design	Combination of both	Flexibility	Complex analysis
Matched Pairs	Participants matched on key variables	Controls individual differences	Matching is difficult

3. Sampling Methods

Key Terms

Population: Entire group of interest

Sample: Subset selected for study

Sampling Frame: List of population members

Representative Sample: Accurately reflects population

Probability Sampling (Random)

Every member has known, non-zero chance of selection. Preferred for generalizability.

Simple Random Sampling

Every member has equal chance of selection. Like drawing names from a hat.

Best for homogeneous populations

Stratified Random Sampling

Divide population into strata (subgroups), then random sample from each.

Ensures representation of subgroups (e.g., by gender, age, region)

Cluster Sampling

Divide population into clusters, randomly select entire clusters.

Cost-effective for geographically dispersed populations

Systematic Sampling

Select every kth member from a list (e.g., every 10th person).

Simple but beware of patterns in list order

Non-Probability Sampling

Selection not random. More convenient but less generalizable.

Convenience Sampling

Use readily available participants (e.g., psychology students).

⚠️ Most biased; limited generalizability

Purposive (Judgment) Sampling

Researcher selects participants based on specific criteria.

Used when expertise needed or for specific populations

Snowball Sampling

Participants recruit other participants through referrals.

Useful for hard-to-reach populations (e.g., drug users)

Quota Sampling

Non-random version of stratified; fill quotas for each subgroup.

Common in market research

Sampling Errors and Bias

• Sampling error: Difference between sample and population (unavoidable)
• Sampling bias: Systematic over/under-representation (avoidable)
• Selection bias: Non-random selection
• Non-response bias: Those who don't respond differ from those who do

4. Data Collection Methods

Surveys & Questionnaires

• Self-report measures
• Open-ended vs. closed-ended questions
• Likert scales (1-5 or 1-7)
• Can reach large samples

Limitations: Social desirability, response bias

Interviews

• Structured: Fixed questions
• Semi-structured: Flexible follow-up
• Unstructured: Open conversation
• Rich, detailed data

Limitations: Time-consuming, interviewer effects

Observation

• Naturalistic: Real-world setting
• Participant: Researcher joins group
• Non-participant: Observer role
• Direct behavior measurement

Limitations: Observer bias, Hawthorne effect

Psychological Tests

• Standardized measures
• Intelligence, personality, aptitude
• Established reliability/validity
• Normative data available

Limitations: Test anxiety, cultural bias

Types of Data

Type	Description	Examples	Statistics
Nominal	Categories, no order	Gender, eye color, diagnosis	Mode, chi-square
Ordinal	Categories with order	Rankings, Likert scales	Median, Spearman rho
Interval	Equal intervals, no true zero	Temperature (°C), IQ scores	Mean, Pearson r, t-test
Ratio	Equal intervals, true zero	Height, weight, reaction time	All statistics applicable

5. Variables & Measurement

Types of Variables

Independent Variable (IV)

Variable manipulated or controlled by researcher. Presumed cause.

Example: Type of therapy given

Dependent Variable (DV)

Variable measured as outcome. Presumed effect.

Example: Depression scores after treatment

Confounding Variable

Uncontrolled variable that affects DV. Alternative explanation for results.

Example: Age differences between groups

Extraneous Variables

Any variable other than IV that could affect DV. Must be controlled.

Example: Room temperature, time of day

Control Techniques

• Random assignment: Each participant has equal chance of being in any condition
• Counterbalancing: Vary order of conditions to control order effects
• Double-blind: Neither participant nor experimenter knows condition
• Single-blind: Only participant is unaware of condition
• Matching: Pair participants on key variables
• Holding constant: Keep variable same for all participants

Validity Types

Internal Validity

Degree to which results can be attributed to IV, not confounds. Can we conclude causation?

Threats: History, maturation, testing effects, selection bias, attrition

External Validity

Degree to which results can be generalized to other settings, populations, times.

Threats: Sample not representative, artificial lab setting

Construct Validity

Degree to which variables measure what they claim to measure.

Are we really measuring "anxiety" or something else?

Common Threats to Validity

• Hawthorne effect: Change behavior when observed
• Placebo effect: Improvement from expectation alone
• Demand characteristics: Clues about expected behavior
• Experimenter bias: Researcher influences results

• Practice effect: Improve due to familiarity
• Fatigue effect: Decline due to tiredness
• Social desirability: Give "acceptable" responses
• Regression to mean: Extreme scores move toward average

6. Descriptive Statistics

Descriptive statistics summarize and describe data. They do not make inferences about the population.

Measures of Central Tendency

Mean (M or X̄)

Arithmetic average. Sum ÷ N

Best for: Normal distribution, interval/ratio data

Limitation: Affected by outliers

Median (Mdn)

Middle value when data ordered

Best for: Skewed data, ordinal data

Strength: Not affected by outliers

Mode

Most frequent value

Best for: Nominal data, bimodal distributions

Note: Can have multiple modes

Measures of Variability (Dispersion)

Range

Highest score - Lowest score. Simple but affected by outliers.

Variance (σ² or s²)

Average of squared deviations from mean. Expressed in squared units.

Formula: Σ(X - M)² / N (population) or N-1 (sample)

Standard Deviation (σ or SD)

Square root of variance. Most commonly used measure of spread.

Expressed in same units as original data

The Normal Distribution

Bell-shaped, symmetrical curve. Mean = Median = Mode. Also called Gaussian distribution.

Empirical Rule (68-95-99.7)

±1 SD = 68% of scores

±2 SD = 95% of scores

±3 SD = 99.7% of scores

Standard Scores

Z-Score

Number of standard deviations from mean.

z = (X - M) / SD

• Mean = 0, SD = 1
• Allows comparison across tests

T-Score

Transformed z-score (eliminates negatives).

T = 10z + 50

• Mean = 50, SD = 10
• Used in MMPI

Skewness and Kurtosis

Skewness (asymmetry):

• Positive skew: Tail extends right; Mean > Median > Mode
• Negative skew: Tail extends left; Mode > Median > Mean

Kurtosis (peakedness):

• Leptokurtic: Tall and thin, heavy tails
• Platykurtic: Flat and wide
• Mesokurtic: Normal

7. Inferential Statistics

Inferential statistics allow us to make inferences about a population based on sample data. They help determine if results are statistically significant.

Hypothesis Testing

1. State null (H₀) and alternative (H₁) hypotheses
2. Set alpha level (usually α = .05)
3. Collect data and calculate test statistic
4. Determine p-value
5. Make decision: Reject or fail to reject H₀

p-value

Probability of obtaining results as extreme or more extreme, if H₀ is true.

• p < .05 = statistically significant
• p < .01 = highly significant
• p < .001 = very highly significant

Alpha Level (α)

Threshold for significance. Probability of Type I error we're willing to accept.

• Convention: α = .05 (5%)
• If p < α, reject H₀
• If p ≥ α, fail to reject H₀

Types of Errors

	H₀ True (No Effect)	H₀ False (Effect Exists)
Reject H₀	Type I Error (α) False positive	Correct Decision Power (1-β)
Fail to Reject H₀	Correct Decision	Type II Error (β) False negative

Common Statistical Tests

t-Test

Compare means of two groups

• Independent samples t-test: Two different groups
• Paired samples t-test: Same group, two conditions
• One-sample t-test: Sample mean vs. population mean

ANOVA (Analysis of Variance)

Compare means of 3+ groups

• One-way ANOVA: One independent variable
• Two-way ANOVA: Two independent variables (can test interaction)
• Repeated measures ANOVA: Same participants in all conditions
• F-ratio is the test statistic

Chi-Square (χ²)

Compare frequencies/proportions (nominal data)

• Goodness of fit: Observed vs. expected frequencies
• Test of independence: Relationship between two categorical variables

Correlation

Measure relationship between two variables

• Pearson r: Interval/ratio data, linear relationship
• Spearman rho (ρ): Ordinal data or non-linear
• Point-biserial: One dichotomous, one continuous

Regression

Predict values of DV from IV(s)

• Simple regression: One predictor
• Multiple regression: Multiple predictors
• R² = variance explained

Effect Size

Measures practical significance (magnitude of effect), not just statistical significance.

• Cohen's d: Difference in means / SD (small=0.2, medium=0.5, large=0.8)
• η² (eta-squared): Proportion of variance explained by IV in ANOVA
• r: Correlation itself is an effect size

8. Research Ethics

APA Ethical Principles

Informed Consent

Participants must be told about the study's purpose, procedures, risks, and their right to withdraw. Must give voluntary consent before participation.

Confidentiality

Protect participants' privacy. Data should be anonymous or confidential. Use codes instead of names.

Debriefing

After study, explain true purpose. Especially important if deception was used. Address any misconceptions or distress.

Minimizing Harm

Benefits must outweigh risks. Participants should leave study in same condition as they entered. Provide resources if needed.

Deception

Only allowed when necessary and no alternative exists. Must not cause significant distress. Full debriefing required afterward.

Right to Withdraw

Participants can leave at any time without penalty. Cannot coerce participation. Must not pressure to continue.

Institutional Review Board (IRB)

Committee that reviews research proposals to ensure ethical standards are met. Required for research involving human subjects at most institutions.

• Exempt review: Minimal risk research
• Expedited review: Minor risks
• Full board review: Greater than minimal risk

Special Populations

Extra protections required for vulnerable populations:

• Children: Parental consent + child assent
• Prisoners: No coercion; limited benefits
• Pregnant women: Risk to fetus considered
• Cognitively impaired: Legal guardian consent
• Students/employees: Avoid power imbalance

Historical Ethical Violations

• Tuskegee Syphilis Study (1932-1972): African American men with syphilis left untreated without informed consent
• Milgram Obedience Study (1961): Psychological distress from believing they harmed others
• Stanford Prison Experiment (1971): Psychological harm to participants; study terminated early
• Little Albert (1920): Classical conditioning of fear in infant without consent; no debriefing

Key Takeaways for the Board Exam

Research Designs

• Experimental = Causation (random assignment)
• Correlational = Association only
• Quasi-experimental = No random assignment

Variables

• IV = Manipulated (cause)
• DV = Measured (effect)
• Confound = Alternative explanation

Statistics

• p < .05 = Significant
• Type I = False positive (α)
• Type II = False negative (β)

Ethics

• Informed consent required
• Confidentiality protected
• Debriefing after deception
• Right to withdraw anytime

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Exam Tips

• Know when to use which statistical test
• Memorize Type I vs Type II errors
• Understand p-values and significance
• Know ethical principles by name