2.3 Hypothesis formation and testing

Hypothesis formation and testing are crucial steps in the scientific method. Scientists develop explanations for phenomena based on observations and existing theories, then design experiments to test these ideas. This process helps separate fact from fiction and build our understanding of the world.

Careful experiment design and data analysis are key to drawing valid conclusions. By controlling variables, using statistical techniques, and interpreting results thoughtfully, researchers can evaluate hypotheses and revise theories. This iterative process drives scientific progress and knowledge accumulation over time.

Hypothesis Formulation

Defining and Generating Hypotheses

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• A hypothesis is a proposed explanation for a phenomenon based on limited evidence that can be tested through further investigation and experimentation
• Hypotheses are often formulated by making inductive generalizations from existing observations (patterns in data) or by making deductive predictions from existing theories (logical consequences of assumptions)
• Testable hypotheses must be logically consistent, empirically falsifiable, and sufficiently precise to generate specific predictions
• Operational definitions specify the exact procedures used to measure or manipulate variables in a way that allows hypotheses to be empirically tested (reaction time, self-report questionnaire)

Types of Hypotheses

• Null and alternative hypotheses are mutually exclusive statements about the relationships between variables, where the null hypothesis predicts no effect or relationship
  • Null hypothesis: There is no difference in mean scores between the treatment and control groups
  • Alternative hypothesis: There is a difference in mean scores between the treatment and control groups
• Directional hypotheses specify the expected direction of an effect or relationship (positive correlation, negative correlation), while non-directional hypotheses only predict the existence of an effect or relationship without specifying its direction
• Causal hypotheses propose that changes in one variable cause changes in another variable, while associative hypotheses only propose that two variables are related without specifying a causal direction

Experiment Design

Types of Experimental Designs

• Controlled experiments systematically manipulate one or more independent variables while holding other variables constant and measuring the effect on one or more dependent variables
  • Independent variable: The variable manipulated by the experimenter (drug dosage)
  • Dependent variable: The variable measured by the experimenter (symptom severity)
  • Confounding variable: An extraneous variable that varies systematically with the independent variable and affects the dependent variable (age, income)
• Random assignment of participants or samples to different experimental conditions minimizes the influence of potential confounding variables
• Between-subjects designs compare different groups of participants exposed to different levels of the independent variable, while within-subjects designs expose the same participants to all levels of the independent variable

Controlling for Extraneous Variables

• Placebos and double-blind procedures are used to minimize demand characteristics and experimenter bias in interventional studies
  • Placebo: An inert substance or procedure that mimics the appearance of an active treatment (sugar pill, sham surgery)
  • Double-blind: Neither the participants nor the experimenters directly interacting with them know which condition each participant is assigned to
• Correlational designs examine the strength and direction of relationships between measured variables without manipulating them directly
  • Positive correlation: Two variables increase or decrease together (height and weight)
  • Negative correlation: One variable increases as the other decreases (hours of sleep and fatigue)
• Quasi-experimental designs lack random assignment but still attempt to establish cause-and-effect relationships by comparing pre-existing groups (males vs. females) or using interrupted time-series (before vs. after policy change)

Data Analysis and Interpretation

Descriptive and Inferential Statistics

• Descriptive statistics such as means, standard deviations, and correlations summarize the main features of a dataset
  • Mean: The arithmetic average of a set of numbers
  • Standard deviation: A measure of the average distance between each data point and the mean
  • Correlation coefficient: A measure of the strength and direction of the linear relationship between two variables (-1 to +1)
• Null hypothesis significance testing uses probability theory to determine the likelihood of obtaining the observed results if the null hypothesis were true
• The p-value represents the probability of obtaining results as extreme or more extreme than those observed, assuming the null hypothesis is true. A p-value below a pre-specified alpha level (e.g., .05) is considered statistically significant

Effect Sizes and Confidence Intervals

• Effect sizes indicate the strength or magnitude of an observed effect or relationship, independent of sample size
  • Cohen's d: A standardized measure of the difference between two means in units of standard deviation
  • Pearson's r: A measure of the strength and direction of the linear relationship between two variables
• Confidence intervals estimate the range of plausible values for a population parameter based on the variability in a sample statistic
  • 95% confidence interval: The range of values that has a 95% probability of containing the true population parameter
• Bayesian inference uses prior probabilities and observed data to calculate the posterior probability of different hypotheses
  • Prior probability: The probability of a hypothesis being true before observing the data
  • Posterior probability: The updated probability of a hypothesis being true after observing the data

Hypothesis Revision

Updating Theories Based on Evidence

• Scientific theories are provisional explanations that can be revised or replaced based on new evidence that contradicts their predictions
• Replication of key findings using similar or different methods is essential for establishing the reliability and generalizability of results
• Hypotheses that are consistently supported by multiple lines of evidence are provisionally accepted, while those that are consistently refuted are rejected or revised

Dealing with Anomalous Results

• Anomalous or unexpected results may suggest the need to modify the scope or boundary conditions of a hypothesis, or to develop entirely new hypotheses
  • Scope: The range of phenomena that a hypothesis attempts to explain (animal learning vs. human learning)
  • Boundary conditions: The specific circumstances under which a hypothesis is expected to hold true (short-term memory vs. long-term memory)
• Meta-analyses statistically combine the results of multiple studies to provide a more precise estimate of the overall size and consistency of an effect
• Converging evidence from multiple methods (experiments, observations, simulations) and sources of data (self-report, behavioral, physiological) provides the strongest support for a scientific hypothesis or theory