Statistical Concepts Quiz

Statistical Concepts

• Statistical Models: Tools used to test hypotheses, predicting outcomes based on predictor variables. Types vary by research question (e.g., linear regression for continuous data, logistic regression for categorical data).
• Populations and Samples: Population is the entire group of interest; a sample is a subset used for drawing conclusions. Larger, random samples represent the population better.
• Parameters: Values describing population characteristics (e.g., mean, variance). Researchers use sample data to estimate parameters.
• Estimation: Process of inferring population parameters from sample data, commonly using least squares to minimize differences between observed and predicted values.
• Standard Error: Reflects how much a sample statistic (e.g., mean) might deviate from the population parameter. Higher standard error indicates less reliable sample representation.
• Confidence Intervals: A range of values likely to contain the population parameter (e.g., 95% confidence interval). Key point: 95% of similar intervals from repeated samples contain the true parameter, not implying 95% certainty in a single interval.
• Null Hypothesis Significance Testing (NHST): Null Hypothesis (H₀): No effect/difference exists. Alternative Hypothesis (H₁): An effect/difference exists. Crucial terms: Alpha level (probability of Type I error, usually 0.05), Beta level (probability of Type II error), and Statistical power (likelihood of correctly rejecting the null hypothesis when it is false; aim for 0.80 or higher).

Statistical Techniques

• t-tests: Compare means between groups. Types include independent (separate groups), dependent (repeated measures/paired data), one-sample (comparing a single sample to a population mean), and paired (comparing means of the same group at different times).
• Analysis of Variance (ANOVA): Compares means across three or more groups. Crucial extensions include planned contrasts (testing specific hypotheses) and post hoc tests (exploring group differences after significant results).
• Analysis of Covariance (ANCOVA): Compares group means, controlling for covariates (other variables).
• Factorial Designs: Experiments with two or more independent variables, evaluating main effects (impact of individual variables) and interaction effects (combined impact of variables).
• Exploratory Factor Analysis (EFA): Identifies clusters of related variables (factors) commonly used in questionnaire design and data reduction.
• Reliability Analysis: Measures consistency of a measure (e.g., survey items) using metrics like Cronbach's α.
• Chi-Square Test: Evaluates relationships between two categorical variables.
• Loglinear Analysis: Examines relationships among more than two categorical variables.
• Logistic Regression: Predicts categorical outcomes based on predictors.
• Regression Analysis: Explores relationships between variables, predicting an outcome based on predictors. Key concepts include R² (proportion of variance explained), F-statistic and p-value (model significance), and regression coefficients (effects of predictors).

Graphing Data

• Common graphs include histograms, boxplots, bar graphs, line charts, and scatterplots, each serving to present data visually and reveal insights.

General Considerations

• Assumptions: Statistical methods often have underlying assumptions about data. Violating these assumptions can lead to invalid results.
• Effect Sizes: Important for providing insights into the practical significance of an effect, which can be valuable beyond just statistical significance.
• Meta-Analysis: Combines results from multiple studies to estimate an overall effect size.
• Bayesian Statistics: An alternative to NHST, focusing on updating prior beliefs with new data.
• Open Science: Encourages practices such as pre-registering studies and sharing data for transparency and reproducibility.

Reporting Results

• Include details like analysis type, sample size, effect sizes, and confidence intervals. Specify statistical software used.

Specific Tests

• Pearson's Chi-Square Test: Assess association between two categorical variables, comparing observed frequencies with expected frequencies.
• Fisher's Exact Test: Used when sample sizes are small or expected counts are low in contingency tables. Important that you report the p-value directly in your results.

Test your understanding of key statistical concepts such as models, populations, samples, parameters, estimation, standard error, and confidence intervals. This quiz covers essential principles that are crucial for data analysis and interpretation. Ideal for students of statistics and research methodologies.