Inferential Statistics for Data Analysis Course

Module 1: Review of Statistical Symbols and Descriptive Statistics

• Refresh understanding of statistical notation used in formulas and analysis.
• Review descriptive statistics including measures of center and spread.
• Reinforce how descriptive statistics support inferential techniques.

Module 2: The Conceptual Framework for Statistical Thinking

• Understand the logic of inferential statistics and its role in decision-making.
• Distinguish between populations, samples, and sampling distributions.
• Recognize the importance of variability and uncertainty in statistical analysis.

Module 3: Determining Minimal Sample Size

• Calculate the minimum sample size for reliable estimation and hypothesis testing.
• Consider factors such as confidence level, margin of error, and population variability.
• Apply formulas and tools to determine required sample sizes.

Module 4: Estimating a Population Mean from a Sample

• Compute point and interval estimates for a population mean.
• Interpret confidence intervals and their relationship to sampling error.
• Understand assumptions for accurate estimation.

Module 5: The Central Limit Theorem

• Explain the central role of the Central Limit Theorem in inferential statistics.
• Understand how sample size affects the shape of the sampling distribution.
• Apply the theorem to make inferences about population parameters.

Module 6: Estimating a Population Proportion from a Sample

• Calculate point and interval estimates for a population proportion.
• Interpret results in the context of sampling variability and confidence levels.
• Understand conditions for valid estimation of proportions.

Module 7: Hypothesis Testing – Statistical Significance of a Large Sample Mean

• Formulate null and alternative hypotheses for mean testing.
• Calculate test statistics and p-values for large samples.
• Interpret statistical significance in practical terms.

Module 8: One-tailed and Two-tailed Tests of Statistical Significance

• Differentiate between one-tailed and two-tailed hypothesis tests.
• Select the appropriate test type based on research objectives.
• Interpret results for directional and non-directional hypotheses.

Module 9: Hypothesis Testing – Statistical Significance of a Sample Proportion

• Conduct hypothesis tests for proportions using sample data.
• Calculate and interpret p-values in the context of proportion testing.
• Understand limitations of small sample proportion tests.

Module 10: Hypothesis Testing – The t Distribution for a Small Sample Mean

• Use the t distribution for inference with small sample sizes.
• Understand degrees of freedom and their impact on test results.
• Apply t-tests to real-world data analysis scenarios.

Module 11: Goodness of Fit – The Chi-Square Test for Frequencies

• Test whether observed frequencies differ from expected frequencies.
• Calculate chi-square statistics and interpret results.
• Recognize assumptions and conditions for valid chi-square testing.

Module 12: Comparing Two Sample Means

• Conduct hypothesis tests to compare means from two independent samples.
• Interpret results in terms of statistical and practical significance.
• Address assumptions for valid comparison testing.

Module 13: Comparing Two Sample Proportions

• Perform tests to compare proportions from two groups.
• Calculate differences and assess significance levels.
• Interpret findings in the context of the research question.

Module 14: Constructing a Scatter Diagram for Two Variables

• Plot data to visualize the relationship between two quantitative variables.
• Identify possible patterns, trends, and outliers.
• Use scatter diagrams as a precursor to correlation and regression analysis.

Module 15: Determining the Correlation between Two Variables

• Calculate correlation coefficients to measure strength and direction of relationships.
• Interpret correlation values in real-world contexts.
• Recognize the difference between correlation and causation.

Module 16: Linear Regression for Two Variables

• Fit and interpret a simple linear regression model.
• Assess model fit using R-squared and residual analysis.
• Use regression results to make predictions and guide decision-making.