• Explain why probability is a core concept in statistics and the use of random sampling.
• Apply concepts in probability to the normal distribution, explain the relationship between z-scores and area under the curve, solving problems involving z-scores and percentiles.
• Explain the theory and purpose of a sampling distribution, calculate statistics for sampling distributions of the mean, and describe the implications of the central limit theorem.
• Explain the logic and process of null hypothesis significance testing, writing hypotheses in formal statistical terms and everyday language, and demonstrating knowledge of null hypothesis significance testing using the z-test.
• Compare and contrast Type I and Type II errors, explaining the probability with which each can be expected to occur
• Outline concerns associated with the reliance on p-values in data analysis, differentiating between statistical significance and importance.
• Buttress the use of hypothesis-testing methods with calculations and interpretation of effect size, confidence intervals, and power.
• Compare and contrast z- and t-distributions, and determine the appropriate test for various research situations.
• Develop and generate hypotheses for differences between means and conduct the corresponding tests.
• Calculate and interpret t-tests, effect sizes, and confidence intervals from raw data and summary statistics in both formal statistical terms and everyday language.
• Calculate effect sizes and required sample sizes to achieve desired statistical power, and interpret power curves for effect size and sample size.
• Generate and interpret confidence intervals for t-tests from raw data and summary statistics.
• Explain when to use chi-square analyses.
• Identify hypotheses appropriate for chi-square analyses.
• Explain the logic of chi-square analyses.
• Explain the assumptions of chi-square analyses.
• Conduct a chi-square goodness-of-fit test.
• Conduct a chi-square test of independence.
• Analyze effect size for chi-square analyses.
