Introducing Null Hypothesis Significance Testing With the z-test

This course is designed to provide students with a comprehensive understanding of core statistical concepts and their practical applications. The curriculum introduces concepts in probability, sampling, hypothesis testing, and data interpretation that are the building blocks of meaningful statistical analyses.

The course begins with an exploration of how concepts in probability theory inform our understanding of such topics as random sampling and sampling error. Next, the course delves into the normal distribution and the relationship between z-scores and the area under the curve.

The theory and purpose of sampling distributions are then introduced, with a focus on sampling distributions of the mean and the central limit theorem and the importance of these concepts for statistical inference.

Much of the course is dedicated to null hypothesis significance testing (NHST). Students will learn the logic and process of NHST, analyze hypotheses in both formal statistical terms and everyday language, and demonstrate their understanding through the application of the z-test. This section emphasizes the nature of Type I and Type II errors and their importance for understanding the logic of hypothesis testing.

Additionally, the course addresses concerns about the use of NHST and the reliance in science on p values for inference. Students will learn to distinguish between statistical significance and practical importance, ensuring a more nuanced interpretation of results. The curriculum also includes methods for calculating and interpreting effect size, confidence intervals, and statistical power, providing students with a comprehensive toolkit for robust data analysis.

Learning objectives

• 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.