Primer on Statistics for Non-Statisticians

Introduction and Contents

We can all look up statistics books, but I decided to include a primer on the subject as a quick reference. I have included the more mathematical parts in red text so they can be skipped, and the principles can still hopefully be understood graphically. The aim is to provide a broad understanding of a few important concepts, such as:

• The difference between normally and non-normally distributed data
• What a p-value means, why 0.05 is considered an important value, and what we mean when we use the term “significant”.
• How to determine if a sample is significantly different from a certain mean value, or if samples are significantly different from one another.
• The difference between saying there is no evidence for a link between x and y and saying there is evidence for no link between x and y.
• Choosing the right statistical test for the right circumstance

The content pages of this primer are listed below. They may be read individually for  reference, or in order as a more formal guide:

• Standard Distribution and Standard Error
• Determining the Standard Error of the Mean
• Estimating the True Mean from a Sample Mean – “Significant Differences”
• One-Tailed versus Two-Tailed Probability
• Confidence Intervals
• No Evidence for a Significant Difference vs Evidence for no Significant Difference
• Determining the False Negative Error
• Power Calculations for One Sample
• Statistical Tests on Normally Distributed Data comparing Two Samples
• Standard Errors and Estimation
• Power Calculations for Two Samples
• Comparing a Sample Proportion with an Expected Proportion
• Comparing Two Sample Proportions
• Student’s t-Test for comparing Two Independent Samples
• Paired t-Test for Dependent Samples
• Comparing Variables of Different Types
• Determining and Comparing Times to a Discrete Event: the Kaplan-Meier Survival Plot
• Summary of Statistical Tests
• Designing a Research Study