### Sample Size

Sample Size and Power Determination

taught by Kuber Deokar

Aim of Course:

This online course, "Sample Size and Power Determination" will offer an introduction to sample size and power analysis and will show how to use it simply and effectively to plan the appropriate sample size for a study. The power of a study (the study's ability to detect a treatment effect of a specified size, if it exists) is determined by such factors as the magnitude of the treatment effect, the sample size, alpha (the level of statistical significance required), and (for survival studies) the study duration.

Since some of these factors are under the researcher's control (such as the significance level and sample size) while others are not (such as unknown parameter values that determine effect magnitudes), the goal of power analysis is to balance them as a series of "What if's." For example "What sample size would we need if the treatment reduces the risk of death by 10%, and what sample size would we need if the treatment reduces the risk of death by 20%?" This process of finding a balance among factors can be aided by the use of graphs that allow the researcher to grasp (and communicate) a range of options in a single picture and find the one that strikes the optimal balance between feasible sample size and acceptable power.

This course may be taken individually (one-off) or as part of a certificate program.

Course Program:

## WEEK 1: Introduction to Sample Size Determination and Power, Including Useful Software

- Hypothesis tests and confidence intervals
- Factors that determine sample size
- Sample size for estimating a population mean
- Examples, including a study from the literature
- External and internal pilot studies
- Ways to estimate sigma
- What should be avoided: Retrospective power and standardized effect sizes
- Ethical issues in power analysis
- Recommended references
- Software

## WEEK 2: Tests on Population Means (continued)

- T-Test or Z-Test for population mean?
- Testing the normality assumption
- Confidence Intervals on Power and/or Sample Size?
- Two-sample study from the literature with unequal sample sizes
- Sample sizes determined by scientist in two stages without software
- Illustration of more efficient sample determination using software

- Using coefficient of variation
- Paired data
- Additional example

## WEEK 3: Tests on Proportions and Variances

- One proportion
- Software disagreement and rectification

- Two proportions
- Options, including transformations built into software, for tests of proportions
- One variance and two variances
- Examples

## WEEK 4: Regression and Design

- Simple linear regression
- Complexity caused by what must be inputted

- Multiple linear regression
- Optional material: Repeated measures designs, Logrank test for survival analysis
- Literature references for sample size determination with more advanced

statistical methods and some information on corresponding software

capability

HOMEWORK:

Homework in this course consists of short answer questions to test concepts and guided data analysis problems using software.

In addition to assigned readings, this course also has supplemental readings available online.

# Sample Size and Power Determination

Who Should Take This Course:

Anyone responsible for the planning of a study, or its subsequent analysis. Investigators writing grant applications or other proposals in which sample size must be specified.

Level:

Intermediate/Introductory

Organization of the Course:

This course takes place online at the Institute for 4 weeks. During each course week, you participate at times of your own choosing - there are no set times when you must be online. Course participants will be given access to a private discussion board. In class discussions led by the instructor, you can post questions, seek clarification, and interact with your fellow students and the instructor.

At the beginning of each week, you receive the relevant material, in addition to answers to exercises from the previous session. During the week, you are expected to go over the course materials, work through exercises, and submit answers. Discussion among participants is encouraged. The instructor will provide answers and comments, and at the end of the week, you will receive individual feedback on your homework answers.

Time Requirement:

About 15 hours per week, at times of your choosing.

Credit:

Students come to the Institute for a variety of reasons. As you begin the course, you will be asked to specify your category:

- You may be interested only in learning the material presented, and not be concerned with grades or a record of completion.
- You may be enrolled in PASS (Programs in Analytics and Statistical Studies) that requires demonstration of proficiency in the subject, in which case your work will be assessed for a grade.
- You may require a "Record of Course Completion," along with professional development credit in the form of Continuing Education Units (CEU's). For those successfully completing the course, CEU's and a record of course completion will be issued by The Institute, upon request.

Course Text:

All necessary materials will be provided online, including a few relevant journal articles. The author's recently published book, Sample Size Determination and Power, is recommended as a reference book.

Software:

Participants should have access to a software package in which they can do power and sample size calculations. Power and Precision, MINITAB, and nQuery are used in the course Notes and examples. Other software packages such as Stata, PASS, and Russ Lenth’s Java applet may be used for the weekly assignments; assistance with these other packages may be available from the teaching assistants.

Click Here for information on obtaining a free (or nominal cost) copy of software for use during the course.

# Sample Size and Power Determination

April 14, 2017 to May 12, 2017November 17, 2017 to December 15, 2017April 13, 2018 to May 11, 2018November 16, 2018 to December 14, 2018