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Determination of Sample Size and Power Analysis with G*Power Software



Doing research is just like playing a game. In a game situation if a player violates a rule he is penalized and similarly if a researcher violates an assumption he/she pays the price in the form of refusal of paper publication. This text is specially prepared for the researchers who wish to determine the optimum sample size in their research studies for achieving sufficient accuracy in estimation or pre defined power in hypothesis testing experiments. In survey studies we are interested in estimating population characteristics such as mean or proportion. Sample size in such experiments depends upon how much accuracy in estimation we require. On the other hand, in hypothesis testing experiments sample size depends upon how much power we desire to have in our test. Sample size determination is a prerequisite of any research because small sample may not be able to detect the effect whereas in large sample even very small effect may become significant. In survey studies sample size depends upon population variability, required accuracy in estimation and the confidence level in such estimations; whereas in hypothesis testing experiments, sample size is decided on the basis of the required power, Type I and Type II errors, variability of the population, minimum detectable difference and the type of test (one tail or two tailed). The most important consideration in hypothesis experiments is the power. Thus, a trade off is required between size of the sample and the power. Sometimes there is a constraint in deciding the sample size and the research cannot take more than available sample in the study, in such cases power should be reported in the findings.

In this text we have discussed the concepts involved in sample size determination in survey studies as well as in hypothesis experiments. The procedure has been shown by solving some of the solved examples manually. Simultaneously, we have shown the procedure of determining the sample size in different situations by using the G*Power software, which is a freeware and can be easily downloaded. The whole book consists of six chapters.

The first chapter is introductory that discusses the importance of sample size determination whereas second chapter discusses the theory of inference. In this chapter we have discussed the concept of estimation and hypothesis testing. The role of effect size in sample size determination and the procedure involved in hypothesis testing experiments by fixing different boundary conditions have been discussed in a crisp manner.

Chapter three discusses the procedure of determining sample size for estimating population mean and proportion in survey studies. Several solved examples have been illustrated to describe the procedures. In chapter four we have discussed the sample size determination procedure in hypothesis experiments. Solved examples in case of one and two sample testing have been illustrated manually to describe the procedure.

Chapter five explains the procedure for downloading the freeware G*Power software and its installation in computer. In chapter six we have discussed the procedure in determining sample size as well as the power in different univariate and multivariate statistical techniques by using the G*Power software. The procedure has been explained by using the screenshots which will be helpful for the researchers to apply even without any statistical and computer background.

I hope that this book will encourage the researchers to determine sample size for specific power in their studies and they will start reporting the power in their studies for authenticity in the findings.

The readers are encouraged to send their suggestions and queries to me via email at and I shall respond to them at the earliest.



I would like to express my gratitude to my professional colleague Prof. Harinder Jaseja who has not only helped me in editing and checking the manuscript but also added his inputs through discussions on many topics. I wish to express my sincere thanks to Prof. Y P Gupta and Prof. V. Sekhar for providing their valuable inputs in completing this text.

I wish to express my sincere thanks to all my research scholars and numerous researchers in India and abroad who had posed a variety of questions on sample size determination and power analysis which helped me in editing the contents of this book.

Above all, I wish to thank my wife, Haripriya, my daughter Prachi, son-in-law Ashish and son Priyam and the rest of my family, who supported and encouraged me in spite of all the time it took me away from them.

J.P.Verma, PhD
Professor (Statistics) and Dean, Students’ Welfare
Lakshmibai National Institute of Physical Education Gwalior, India