Power and sample size

Effects of variables on type II error

is the difference between the two means. As the value of increases the two curves will separate and the power of the study will increase. As gets smaller, the curves will overlap and the power of the study will decrease.

is usually set at 5%. Sometimes is set at 1%, moving away from the centre of the distribution,and this will reduce the power of the study. In this simulation, has a maximum value of 10%, to show that this increases the power of the study, but it would not be set at that level in a real situation.

n is the number or size of the samples. This affects the standard error. When n is low the sample size is small, the curves are flatter and overlap more so, assuming is held constant, this reduces the power of the study. As n increases the standard error decreases and the curves have narrower distributions, hence they overlap less. So the effect of increasing the sample size is to increase the power of the study, again, if is held constant.

is the standard deviation of the measurement you're interested in. Generally speaking a researcher has no control over this, but sometimes you can design your study so you reduce , for example there are some well defined protocols for measuring blood pressure that reduce measurement error. Or you can restrict your study to a more homogeneous population, for example blood pressure of men aged 40 - 45. When is reduced the effect is to make the width of the distributions smaller and hence the curves overlap less. So this increases the power assuming you hold constant. Conversely, as increases, the width of the distributions get bigger and the curves overlap more so the power of the study is reduced