# Statistical power and sample size relationship objects

### Sample size estimation and power analysis for clinical research studies

CONSORT statements provide a check list for required items for RCT, and used by many A statistical test with a larger sample size can decrease both type I and II errors. We try to . ICC (correlation among repeated measures) and power. Power analysis allows us to determine the sample sizes needed to detect statistical effects with high probability. Experimenters often guard against false positives with statistical significance There is a direct relation between Type II error and power, as Power .. The flat rectangular objects could represent glass slides. Key words: statistical power analysis, sample size, effect size, Type I error, relationship between two variables present in population [Ferguson, Ketchen, ]. .. not have a scientific base and it depends on different cases, objects and.

It is important to be aware of this because all too often studies are reported that are simply too small to have adequate power to detect the hypothesized effect.

## Sample size estimation and power analysis for clinical research studies

In other words, even when a difference exists in reality it may be that too few study subjects have been recruited. The result of this is that P values are higher and confidence intervals wider than would be the case in a larger study, and the erroneous conclusion may be drawn that there is no difference between the groups.

This phenomenon is well summed up in the phrase, 'absence of evidence is not evidence of absence'. In other words, an apparently null result that shows no difference between groups may simply be due to lack of statistical power, making it extremely unlikely that a true difference will be correctly identified.

### The Importance and Effect of Sample Size - Select Statistical Consultants

Given the importance of this issue, it is surprising how often researchers fail to perform any systematic sample size calculations before embarking on a study. Instead, it is not uncommon for decisions of this sort to be made arbitrarily on the basis of convenience, available resources, or the number of easily available subjects.

A study by Moher and coworkers [ 1 ] reviewed randomized controlled trials published in three journals Journal of the American Medical Association, Lancet and New England Journal of Medicine in order to examine the level of statistical power in published trials with null results.

Note that a smaller difference is more difficult to detect and requires a larger sample size; see below for details. The situation is slowly improving, and many grant giving bodies now require sample size calculations to be provided at the application stage. Many under-powered studies continue to be published, however, and it is important for readers to be aware of the problem. Finally, although the most common criticism of the size, and hence the power, of a study is that it is too low, it is also worth noting the consequences of having a study that is too large.

As well as being a waste of resources, recruiting an excessive number of participants may be unethical, particularly in a randomized controlled trial where an unnecessary doubling of the sample size may result in twice as many patients receiving placebo or potentially inferior care, as is necessary to establish the worth of the new therapy under consideration.

Factors that affect sample size calculations It is important to consider the probable size of study that will be required to achieve the study aims at the design stage. The calculation of an appropriate sample size relies on a subjective choice of certain factors and sometimes crude estimates of others, and may as a result seem rather artificial.

However, it is at worst a well educated guess, and is considerably more useful than a completely arbitrary choice. The choice of each of these factors impacts on the final sample size, and the skill is in combining realistic values for each of these in order to achieve an attainable sample size.

The ultimate aim is to conduct a study that is large enough to ensure that an effect of the size expected, if it exists, is sufficiently likely to be identified. Suppose in the example above that we were also interested in whether there is a difference in the proportion of men and women who own a smartphone. We can estimate the sample proportions for men and women separately and then calculate the difference. When we sampled people originally, suppose that these were made up of 50 men and 50 women, 25 and 34 of whom own a smartphone, respectively.

The difference between these two proportions is known as the observed effect size. Is this observed effect significant, given such a small sample from the population, or might the proportions for men and women be the same and the observed effect due merely to chance?

We find that there is insufficient evidence to establish a difference between men and women and the result is not considered statistically significant.

It is chosen in advance of performing a test and is the probability of a type I error, i. What happens if we increase our sample size and include the additional people in our sample?

Suppose that overall these were made up of women and men, and of whom own a smartphone, respectively. The effect size, i. Increasing our sample size has increased the power that we have to detect the difference in the proportion of men and women that own a smartphone in the UK.

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We can clearly see that as our sample size increases the confidence intervals for our estimates for men and women narrow considerably. With a sample size of onlythe confidence intervals overlap, offering little evidence to suggest that the proportions for men and women are truly any different.

- Statistics review 4: Sample size calculations

On the other hand, with the larger sample size of there is a clear gap between the two intervals and strong evidence to suggest that the proportions of men and women really are different. The Binomial test above is essentially looking at how much these pairs of intervals overlap and if the overlap is small enough then we conclude that there really is a difference.

The data in this blog are only for illustration; see this article for the results of a real survey on smartphone usage from earlier this year. Figure 2 If your effect size is small then you will need a large sample size in order to detect the difference otherwise the effect will be masked by the randomness in your samples.

The ability to detect a particular effect size is known as statistical power.

More formally, statistical power is the probability of finding a statistically significant result, given that there really is a difference or effect in the population. So, larger sample sizes give more reliable results with greater precision and power, but they also cost more time and money. Glossary Margin of error — This is the level of precision you require.

**What is Statistical Power?**

It is the range in which the value that you are trying to measure is estimated to be and is often expressed in percentage points e. A narrower margin of error requires a larger sample size. Confidence level — This conveys the amount of uncertainty associated with an estimate.

It is the chance that the confidence interval margin of error around the estimate will contain the true value that you are trying to estimate.