# Power and sample size relationship photography

### STATISTICA Help | Example 1: Power and Sample Size Calculation for the Independent Sample t-Test

With just a few samples, the picture is so fuzzy that we'd only be To follow along in Minitab, go to: Stat > Power and Sample Size > 2-sample t. There are four basic types of analyses: Power Calculation, Sample Size Calculation, . One step is to examine the relationship between power and sample size, to see command selected from the Insert menu) gives an even clearer picture. Overview of Power Analysis and Sample Size Estimation head and neck cancer patients is planned, with a ratio of patients on resveratrol (an .. above picture, the pencils appear next to the Solving For and the Type I Error screen names.

The size of a sample influences two statistical properties: To use an example, we might choose to compare the performance of marathon runners who eat oatmeal for breakfast to the performance of those who do not.

Since it would be impossible to track the dietary habits of every marathon runner in the world, we have little choice but to focus on a segment of that larger population.

This might mean randomly selecting only runners for our study. The sample size, or n, in this scenario is No matter how careful we are about choosing our runners, there will still be some margin of error in the study results.

This measure of error is known as sampling error. It influences the precision of our description of the population of all runners. Sampling error, though unavoidable, can be eased by sample size.

Larger samples tend to be associated with a smaller margin of error.

To get an accurate picture of the effects of eating oatmeal on running performance, we need plenty of examples to look at and compare.

However, there is a point at which increasing sample size no longer impacts the sampling error. This phenomenon is known as the law of diminishing returns. Clearly, determining the right sample size is crucial for strong experimental design. But what about power?

In our study of marathon runners, power is the probability of finding a difference in running performance that is related to eating oatmeal. We calculate power by specifying two alternative scenarios.

In our study of marathoners, the null hypothesis might say that eating oatmeal has no effect on performance. The second is the alternative hypothesis. This is the often anticipated outcome of the study. In our example, it might be that eating oatmeal results in consistently better performance. Parameters - Quick tabyou enter the fixed, or baseline, parameters for the analysis in the fields in the Fixed Parameters group box.

The Independent Sample t-Test is one of the classic tests in statistics. In the two-tailed version of the test, the null hypothesis H0 is tested against the alternative H1, where H0: The Two-Sample t-Test assumes that the two populations compared have normal distributionsand that the standard deviations are the same in the two populations.

To analyze power for a particular situation, you enter the baseline parameters for the situation in this dialog box. Suppose, for example, you are in the planning stages of an experiment in which you intend to compare two groups on a characteristic where the population standard deviation is 15 in both groups.

Subjects are reasonably expensive and difficult to obtain in your line of research, and you anticipate running the study with 25 subjects in each group. Group 2, the control group in the study, can be reasonably assumed to have a population mean of Ascertaining the mean for Group 1, the experimental group, is of course the whole purpose for running the experiment, but you would be disappointed if the treatment were not effective enough to elevate the Group 1 mean to Enter the above numbers into the fields on the Quick tab as shown below.

Click the OK button to move to the next stage of the analysis. Calculating power The Independent Sample t-Test: Results dialog box is used to investigate power for the situation specified in the Independent Sample t-test: The summary box at the top of the dialog box shows the baseline parameters that have been established for the analysis.

Es, calculated in this case as: Baseline parameters can be altered at any time by returning to the Power Calculation parameters dialog box in this case, Independent Sample t-Test: There are two ways of returning to the previous dialog box.

### r - How to best display graphically type II (beta) error, power and sample size? - Cross Validated

Click the Back button in the Results dialog box, or press the Esc key to return to the preceding dialog box without recording changes to the X-Axis Graphing Parameters on the Power Calculation parameters Quick tab. Click the Change Params button to return to the preceding dialog box and save any changes to the X-Axis Graphing Parameters that have been entered.

To calculate statistical power for the baseline parameters currently in effect, click the Calculate Power button. A spreadsheet containing the result of the power calculation is produced. The spreadsheet reports Power as. For the convenience of the user who must report power calculations e. To display this dialog box, click the Options button in the Results dialog box, and select Output. From the Supplementary detail drop-down list, select Comprehensive. Clearly, in this case, the power is inadequate.

To analyze why, we first digress briefly. Above, we discussed the notion of a Standardized Effect Es. To understand the full importance of this notion, reflect briefly on the artificiality of the example as we have presented it so far. We have imagined a situation in which the experimenter, to calculate power, considers, in advance, a particular effect i. Many examples use IQ scores, which are assumed to have a standard deviation of 15, because that is the way they are normed.

Es has a number of advantages, one of the most significant being that it is invariant under linear scale changes. So, for example, a standardized effect calculated for height in inches would remain the same if height were rescaled into centimeters.

- Sample size and power

Writers on power analysis have established a number of conventions regarding the meaning of Es. For example, Cohenin his classic text Statistical Power Analysis for the Behavioral Sciences, suggests the following conventions: It in turn implies that, in this case, the standardized effect corresponds to a medium effect size.

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

This suggests that sample size is too small to reliably detect a medium-sized effect in this situation. To investigate how large a sample size might be required to achieve a reasonable level of power, you have several options, which we explore in the next section. Graphical analysis of statistical power Since power of. One step is to examine the relationship between power and sample size, to see just how bad the situation is.

### Power and Sample Size

On the Independent Sample t-Test: Results - Quick tabin the Power Charts group box, click the Power vs. N button to produce a plot of power versus sample size. The chart demonstrates that, in order to attain power of.

To boost power to approximately. This is a rather disappointing result, given the fact that the Type I error rate is already set at. The relationship between power and Type I Error rate a can be examined by clicking the Power vs. Alpha button to produce the following plot. The graph demonstrates the well-known result that power increases as a increases.