# Power Analysis for Normal Distribution:

### From Socr

## Contents |

## List of Functionalities

### Finding Power with Sample Size ("Part 1")

finding power, with given information (including the sample size, standard deviation (SD), mean of the null (mu_0) and alternative (mu_A) hypothesis, significance level and hypothesis type).

### Finding Sample Size with Power ("Part 2")

finding sample size, with given information (including the power, standard deviation, mean of the null and alternative hypothesis, significance level and hypothesis type).

### Finding Z-Score ("Part 3")

finding the z-score with given information (including the mean, standard deviation, and the specific point of interest).

### Details of Computation Steps

#### How to do part (1) and what's in there?

You can do part (1) in two ways:

=====A. Without Generating Raw Data===== just click on "SELECT PARAMETERS". Make sure "Get Power Using Sample Size " is selected. and input the information stated above in (1). You'll need to: input all these in order for the program to continue. Remember to select one from the three hypothesis types, i.e. set the relationship of the null and alternative's means, to be less than, greater than, or not equal.

Then click on the "CALCULATE" button to get the computed results. Then you could click on the "RESULT" button to see the statistical output, and click on "GRAPH" tab to see a plot of "power vs. mean", and click on "COMPARE CURVES" to see the normal curves. The top curve is generated using the SD inputted, and the bottom curve using the SE of sample mean.

=====B. With Raw Data Generated ===== To see how this work with data, click on "RANDOM EXAMPLE" and a set of data will be generated. Click on the "DATA" tab if you would like to see the data.

Then go to "SELECT PARAMETER" panel. Make sure "Get Power Using Sample Size " is selected, and input the information stated above in (1).

Click on the "CALCULATE" button to obtain the mean and SD of this data set. Next input your own mean of alternative hypothesis. Remember to select hypothesis type. Then, click on the "CALCULATE" button AGAIN, to obtain the result, graph, and normal curves, as in (A).

Note that in (B)'s normal curve, the data are ploted in pink (based on frequency).

For both (A) and (B), You can move around the curve of sample mean, alternative hypothesis (bottom panel, red curve), by click on it's area inside. The part(s) that's rejected by the null, is painted yellow.

#### How to do part (2) and what's in there?

Very similar to 1A: just click on "SELECT PARAMETERS". Make sure "Get Sample Size Using Power" is selected. And input the information stated above in (2). Instead of specifying the sample size, you specify the power. Use a decimal number beteen 0 and 1 (e.g. 0.95). You'll need toinput all these in order for the program to continue. Remember to select one from the three hypothesis types. Then, once you click on the "CALCULATE" button, see the result, graph and normal curves by clicking on "RESULT", "GRAPH" and "COMPARE CURVES" tabs.

You can move around the curve of sample mean, alternative hypothesis (bottom panel, red curve), by click on it's area inside. The part(s) that's rejected by the null, is painted yellow.

#### How to do part (3) and what's in there?

This is even easier than (1) and (2). Just click on "SELECT PARAMETERS", enter all the information, then click on "CALCULATE". Then click on "RESULT" for the result.