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Sigma Magic Help Version 19

Sample Size

Overview

Sample Size Analysis can be used to determine the minimum sample size required for a given level of alpha and beta error. Sample Size can be determined for 1-sample Z test, 1-sample t-test, 2-sample t-test, ANOVA, 1-sample stdev, 2-sample stdev, 1-proportion test, and 2-proportion test. This analysis can determine how many data points we should collect before we perform hypothesis testing to minimize both Type I and Type II errors. Ensure that any data you collect is unbiased, fully randomized, and representative of the population.

This tool can be added to your active workbook by clicking on Stats and then selecting Sample Size.

Inputs

Click on Analysis Setup to open the menu options for this tool.

Setup

A sample screenshot of the setup menu is shown below.
inputs

Data Type: Specify the type of data for your analysis. The available options are:

Option	Description
Discrete	Discrete data is like count data that has only a finite set of values (like the number of defects in a product or the number of defective products manufactured in one month).
Continuous	Continuous data can take any arbitrary value (like the temperature of the room example 34.53 degrees centigrade).

Comparison: Specify the type of comparison you want to make for your data. The available options are:

Option	Description
Mean	We want the required sample size to compare the average value of one or more data sets.
Stdev	We want the required sample size to compare the standard deviation value of one or more data sets.
Proportion	We want the required sample size to compare the proportion of defects or defects in the data.

Num Samples: Specify the number of samples(data sets) you are comparing.

Hypothesis Test: Specify the specific hypothesis test you plan to use, and the sample size will be determined for this test. The available options are:

Option	Description
1-Sample Z	Comparing the mean of one sample with the external standard when std. deviation is known
1-Sample t	Comparing the mean of one sample with the external standard when std. deviation is unknown
2-Sample t	Comparing two sample means with each other
paired t	Comparing two sample means with each other and tests conducted in paired manner
ANOVA	Comparing more than two sample means with each other
ChiSq	Comparing the standard deviation of one sample with external standard
F	Comparing two sample standard deviations with each other
Bartlett	Comparing more than two sample standard deviations with each other
ANOVA	Comparing more than two sample means with each other
1-S Defectives	Comparing one proportion to an external standard
2-S Defectives	Comparing two proportions with each other
Chi-Squared	Comparing more than two proportions with each other

Help Button: Click on this button to open the help file for this topic.

Cancel Button: Click on this button to cancel all changes to the settings and exit this dialog box.

OK Button: Click on this button to save all changes and compute the outputs for this analysis.

Hypothesis

A sample screenshot of the hypothesis menu for continuous data is shown below. However, the menu options for the discrete case are also very similar.
inputs 2

1	Null Hypothesis: Specify the null hypothesis. Currently, this menu option is set to 0 and disabled. The information about the null hypothesis is extracted from the information you enter in the Data tab.
2	Alt Hypothesis: Specify the alternate hypothesis (less than, greater than, or not equal). The default setting is Not Equal. The software will perform a one-sided hypothesis test if you select either less than or greater than.
3	Confidence Level: Enter the confidence level required for your analysis. This controls your Type I or Alpha error (1 - Confidence Level). The default value for this is 95%.
4	Population Size: For certain types of analysis, the population size may be small. In these cases, we can specify the population size here so that the sample size calculator will take into account the limited size of the population when recommending an adequate sample size for analysis. For most cases, the population size is very large, and in those cases, you can use the character string INF to denote a very large population size.

Data

You will see the following dialog box if you click the Data button. Data

Objective: Specify the objective of this study. The available options are:

Option	Description
Sample Size	Determine the minimum number of samples required to detect a difference of delta with a given level of power of the test.
Delta	Determine the minimum difference we can detect between samples when the sample size is fixed, and we want to achieve a certain power of the test.
Power	Determine the maximum power of the test to detect a difference of delta with a given number of samples.

Sample Size: Unless you have specified an objective of determining the sample size, you must specify the number of samples available for your study. This field is not enabled by default, as the software will determine the minimum sample size you need. Note that the minimum sample size is across all the samples (or data sets) you use for the comparison.

Power of the Test: You will only need to specify the required power for your study if you have specified an objective of determining the power of the test. By default, this value is 90%. The power value also equals 1 - beta (type II error). Hence, if you specify the power as 90%, you accept that this study may have a Type II error of up to 10%.

Delta (Difference): Unless you have specified an objective of determining the minimum difference (delta), you will need to specify the value for this parameter. The value you specify depends on the comparison you are making. The following options are available:

Comparison	Description
Mean	Specify the minimum difference in the mean values that you want to detect in your study.
Standard Deviation	Specify the minimum ratio of the standard deviations you want to detect in your study.
Proportion	Specify the alternative or comparative proportion that you want to detect in your study.

Standard Deviation: For continuous data type, you will need to specify the standard deviation value for your study. How much variation do you have in your data values? The more variation (or standard deviation) there is, the more samples will be required for your analysis. For discrete data types, you will need to specify the baseline proportion.

Hypothesis Statement: The statement about the specific hypothesis test being run is displayed here. Check this statement to ensure all your inputs are correct; if not, you may need to adjust your analysis inputs.

Charts

You will see the following dialog box if you click the Charts button. Charts

1	Title: The system will automatically pick a title for your chart. However, if you want to override that with your title, you can specify a title for your chart here. Note that this input is optional.
2	Sub Title: The system will automatically pick a subtitle for your chart. However, if you want to override that with your subtitle, specify a subtitle for your chart here. Note that this input is optional.
3	X Label: The system will automatically pick a label for the x-axis. However, if you would like to override that with your label for the x-axis, you can specify a different label here. Note that this input is optional.
4	Y Label: The system will automatically pick a label for the y-axis. However, if you would like to override that with your label for the y-axis, you can specify a different label here. Note that this input is optional.
5	X Axis: The system will automatically pick a scale for the x-axis. However, if you would like to override that with your values for the x-axis, you can specify them here. The format for this input is to determine the minimum, increment, and maximum values separated by a semi-colon. For example, if you specify 10;20, the minimum x-axis scale is set at 10, and the maximum x-axis scale is set at 20. If you specify 10;2;20, then in addition, the x-axis increment is set at 2. Note that this input is currently disabled, and you will not be able to change this setting.
6	Y Axis: The system will automatically pick a scale for the y-axis. However, if you would like to override that with your values for the y-axis, you can specify them here. The format for this input is to determine the minimum, increment, and maximum values separated by a semi-colon. For example, if you specify 10;20, the minimum y-axis scale is set at 10, and the maximum y-axis is set at 20. If you specify 10;2;20, then, in addition to minimum and maximum values, the y-axis increment is set at 2. Note that this input is optional.
7	Horizontal Lines: If you want to add a few extra horizontal reference lines on top of your chart, you can specify the values here. The format for this input is numeric values separated by semi-colon. For example, if you specify 12;15, two horizontal lines are plotted at Y = 12 and Y = 15, respectively. Note that this input is optional.
8	Vertical Lines: You can specify the values here if you want to add a few extra vertical reference lines on top of your chart. The format for this input is numeric values separated by semi-colon. For example, if you specify 2;5, two vertical lines are plotted at X = 2 and X = 5, respectively. Note that this input is optional.

Optional Chart Formating

If a chart has already been created earlier and you have made any changes to the chart format directly on the chart, it is possible to copy the settings and save them to memory. The next time you regenerate the chart, the same settings will be applied by the software, and you won't have to reapply them manually. The following image appears in the Charts tab if a valid chart exists on the worksheet. If no charts are found on the worksheet, the image shown below is hidden and will not appear in your dialog box. Chart Format

1	Copy Format: Click on this button to copy the chart settings to memory. The chart settings will be saved and reapplied the next time you regenerate the chart.
2	Clear Format: Click on this button to clear any existing settings you have made to the chart. The default software settings will be applied to your chart.

Verify

If you click the Verify button, the software will perform some checks on the data you entered. A sample screenshot of the dialog box is shown in the figure below. Verify

The software checks if you have correctly specified the input options and entered the required data on the worksheet. The results of the analysis checks are listed on the right. If the checks are passed, they are shown as green-colored checkmarks. If the verification checks fail, they are shown as a red-colored cross. If the verification checks result in a warning, they are shown in the orange exclamation mark, and finally, any checks that are required to be performed by the user are shown as blue info icons.

1	Item: The left-hand side shows the major tabs and the items checked within each section
2	Status: The right-hand side shows the status of the checks.
3	Overall Status: The overall status of all the checks for the given analysis is shown here. The overall status check shows a green thumps-up sign if everything is okay and a red thumps-down sign if any checks have not passed. Note that you cannot proceed with generating analysis results for some analyses if the overall status is not okay.

Outputs

Click on Compute Outputs to update the output calculations. A sample screenshot of the worksheet is shown below. outputs

The analysis reports the minimum number of samples needed to achieve a certain level of alpha and beta errors. The graph shows the power variation for different sample size values. The red dot shows the recommended setting for the minimum sample size. If you are unable to get these many samples, this graph can be used to estimate how much power you lose in your analysis by having a smaller sample size.

Notes

Here are a few pointers regarding this analysis:

Note that each data set's minimum sample size is reported. So, if you have two data sets, then each data set should have at least the minimum number of sample size.
If you have fewer samples than the one mentioned by the analysis, you will make larger Type I and Type II errors when you perform hypothesis tests.

Examples

The following examples are in the Examples folder.

Determine the minimum sample size required for checking if the time to respond to a call is similar to the industry average. The data for this example is in the reference file (Sample Size 1.xlsx).
Determine the minimum sample size required for comparing Department 1 and Department 2 cycle times. The data for this example is in the reference file (Sample Size 1.xlsx).
Determine the minimum sample size required for comparing the number of defects by two suppliers. The data for this example is in the reference file (Sample Size 1.xlsx).