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Design of Experiments Guide > Sample Size Explorers > Power Explorers for Hypothesis Tests > Power for Two Independent Sample Counts Per Unit
Publication date: 04/21/2023

Power for Two Independent Sample Counts Per Unit

Use the Power for Two Independent Sample Counts per Unit Explorer to determine a sample size for a test of count per unit between two groups. Select DOE > Sample Size Explorers > Power > Power for Two independent Sample Counts per Unit. Explore the trade offs between variability assumptions, sample size, power, and significance. Sample size and power are associated with the following hypothesis test:

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versus the two-sided alternative:

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or versus a one-sided alternative:

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where λ1 and λ2 the are the rates of the counts per unit for each group.

Power Explorer Two Independent Sample Counts per Unit Settings

Set study assumptions and explore sample sizes using the radio buttons, text boxes, and menus. The profiler updates as you make changes to the settings. Alternatively, change settings by dragging the cross hairs on the profiler curves.

Test Type

Specifies a one or two-sided hypothesis test.

Preliminary Information

Alpha

Specifies the probability of a type I error, which is the probability of rejecting the null hypothesis when it is true. It is commonly referred to as the significance level of the test. The default alpha level is 0.05.

Assumed Ratio

Specifies the assumed ratio of Group 2 counts per unit to Group 1 counts per unit.

Power Explorer Two Independent Sample Counts per Unit Profiler

The profiler enables you to visualize the impact of sample size assumptions on the power calculations.

Total Sample Size

Specifies the total number of observations (runs, experimental units, or samples) needed for your experiment. Select Lock to lock the total sample size

Solve for

Enables you to solve for a sample size, ratio to detect, or counts per unit in Group 1.

Power

Specifies the probability of rejecting the null hypothesis when it is false. With all other parameters fixed, power increases as sample size increases.

Group 1 Sample Size

Specifies the number of units needed for Group 1 in your experiment.

Group 2 Sample Size

Specifies the number of units needed for Group 2 in your experiment.

Ratio to detect

Specifies the alternative ratio of Group 2 to Group 1 counts per unit.

Group 1 Counts per Unit

Specifies the assumed Group 1 counts per unit. The assumed Group 2 counts per unit is specified by the Group 1 counts per unit and the ratio to detect.

Power Explorer Two Independent Sample Counts per Unit Options

The Explorer red triangle menu and report buttons provide additional options:

Simulate Data

Opens a data table of simulated data based on the explorer settings. View the simulated response column formula for the settings used.

Make Data Collection Table

Creates a new data table that you can use for data collection. The table includes scripts to facilitate data analysis.

Save Settings

Saves the current settings to the Saved Settings table. This enables you to save a set of alternative study plans. See Saved Settings in the Sample Size Explorers.

Help

Opens JMP help.

Statistical Details for the Power Explorer for Two Independent Sample Counts per Unit

The power calculations for testing two independent sample counts using the ratio of defect counts per units is based on the asymptotic normal distribution of the ratio of Poisson rates. See Gu, et al. (2008), Li, et al. (2013), or Mathews (2010).

For the one-sided lower alternative:

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Equation shown here

For the one-sided upper alternative:

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Equation shown here

For a two-sided alternative:

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Equation shown here

Equation shown here

where:

α is the significance level

n1 and n2 are the group sample sizes

ρ0 is the assumed ratio between the group defect rates

ρA is the alternative ratio between the group defect rates

λ1 is the assumed rate for Group 1

z1-α is the (1 - α)th quantile of the normal distribution

Φ(x) is the cumulative distribution function of the normal distribution.

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