2 Proportions

Overview | How to | Example

 

 

Overview

The 2 Proportions conducts a hypothesis test of the difference between two proportions and calculates a confidence interval.

Test Null Hypothesis, H0 Alternate Hypothesis, H1
One-tailed p1 - p2 = p0 p1 - p2 < p0 or p1 - p2 > p0
Two-tailed p1 - p2 = p0 p1 - p2 <> p0

where p1 and p2 are the proportions of success in populations 1 and 2 respectively, and p0 is the hypothesized difference between the two proportions.

 

 

How to

At the Excel Menu (For Excel 2007, go to Add-ins first)

  1. Choose ProcessMA > Statistics > Basic Statistics > 2 Proportions

  2. For Summarized Data:

    1. In No. of Trials (1), enter the number of trials for the first sample (Integer, >=Successes)

    2. In No. of Successes (1), enter the number of successes within the set of trials for the first sample (Integer, >=0)

    3. In No. of Trials (2), enter the number of trials for the second sample (Integer, >=Successes)

    4. In No. of Successes (2), enter the number of successes within the set of trials for the second sample (Integer, >=0)

  3. For Raw Data:

    1. In Variable 1, select the column containing the raw data for the first sample (Exactly 2 distinct values, success and failure)

    2. In Variable 2 , select the column containing the raw data for the second sample (Exactly 2 distinct values, success and failure)

  4. In Test Difference , enter hypothesized proportion (Numeric, >-1 & <1)

  5. In Alternate, select the appropriate alternate test

  6. In Confidence Level, enter value for confidence level (Numeric, >0 & <1)

  7. Click OK

 

 

Example

You are the property manager and you need to decide whether to change the brand of light bulb you are using for the entire building. You want to use the brand of light bulbs that blow their fuses less often. You installed 400 light bulbs of the existing brand and 600 light bulbs of the new brand. After two months, you found out that 45 light bulbs of the existing brand 71 light bulbs of the new brand blew their fuses.

  1. Open data worksheet by choosing ProcessMA > Tools > Data

  2. Choose ProcessMA > Statistics > Basic Statistics > 2 Proportions

  3. Click Summarized Data

  4. In No. of Trials (1), enter 400

  5. In No. of Successes (1), enter 45

  6. In No. of Trials (2), enter 600

  7. In No. of Successes (2), enter 71

  8. In Alternate, select Less than

  9. Click OK

 

Results & Interpretation

For a desired a = 0.05, since p = 0.3884 > a, we fail to reject H0. Therefore, we conclude that there is no significant evidence that the new brand of light bulbs blow their fuses less often the existing brand.

 

 

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