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 ¹ 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.
1. Choose ProcessMA > Basic Statistics > 2 Proportions.
2. In Data in, choose how your data is stored.
· If your data in stored in a single column:
- In Variable, select the column containing the raw data.
- In Category, select the column containing the subgroup codes.
· If your data in stored in different columns:
- In Sample 1, select the column containing the first sample.
- In Sample 2, select the column containing the second sample.
· If your data in stored in summarised data:
- In Number of trials(1), enter the number of trials for the first sample.
- In Number of successes(1), enter the number of successes within the set of trials for the first sample.
- In Number of trials(2), enter the number of trials for the second sample.
- In Number of successes(2), enter the number of successes within the set of trials for the second sample.
3. In Test difference, enter the hypothesised difference between the two proportions.
4. Click OK.
Optional
5. In Alternate, select the type of test.
6. In Confidence level, enter the desired confidence level for the confidence interval.
Note To select a column of data into a textbox, double-click on any of the column names shown in the list on the left of the dialog box while in the textbox.
Variable: Text or numeric; Must contain 2 distinct categories (e.g. Pass and Fail, 0 and 1).
Category: Text or numeric; Must contain 2 distinct categories.
Sample 1: Text or numeric; Must contain 2 distinct categories (e.g. Pass and Fail, 0 and 1).
Sample 2: Text or numeric; Must contain 2 distinct categories (e.g. Pass and Fail, 0 and 1).
Number of trials(1): Integer.
Number of successes(1): Integer.
Number of trials(2): Integer.
Number of successes(2): Integer.
Test difference: Numeric; Between 0 and 1
Confidence level: Numeric; Between 0 and 100.
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. Choose ProcessMA > Basic Statistics > 2 Proportions.
2. In Data in, select summarised data.
3. In Number of trials(1), enter 400.
4. In Number of successes(1), enter 45.
5. In Number of trials(2), enter 600.
6. In Number of successes(2), enter 71.
7. In Test difference, enter 0.
8. In Alternate, select Less than.
9. In Confidence level, enter 95.
10. Click OK.
Interpretation
For a desired a = 0.05, since p = 0.6116 > 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.