Example of 2 Proportionsmain topic interpreting results session command see also
Example of 2 ProportionsAs your corporation's purchasing manager, you need to authorize the purchase of twenty new photocopy machines. After comparing many brands in terms of price, copy quality, warranty, and features, you have narrowed the choice to two: Brand X and Brand Y. You decide that the determining factor will be the reliability of the brands as defined by the proportion requiring service within one year of purchase.
Because your corporation already uses both of these brands, you were able to obtain information on the service history of 50 randomly selected machines of each brand. Records indicate that six Brand X machines and eight Brand Y machines needed service. Use this information to guide your choice of brand for purchase.
1 Choose Stat > Basic Statistics > 2 Proportions.
2 Choose Summarized data.
3 Under Sample 1, in Number of events, enter 44. In Number of trials, enter 50.
4 Under Sample 2, in Number of events, enter 42. In Number of trials, enter 50. Click OK.
Session window output
Test and CI for Two Proportions
Sample X N Sample p 1 44 50 0.880000 2 42 50 0.840000
Difference = p (1) - p (2) Estimate for difference: 0.04 95% CI for difference: (-0.0957903, 0.175790) Test for difference = 0 (vs ≠ 0): Z = 0.58 P-Value = 0.564
Fisher’s exact test: P-Value = 0.774 |
For this example, the normal approximation test is valid because, for both samples, the number of events is greater than four, and the difference between the numbers of trials and events is greater than four. The normal approximation test reports a p-value of 0.564, and Fisher's exact test reports a p-value of 0.774. Both of these p-values are larger than commonly chosen a levels. Therefore, the data are consistent with the null hypothesis that the population proportions are equal. In other words, the proportion of photocopy machines that needed service in the first year did not differ depending on brand. As the purchasing manager, you need to find a different criterion to guide your decision on which brand to purchase.
Because the normal approximation is valid, you can draw the same conclusion from the 95% confidence interval. Because zero falls in the confidence interval of (-0.0957903 to 0.175790) you can conclude that the data are consistent with the null hypothesis. If you think that the confidence interval is too wide and does not provide precise information as to the value of p1 - p2, you may want to collect more data in order to obtain a better estimate of the difference.