Interpret all statistics for 2 Proportions

Find definitions and interpretation guidance for every statistic that is provided with the 2 proportions test.

Confidence interval (CI for difference) and bounds

The confidence interval provides a range of likely values for the population difference. Because samples are random, two samples from a population are unlikely to yield identical confidence intervals. But, if you repeated your sample many times, a certain percentage of the resulting confidence intervals or bounds would contain the unknown population difference. The percentage of these confidence intervals or bounds that contain the difference is the confidence level of the interval. For example, a 95% confidence level indicates that if you take 100 random samples from the population, you could expect approximately 95 of the samples to produce intervals that contain the population difference.

An upper bound defines a value that the population difference is likely to be less than. A lower bound defines a value that the population difference is likely to be greater than.

The confidence interval helps you assess the practical significance of your results. Use your specialized knowledge to determine whether the confidence interval includes values that have practical significance for your situation. If the interval is too wide to be useful, consider increasing your sample size. For more information, go to Ways to get a more precise confidence interval.

Estimation for Difference
Difference

In these results, the estimate of the population difference in proportions in summer employment for male and female students is 0 approximately 0.099. You can be 95% confident that the ratio of population standard deviations is between approximately 0.06 and 0.13.

Difference: p1 – p2

The difference is the unknown difference between the population proportions that you want to estimate. Minitab indicates which population proportion is subtracted from the other.

Difference

The difference is the difference between the proportions of the two samples.

Because this value is based on sample data and not on the entire population, it is unlikely that the sample difference equals the population difference. To better estimate the population difference, use the confidence interval for the difference.

Event

The number of events (also called the number of successes) is the number of observations that have a specific characteristic within a sample. The Method table displays the value in the sample that represents the event.

Minitab uses the number of events to calculate the sample proportion, which is an estimate of the population proportion.

Interval plot

The interval plot shows the confidence interval for the difference with a reference line that indicates the hypothesized difference of 0.

The confidence interval provides a range of likely values for the population difference. Because samples are random, two samples from a population are unlikely to yield identical confidence intervals. But, if you repeated your sample many times, a certain percentage of the resulting confidence intervals or bounds would contain the unknown population difference. The percentage of these confidence intervals or bounds that contain the difference is the confidence level of the interval. For example, a 95% confidence level indicates that if you take 100 random samples from the population, you could expect approximately 95 of the samples to produce intervals that contain the population difference.

Interpretation

The confidence interval helps you assess the practical significance of your results. Use your specialized knowledge to determine whether the confidence interval includes values that have practical significance for your situation. If the interval is too wide to be useful, consider increasing your sample size. For more information, go to Ways to get a more precise confidence interval.

In these results, the estimate of the population difference in proportions in summer employment for male and female students is 0 approximately 0.099. You can be 95% confident that the ratio of population standard deviations is between approximately 0.06 and 0.13.

N

The sample size (N) is the total number of observations in the sample.

Interpretation

The sample size affects the confidence interval and the power of the test.

Usually, a larger sample size results in a narrower confidence interval. A larger sample size also gives the test more power to detect a difference. For more information, go to What is power?.

Null hypothesis and alternative hypothesis

The null and alternative hypotheses are two mutually exclusive statements about a population. A hypothesis test uses sample data to determine whether to reject the null hypothesis.
Null Hypothesis
The null hypothesis states that a population parameter (such as the mean, the standard deviation, and so on) is equal to a hypothesized value. The null hypothesis is often an initial claim that is based on previous analyses or specialized knowledge.
Alternative Hypothesis
The alternative hypothesis states that a population parameter is smaller, greater, or different than the hypothesized value in the null hypothesis. The alternative hypothesis is what you might believe to be true or hope to prove true.

Interpret

Test
Method
Z-Value
P-Value

In these results, the null hypothesis is that the population difference is equal to 0. The alternative hypothesis is that the difference is not equal to 0.

P-value

The p-value is a probability that measures the evidence against the null hypothesis. A smaller p-value provides stronger evidence against the null hypothesis.

Interpretation

Use the p-value to determine whether the difference in population proportions is statistically significant.

To determine whether the difference between the population proportions is statistically significant, compare the p-value to the significance level. Usually, a significance level (denoted as α or alpha) of 0.05 works well. A significance level of 0.05 indicates a 5% risk of concluding that a difference exists when there is no actual difference.
P-value ≤ α: The difference between the proportions is statistically significant (Reject H0)
If the p-value is less than or equal to the significance level, the decision is to reject the null hypothesis. You can conclude that the difference between the population proportions is statistically significant. Use your specialized knowledge to determine whether the difference is practically significant. For more information, go to Statistical and practical significance.
P-value > α: The difference between the proportions is not statistically significant (Fail to reject H0)
If the p-value is greater than the significance level, the decision is to fail to reject the null hypothesis. You do not have enough evidence to conclude that the difference between the population means is statistically significant. You should make sure that your test has enough power to detect a difference that is practically significant. For more information, go to Increase the power of a hypothesis test.

Minitab uses the normal approximation method and Fisher's exact method to calculate the p-values for the 2 proportions test. If the number of events and the number of nonevents is at least 5 in both samples, use the smaller of the two p-values. If either the number of events or the number of nonevents is less than 5 in either sample, the normal approximation method may be inaccurate. Fisher's exact method is valid for all samples, but tends to be conservative. A conservative p-value understates the evidence against the null hypothesis.

Pooled estimate of the proportion

The pooled estimate of the proportion is a weighted average of the proportions from the two samples. Minitab uses this value to calculate the p-value for each test. Some introductory statistics textbooks mention the possibility of using a pooled estimate of the proportion because it is easier to calculate manually and saves time. The 2 Proportions test includes this option to help students replicate their manual calculations in Minitab.

To have Minitab display this value in the output, on the Options tab, select Use the pooled estimate of the proportion for Test method.

Sample p

The sample proportion equals the number of events divided by the sample size (N).

Interpretation

The proportion of each sample is an estimate of the population proportion of each sample.

Z

The Z-value is a test statistic for Z-tests that measures the difference between an observed statistic and its hypothesized population parameter in units of standard error.

Interpretation

You can compare the Z-value to critical values of the standard normal distribution to determine whether to reject the null hypothesis. However, using the p-value of the test to make the same determination is usually more practical and convenient.

To determine whether to reject the null hypothesis, compare the Z-value to your critical value. The critical value is Z1-α/2 for a two–sided test and Z1-α for a one–sided test. For a two-sided test, if the absolute value of the Z-value is greater than the critical value, you reject the null hypothesis. If the absolute value of the Z-value is less than the critical value, you fail to reject the null hypothesis. You can calculate the critical value in Minitab or find the critical value from a standard normal table in most statistics books. For more information, go to Using the inverse cumulative distribution function (ICDF) and click "Use the ICDF to calculate critical values".

The Z-value is used to calculate the p-value.
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