Interpret all statistics for 1 Proportion

Find definitions and interpretation guidance for every statistic that is provided with the 1 proportion analysis.

Confidence interval (CI) and bounds

The confidence interval provides a range of likely values for the population proportion. 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 proportion. The percentage of these confidence intervals or bounds that contain the proportion 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 proportion.

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

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 sample proportion with a reference line that indicates the hypothesized proportion.

The confidence interval provides a range of likely values for the population proportion. 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 proportion. The percentage of these confidence intervals or bounds that contain the proportion 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 proportion.

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 proportion for households that made a purchase is 0.087. You can be 95% confident that the population proportion is between approximately 0.07 and 0.106.

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.

Interpretation

In the output, the null and alternative hypotheses help you to verify that you entered the correct value for the hypothesized proportion.

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 population proportion is statistically different from the hypothesized proportion.

To determine whether the difference between the population proportion and the hypothesized proportion 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 proportion and the hypothesized proportion 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 proportion and the hypothesized proportion 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.

Sample p

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

Interpretation

The sample proportion is an estimate of the population proportion.

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

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