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

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 the hypothesis of "no difference" or "no effect."
- Alternative hypothesis
- The alternative hypothesis states that a population parameter is smaller, larger, or different from the hypothesized value in the null hypothesis. The alternative hypothesis states what you suspect is true that is contrary to the statement of the null hypothesis. Often, the goal of a hypothesis test is to show that the sample data provide enough evidence to reject the null hypothesis. The rejection of the null hypothesis supports the alternative hypothesis.

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

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

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?.

The event is the value of interest in the sample. Minitab uses the number of events to calculate the sample proportion, which is an estimate of the population proportion. You can change the value Minitab uses as the event by selecting the other value when you specify the analysis. Select the event according to the proportion that you want the analysis to estimate.

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

The sample proportion is an estimate of the population proportion of the event of interest.

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.

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 cover the unknown population proportion. The percentage of these confidence intervals or bounds that cover 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 cover 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.

N | Event | Sample p | 95% CI for p |
---|---|---|---|

1000 | 87 | 0.087000 | (0.070617, 0.106130) |

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.

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

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 H
_{0}) - 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 H
_{0}) - 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 Power and Sample Size for 1 Proportion.

The Z–value is the observed score test statistic. The value
measures the difference between the sample proportion of the event of interest and the
hypothesized population parameter value in units of the standard error under the null
hypothesis. The standard error under the null hypothesis has the following
form:
where *p*_{0} is the hypothesized population proportion and
*n* is the number of trials.

The results include the Z-value when the calculations use Wilson-Score without a continuity correction.

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 the critical value. The critical value is Z_{1-α/2}
for a two–sided test and Z_{1-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 it is not, 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.