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 median is the midpoint of the data set. This midpoint value is the point at which half the observations are above the value and half the observations are below the value. The median is determined by ranking the observations and finding the observation that are at the number [N + 1] / 2 in the ranked order. If the number of observations are even, then the median is the average value of the observations that are ranked at numbers N / 2 and [N / 2] + 1.
The median of the sample data is an estimate of the population median.
Because the median is based on sample data and not on the entire population, it is unlikely that the sample median equals the population median. To better estimate the population median, use the confidence interval.
The confidence interval provides a range of likely values for the population median. 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 median. The percentage of these confidence intervals or bounds that contain the median 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 median.
An upper bound defines a value that the population median is likely to be less than. A lower bound defines a value that the population median 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.
The 1sample Wilcoxon test does not always achieve the confidence level that you specify because the Wilcoxon statistic is discrete. Because of this, Minitab uses a normal approximation with a continuity correction to calculate the closest achievable confidence level.
 

In these results, the estimate of the population median for reaction time is 11.55. You can be approximately 94.8% confident that the population median is less than 12.5.
The 1sample Wilcoxon test does not always achieve the confidence level that you specify because the Wilcoxon statistic is discrete. Because of this, Minitab uses a normal approximation with a continuity correction to calculate the closest achievable confidence level.
The achieved confidence indicates how likely it is that the population median is contained in the confidence 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 median.
In the output, the null and alternative hypotheses help you to verify that you entered the correct value for the hypothesized median.
The significance level (denoted as α or alpha) is the maximum acceptable level of risk for rejecting the null hypothesis when the null hypothesis is true (type I error). Usually, you choose the significance level before you analyze the data. In Minitab, you can select the significance level by specifying the Confidence level on the Options tab, because the significance level equals 1 minus the confidence level. Because the default confidence level in Minitab is 0.95, the default significance level is 0.05.
Compare the significance level to the pvalue to decide whether to reject or fail to reject the null hypothesis (H_{0}). If the pvalue is less than the significance level, the usual interpretation is that the results are statistically significant, and you reject H_{0}.
To calculate N for a 1sample Wilcoxon test, Minitab eliminates the observations that are equal to the hypothesized median. N for a 1sample Wilcoxon test equals the number of remaining observations.
N for a 1sample Wilcoxon test affects the power of the test. A larger value gives the test more power to detect a difference. For more information, go to What is power?.
The Wilcoxon statistic equals the number of pairwise averages (also called Walsh averages) that are greater than the hypothesized median, plus one half of the number of pairwise averages that are equal to the hypothesized median.
Minitab uses the Wilcoxon statistic to calculate the pvalue, which is a probability that measures the evidence against the null hypothesis.
Because the interpretation of the Wilcoxon statistic depends on the sample size, you should use the pvalue to make a test decision. The pvalue has the same meaning for any sample size.
The pvalue is a probability that measures the evidence against the null hypothesis. A smaller pvalue provides stronger evidence against the null hypothesis.
Use the pvalue to determine whether the population median is statistically different from the hypothesized median.
A boxplot provides a graphical summary of the distribution of a sample. The boxplot shows the shape, central tendency, and variability of the data.
Use a boxplot to identify any potential outliers. Boxplots are best when the sample size is greater than 20.
Try to identify the cause of any outliers. Correct any data–entry errors or measurement errors. Consider removing data values for abnormal, onetime events (also called special causes). Then, repeat the analysis. For more information, go to Identifying outliers.
A histogram divides sample values into many intervals and represents the frequency of data values in each interval with a bar.
Use the graphs to look for symmetry and to identify potential outliers.
A distribution is symmetric when a vertical line can be drawn down the middle and the two sides will mirror each other. When the data are not symmetric, they are skewed to one side or the other.
If your data do not come from a symmetric distribution, use a 1Sample Sign.
Outliers, which are data values that are far away from other data values, can strongly affect the results of your analysis. Often, outliers are easiest to identify on a boxplot.
Try to identify the cause of any outliers. Correct any data–entry errors or measurement errors. Consider removing data values for abnormal, onetime events (also called special causes). Then, repeat the analysis. For more information, go to Identifying outliers.
An individual value plot displays the individual values in the sample. Each circle represents one observation. An individual value plot is especially useful when you have relatively few observations and when you also need to assess the effect of each observation.
Use an individual value plot to examine the spread of the data and to identify any potential outliers. Individual value plots are best when the sample size is less than 50.
A distribution is symmetric when a vertical line can be drawn down the middle and the two sides will mirror each other. When the data are not symmetric, they are skewed to one side or the other.
If your data do not come from a symmetric distribution, use a 1Sample Sign.
Outliers, which are data values that are far away from other data values, can strongly affect the results of your analysis. Often, outliers are easiest to identify on a boxplot.
Try to identify the cause of any outliers. Correct any data–entry errors or measurement errors. Consider removing data values for abnormal, onetime events (also called special causes). Then, repeat the analysis. For more information, go to Identifying outliers.