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). The default value is 0.05.
Use the significance level to decide whether to reject or fail to reject the null hypothesis (H0). If the probability that an event occurs is less than the significance level, the usual interpretation is that the results are statistically significant, and you reject H0.
The sample size (N) is the total number of observations in the sample.
The sample size affects the power of the test.
Usually, a larger sample size gives the test more power to detect an outlier. For more information, go to What is power?.
The mean is the average of the data, which is the sum of all the observations divided by the number of observations.
Use the mean to describe the sample with a single value that represents the center of the data. Many statistical analyses use the mean as a standard measure of the center of the distribution of the data.
The standard deviation is the most common measure of dispersion, or how spread out the data are about the mean. The symbol σ (sigma) is often used to represent the standard deviation of a population, while s is used to represent the standard deviation of a sample. Variation that is random or natural to a process is often referred to as noise.
Because the standard deviation is in the same units as the data, it is usually easier to interpret than the variance.
Use the standard deviation to determine how spread out the data are from the mean. A higher standard deviation value indicates greater spread in the data. A good rule of thumb for a normal distribution is that approximately 68% of the values fall within one standard deviation of the mean, 95% of the values fall within two standard deviations, and 99.7% of the values fall within three standard deviations.
The maximum is the largest data value.
In these data, the maximum is 19.
13 | 17 | 18 | 19 | 12 | 10 | 7 | 9 | 14 |
Use the maximum to identify a possible outlier or a data-entry error. One of the simplest ways to assess the spread of your data is to compare the minimum and maximum. If the maximum value is very high, even when you consider the center, the spread, and the shape of the data, investigate the cause of the extreme value.
The minimum is the smallest data value.
In these data, the minimum is 7.
13 | 17 | 18 | 19 | 12 | 10 | 7 | 9 | 14 |
Use the minimum to identify a possible outlier or a data-entry error. One of the simplest ways to assess the spread of your data is to compare the minimum and maximum. If the minimum value is very low, even when you consider the center, the spread, and the shape of the data, investigate the cause of the extreme value.
An outlier is an unusually large or small observation. Try to identify the cause of any outliers. Correct any data–entry errors or measurement errors. Consider removing data values for abnormal, one-time events (also called special causes).
The row in the worksheet that contains the outlier. Minitab displays this value only when an outlier exists.
When you use one of Dixon's ratio tests, Minitab displays more observations in the test table, in addition to the minimum and maximum. The value in the brackets indicates the size of the observation relative to the other values. For example, x[2] denotes the 2nd smallest observation and x[N-1] denotes the 2nd largest observation.
Grubbs' test statistic (G) is the difference between the sample mean and either the smallest or largest data value, divided by the standard deviation. Minitab uses Grubbs' test statistic to calculate the p-value, which is the probability of rejecting the null hypothesis when it is true.
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.
Use the p-value to determine whether an outlier exists.
An outlier plot is similar to an individual plot. Use the outlier plot to visually identify an outlier in the data. If an outlier exists, Minitab represents it on the plot as a red square. Try to identify the cause of any outliers. Correct any data–entry errors or measurement errors. Consider removing data values for abnormal, one-time events (also called special causes).