# Interpret all statistics and graphs for Outlier Test

Find definitions and interpretation guidance for every statistic and graph that is provided with an outlier test.

## 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 all the data values come from the same normal distribution.
Alternative hypothesis
The alternative hypothesis states that either the smallest or largest data value is an outlier.

## Significance level

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.

### Interpretation

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.

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.
• Choose a higher significance level, such as 0.10, to be more certain that you detect any difference that possibly exists. For example, a quality engineer compares the stability of new ball bearings with the stability of current bearings. The engineer must be highly certain that the new ball bearings are stable because unstable ball bearings could cause a disaster. The engineer chooses a significance level of 0.10 to be more certain of detecting any possible difference in stability of the ball bearings.
• Choose a lower significance level, such as 0.01, to be more certain that you detect only a difference that actually exists. For example, a scientist at a pharmaceutical company must be very certain about a claim that the company's new drug significantly reduces symptoms. The scientist chooses a significance level of 0.001 to be more certain that any significant difference in symptoms does exist.

## N

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

### Interpretation

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?.

## Mean

The mean is the average of the data, which is the sum of all the observations divided by the number of observations.

For example, the wait times (in minutes) of five customers in a bank are: 3, 2, 4, 1, and 2. The mean waiting time is calculated as follows:
On average, a customer waits 2.4 minutes for service at the bank.

### Interpretation

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 median and the mean both measure central tendency. But unusual values, called outliers, can affect the median less than they affect the mean. If your data are symmetric, the mean and median are similar.

## StDev

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.

### Interpretation

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 standard deviation can also be used to establish a benchmark for estimating the overall variation of a process.

## Maximum

The maximum is the largest data value.

In these data, the maximum is 19.

 13 17 18 19 12 10 7 9 14

### Interpretation

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.

## Minimum

The minimum is the smallest data value.

In these data, the minimum is 7.

 13 17 18 19 12 10 7 9 14

### Interpretation

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.

## Outlier

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).

## Row

The row in the worksheet that contains the outlier. Minitab displays this value only when an outlier exists.

## x[i] and x[N-i]

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.

## G

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.

## P

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 an outlier exists.

To determine whether an outlier exists, 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 an outlier exists when no actual outlier exists.
P-value ≤ α: An outlier exists (Reject H0)
If the p-value is less than or equal to the significance level, the decision is to reject the null hypothesis and conclude that an outlier exists. Try to identify the cause of any outliers. Correct any data–entry errors or measurement errors. Consider removing data values that are associated with abnormal, one-time events (special causes).
P-value > α: You cannot conclude an outlier exists (Fail to reject H0)
If the p-value is greater than the significance level, the decision is to fail to reject the null hypothesis because you do not have enough evidence to conclude that an outlier exists. You should make sure that your test has enough power to detect an outlier. For more information, go to Increase power.

## Outlier plot

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).

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