# One-Way ANOVA

## Summary

Analyzes observed differences in the process mean at different levels (settings) of an input. To use the one-way ANOVA procedure, you must collect a sample of data at each level of the X-variable.

Answers the questions:
• If you change an input from one level to another level, does the mean of the process stay the same or does it change?
• Is the process variation the same before and after you make a change to the process?
When to Use Purpose
Mid-project Fixing an input at two or more different settings (levels) helps to determine which inputs have significant influence on the mean of the output.
Mid-project Verify that changes to inputs result in significant differences from the pre-project mean.

### Data

Continuous Y, a single X at two or more levels (generally three or more).

## How-To

1. Verify the measurement systems for the Y data and the input X are adequate.
2. Develop a data collection strategy (who will collect data, where, when, how much, how precise, how to record, and so on).
3. You can use one of two methods to enter data in Minitab:
• Enter data in separate columns, one column for each factor level. Use ANOVA > One-Way (Unstacked) for data set up this way.
• Enter Y data in one column, factor levels (X) in a second column. Use ANOVA > One-Way for data set up this way.
4. Determine your hypotheses. The null hypothesis (Ho) in a one-way ANOVA is whether the mean of the output is the same at all levels of the input. The alternative hypothesis (Ha) is whether the mean of at least one level is significantly different from the others.
5. If you determine the means of the levels are not equal, you can use multiple comparisons to determine which means are different. There are alternative methods for making multiple comparisons. The method you choose can depend on the question you want answered or on the amount of risk you are willing to accept. Tukey’s method is often used, because it is a conservative approach.

## Guidelines

• Develop a sound data collection strategy to ensure that your conclusions are based on truly representative data.
• Use Minitab’s Power and Sample Size command to determine the sample size necessary to detect the smallest difference of interest with sufficient power.
• The residuals must be independent, reasonably normal, and have reasonably equal variances. ANOVA is very robust to nonnormality (especially for large sample sizes) and unequal variances (especially when sample sizes are equal or nearly equal).
• You should always graph your data whenever you use a statistical test. For one-way ANOVA, the residuals are usually analyzed by a histogram, a normal plot, a residuals versus fits plot, and a residuals versus order plot. In addition, you can create a boxplot or individuals value plot on the raw data to identify any outliers.
• Minitab’s standard output only evaluates the alternate hypothesis (at least one of the levels has a different mean than at least one other level). However, the Comparisons option provides various pairwise comparisons of all level means versus all other level means.
• If you have discrete numeric data from which you can obtain every equally spaced value and you have measured at least 10 possible values, you can evaluate these data as if they are continuous.
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