OneWay Analysis of Variance, ANOVA, is used to compare the means of two or more samples against each other. This calculation determines whether it is likely that the samples came from populations with the same mean. This is similar to a 2Sample tTest except that three or more samples can be examined with this statistical test.
(ANOVA) can also be used to examine multiple variables and levels at the same time, but here the focus is primarily on the OneWay. OneWay examines just one variable and multiple levels. For example, a team might need to determine if 3 operators are different
For Example
Measure 15 points for each operator to preform a task. Use the ANOVA test to make the judgment and see if all the operators' average (mean) task times are the same
Level Of Confidence
You will need to determine the the level of confidence, such as 90% or 95% for the calculation. This depends your required level of certainty from the analysis of variation calculation.
Explanation
This is shown graphically in the Figure below . The upper curves represent the distributions of the three operators' times (known as the populations). The exact nature of these distributions is unknown to the team, because they represent all data points for all time. However, the team can see the sample's distrubution. Shown as the lower curves.
ANOVA examines the sample data with the aim of making an inference on the location of the population means (μ) relative to each other. It does this by breaking down the variation (using variances) in all the sample data into separate pieces, hence the name Analysis Of Variance.
It compares the size of the variation between the samples versus the variation within the samples.
If the variation between the samples is large relative to the variation within the samples, then it means the samples are spread widely (between) compared with the background noise (within). This would imply that the means of the parent distributions are different
If the between variation is not large compared to the within variation, then it is likely that the means of the parent distribution are about the same. More specifically the test cannot distinguish between them.
The result of the test is a number called the pvalue, which stands for probability. A high pvalue means the samples come from populations with the same mean. The reverse is also true. A low pvalue tells us the populations are significantly different. In our example the pvalue tells us the probability that the mean operator times are the same or different. If the pvalue is low, then at least one of the mean operator times is distinguishable from the others; if the pvalue is high, they all are not distinguishable.
Roadmap
The roadmap of the test analysis itself is shown graphically in Figure below
OneWay Anova Roadmap
Roadmap adapted from SBTI's Process Improvement Methodology training material.
Step 1.Identify the metric and levels to be examined (for example, three operators). Make the metric well defined and understood by the team.
Step 2.Determine the sample size. Use a sample size calculator.
Step 3.Collect the sample data set, one from each level of the variable. Follow the rules of good experimentation. If the sample size calculator determined a sample size of ten data points, then ten points need to be collected for each and every level. For example, if the variable is operator and there are three levels (three operators), then 3 x 10 = 30 data points are collected in total.
Step 4.Examine stability of all sample data sets using a Control Chart for each, typically an Individuals and Moving Range Chart (IMR). A Control Chart identifies whether the processes are stable, having
This is important; if the processes are not stable, Then the study will give an incorrect answer.
Step 5.Examine normality of the sample data sets using a Normality Test for each.
Step 6.Perform the ANOVA test if all of the sample data sets were determined to be normal in Step 5
It is beyond the scope of this page to show you the calculations. We recommend using Mini tab to easily conduct the calculations. Below we discuss how to interpret the results of the calculations.
Interpreting The Output
This test calculates a ratio of the signal (variation due to the variable, the "between") relative to the noise (any other variation not due to the variation, the "within"). If the signaltonoise ratio gets large enough then this would be considered to be unlikely to have occurred purely by random chance and the variable is thus considered statistically significant.
This is achieved by looking up the signaltonoise ratio in a reference distribution (FTest), which returns a pvalue. The pvalue represents the likelihood that an effect this large could have occurred purely by random chance even if the populations were the same.
Based on the pvalues, statements can be generally formed as follows:
Example Output From An ANOVA
ANOVA results for a comparison of samples of Bob's vs Jane's vs Walt's performance (output from Minitab v14).
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