Analysis of Means

Overview | How to | Example

 

 

Overview

Analysis of Means (ANOM) is used to test the equality of population means and it's function is similar to ANOVA. An ANOM chart looks like a control chart and is used to detect population means that are different from others. You can assume if the response data follows a Normal, Binomial distribution or Poisson distribution. For Normal distribution, you can also choose between the one-way or two-way design.

For Normal data, one-way designs can be balanced or unbalanced and two-way designs must be balanced.

For Binomial data, the sample size must be sufficiently large to ensure a valid Normal approximately to Binomial since decision limits are based on Normal distribution. Therefore, a general rule to use ANOM for Binomial data is where np > 5 and n(1-p) > 5, where n is the sample size and p is the proportion of defectives

For Poisson data, the sample size must be constant. The Poisson mean must also be sufficiently large to ensure a valid Normal approximately to Poisson since decision limits are based on Normal distribution. Therefore, a general rule to use ANOM for Poisson data, the mean of the Poisson distribution is >=5.

 

 

How to

At the Excel Menu (For Excel 2007, go to Add-ins first)

  1. Choose ProcessMA > Statistics > ANOVA > Analysis of Means

  2. For Normal (1 Factor):

    1. In Variable, select the column containing the response data (Numeric)

    2. In Factor 1, select the column containing factor levels (>=2 levels)

  3. For Normal (2 Factors):

    1. In Variable, select the column containing the response data (Numeric)

    2. In Factor 1, select the column containing first factor levels. Two-way designs must be balanced (>=2 levels)

    3. In Factor 2 , select the column containing second factor levels (>=2 levels)

  4. For Binomial:

    1. In Variable, select the column containing the response data (Integer, >=0, Up to 500 rows)

    2. In Sample Size, enter the sample size (Positive integer)

  5. For Poisson:

    1. In Variable, select the column containing the response data (Integer, >=0, Up to 500 rows)

  6. In Alpha Level, enter a value for the error rate (Numeric, >0 & <1)

  7. Click OK

 

 

Example

You conducted an experiment to study how well organisms multiple in different temperatures (Factor 1) and in the presence of different catalysts (Factor 2). You prepared 18 dishes of organisms and placed them at three different temperatures and added three different types of catalyst. You recorded the number of organism in each dish after 10 days.

  1. Open data worksheet by choosing ProcessMA > Tools > Data

  2. Choose ProcessMA > Statistics > ANOVA > Analysis of Means

  3. For Normal (1 Factor):

    1. In Variable, select L - Organism

    2. In Factor 1, select M - Temperature

  4. For Normal (2 Factors):

    1. In Variable, select L - Organism

    2. In Factor 1, select M - Temperature

    3. In Factor 2 , select N - Catalyst

  5. For Binomial:

    1. In Variable, select L - Organism

    2. In Sample Size, enter 1000

  6. For Poisson:

    1. In Variable, select L - Organism

  7. Click OK

 

Results & Interpretation

For normal data with one factor (temperature): The main effects are within the decision limits, indicating no significant evidence of main effects.

For normal data with 2 factors: The interactions effects are within the decision limits, indicating no significant evidence of interaction. For the main effects, The main effects for level 2 and 3 of Factor 2 (Catalyst) are outside the decision limits, indicating that these means are different from the grand mean.

For Binomial data: The samples that falls outside the decision limits indicate that the sample is different from the grand mean.

For Poisson data: The samples that falls outside the decision limits indicate that the sample is different from the grand mean.

 

 

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