## How can I use XLSTAT to run a repeated measures ANOVA?

Kovach Computing Services The easy and inexpensive way to analyze your trenbolone acetate kura. An Excel sheet with both the data and the results can be downloaded by clicking here. The data correspond to an experiment in which a treatment for depression is studied. Two groups of patients 1: The dependant variable is a depression score. We have performed a repeated measures ANOVA in**two way anova xlstat**to determine the effect of the treatment and the effect of time on

**two way anova xlstat**depression score. The difference between classical ANOVA and repeated measures ANOVA is that measures on the same patient at different times are not supposed to be independent and, thus, the covariance matrix of e is not diagonal.

## XLSTAT - ANOVA (Analysis of Variance)

To help introduce the basic concepts we start with the following example. A new fertilizer has been developed to increase the yield on crops, and the makers of the fertilizer want to better understand which of the three formulations blends of this fertilizer are most effective for wheat, corn, soy beans and rice crops. They test each of the three blends on one sample of each of the four types of crops. The crop yields for the 12 combinations are as shown in Figure 1.

Figure 1 — Data for Example 1. We interrupt the analysis of this example to give some background, after which we will resume the analysis.

We define the structural model as follows. A factor is an independent variable. A level is some aspect of a factor; these are what we called groups or treatments in the one factor analysis discussed in Basic Concepts for ANOVA.

In Example 1 there are two factors: The blend factor has 3 levels and the crop factor has 4 levels. In general, suppose we have two factors A and B. Factor A has r levels and factor B has c levels. We organize the levels for factor A as rows and the levels for factor B as columns. We use the index i for the rows i. It is easy to show that. The term x ij in the formula for SS E in the above table should not have a bar over it.

If we square both sides of the equation, sum over i, j and then simplify with various terms equal to zero as in the proof of Property 2 of Basic Concepts for ANOVA , we get the first result. Suppose a sample is made as described in Definitions 1 and 2, with the x ij independently and normally distributed. The result follows from Property 2 and Theorem 1 of F Distribution. Two-factor Without Replication data analysis tool.

The output from the data analysis tool is shown in Figure 2. There are two null hypotheses: The most interesting cells are the ones corresponding to the four sum squares. We show how to calculate the values for each of those cells in Figure 3.

Figure 3 — Key formulas for analysis from Figure 2. Alternatively we can take squared deviations from the sums of each group, as is done in Figure 3. Real Statistics Excel Capabilities: Thanks J for finding the typo. The figure is correct but the opening paragraph is not. The website has now been corrected.

Thanks again for catching the error. Sir I think there is a mistake about SSE in the table of definition 2. It may be a typo. Sir Sorry, you are right. The SSE formula is different with the textbook I read, but it is correct. Jeff, Yes, you are correct. Thanks for catching this typing mistake. I have now corrected the caption on the webpage. Chris, Thanks for catching this typo. Suppose the Row factor has 3 levels and the Column factor has 4 levels.

Nice work and thanks. Posting the above comment also dropped the decimal on my first example for the correction. Must be something in the way the HTML is conveyed. Dave, Thanks for catching this typo and for helping improve the accuracy of the website. I have now revised the webpage to include the decimal point.

Because the degree freedom of error is equal to zero when trying to calculate the interaction effect,so we can conclude that their are no interaction effects in this case?

Which follow up test is best depends on a number of things equal sampler size or not, homogeneity of variances or not, etc. See the following webpage: Hence I cannot understand how to arrive at the output for this example. Then in the dialog box that appears insert 1 in the Number of Rows per Sample field.

My data is having 6 columns and 24 rows for each column. I am confuse what is happening. Which post hoc test should I use in the excel toolpack when I find significance in the results of the two factor anova without replication? You can use the usual post hoc tests for ANOVA with replication, except those that test the interaction since you are assuming there is no interaction.

Question 3 of the Spring exam from http: What is the problem with my data? Hilary, If you send me an Excel file with your data and calculations and I will try to figure out what is going on. You can get my email address on the webpage Contact Us Charles. Hope you can assist as well.

You need to fill in the contrast column labeled c in the output with 1 for one group and -1 for another group. In this way you compare two groups. I have the same problem. Could you please give me any suggestion? In the case where there is no replication, there is no interaction factor, and so you cannot analyze it.

You can, however, analyze the two main factors, as described on the referenced webpage. Can you please tell me why I get a p value 2. Anila, A p value of 2. This value is written in what is called scientific notation. You will need to do this yourself. I am providing you the tools and explanations, but you need to do the work. Charles, Which test can I use when the assumptions for using a Two Factor Anova, especially the one of a common variance, are not met?

Thank you again, Erik. This test has limited power, but it is a possible approach. This seems to be producing inaccurate results. The Two Factor Anova supports two input data formats: Excel format and standard i. When Excel format is used, I believe that marginal means are based on the original data, but when standard format is used then the marginal means are the average of the group means, as you have observed.

For balanced models when all interactions have the same number of elements , both approaches yield the same result. This is not the case for unbalanced models. For unbalanced models, you should choose the Regression option on the Two Factor Anova dialog box.

This will use the standard format approach to calculating the marginal means. This is the preferred approach as described on the following webpage:.

Unbalance Approach to Two Factor Anova. The distinction between balanced and unbalanced models was what I was missing, thank you! Your site is an excellent resource, and it is very much appreciated! I have done carried out a biofilm assay with two different nanoparticles with 6 different concentrations 0, , ,,, without replication. I find significant difference betwee the two types of nanoparticles when I do the test.

However, there is no significant differences between different concentrations. What I am confused is that the difference between columns diff concentrations is for both types of nanoparticles.

However, when I replicate and do t-test assuming equal variance between control and different concentrations of nanoparticles, I find there is a significant difference. Please let me know which method and analysis is appropriate. The differences between the columns is for both types of nanoparticles combined.

If you like, you can send me an Excel file with this data and analysis so that I can better understand what you are trying to do. Hello, Thank you for your great addin. Am I misunderstanding a variable, or should the top formula be used? Neil, I believe that I am using the formula with gage and not total variation. Hi Charles, I want to know if which two ANOVA is appropriate to calculate the significant difference in the means of some data with two treatments across three different age groups.

Ajibola, You have 2 levels for the Treatment factor and 3 levels for the Age factor.

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