You are watching: In the analysis of variance procedure (anova), "factor" refers to

The procedure is made up of just three basic stages. After looking at the procedure, we would apply it in a real problem.

**The Seven Steps are****Step 1: Calculate the MeanStep 2: Setup the null and alternate hypothesisStep 3: Calculate the Sum of SquaresStep 4: Calculate the Degrees of FreedomStep 5: Calculate the Mean SquaresStep 6: Calculate the F StatisticStep 7: Look up statistical Table and state your conclusion**

**Veiw a solve example!**

**Before we begin, take some time to examine Figure 1. This figure summarizes what needs to be calculated to perform a one-way ANOVA.**

Figure 1: Analysis of Variance Table

** **

**Step 1: Calculate all the means**

**You need to calculate all the means for all the groups in the question. Then you also need to calculate to overall means with all the data combined as one single group.Go to solved example **

**Step 2: Set up the null and alternate hypothesis and the Alpha**

**The null hypothesis assumes that there is no variance data in different groups. In other words, the means are the sameThe alternate hypothesis states the means are different. So we can state as follows:**

**H0:** μ1 = μ2 = μ3**Ha**: μ1 ≠ μ2 ≠ μ3

**Step 3: Calculate the Sum of Squares**

**Calculate the Sum of Squares Total (SST): The SStotal is the Sum of Squares(SS) based on the entire set in all the groups. In this case, you treat all the data from all the groups like on single combined set of data**

Calculate the Sum of Squares Within Groups (SSW): The is the sum of squares within each group. After calculating the sum of squares for each group, then you add them together for all the groups. That is why you have the sum symbol twice in the formular

The internal sum is for within the groupThe external sum is to sum the sums!Note: If you have calculated the first two sum of squares, you can the go ahead to calculate the the third on using the first two values using the formulaBut for learning purposes, we would calculate the third one. So let’s keep moving!

Calculate the Sum of Squares Between Groups (SSB): This is the sum of squares with the groups taken as single elements.

Assumming there are three groups you will have to do the the following:(group1_mean – total_mean)2 + (group2_mean – total_mean)2 + group3_mean – total_mean)2

Verify thatSStotal = SSbetween + SSwithin

### Step 4: Calculate the Degrees of Freedom (df)

**Calculate the Degrees of Freedom Total (DFT)**

where n is to total of all the data sets combined

Calculate the Degrees of Freedom Within Groups (DFW)

where k is the number of groups.So, if there are three groups of measurements, then k = 3

Calculate the Degrees Between Groups (DFB)

Note: You could actually calculate the third degree of freedom if you have two of them just like in the case of sum of square

You can verify that:dft = dfw + dfb

### Step 5: Calculate the Mean Squares

**Calculate the Mean Squares Between (MSB)**

Calculate the Mean Squares Within (MSW)

### Step 6: Create a Summary Table and Calculate the F Statistic

**This is the same table you created in Step 2. You just have to fill it with actual results based on your calculations. Stating with this table makes the problem easier to solve.Calculate the F Statistic using the fomular**

### Step 7: Look up F from table

Lood up the tabulated value of F(critical value) of F from the statistical table and compare it with the value you calculated (absolute value).If the absolute value is greater than the critical value, we reject the null hypothesis and conclude that there is significant different between the means of the populations. Otherwise, accept the null hypothesis or fail to reject the null hypothesis.

On to a Solved Example!

TaggedHypothesis Testing

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2 years ago

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Frank

1 year ago

The SSbetween calculation is wrong. The value of (x(mean) – X(mean)^2 needs to be multiplied by nj.

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Ramesh Savaliya

1 year ago

Very good explanation, easy to understand. Thank you.

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Hypothesis Testing Problems - Question 10(Sussan Sound predicts that....) - The Genius Blog

10 months ago

<…> Learn about Anova and the steps to follow <…>

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One-Way ANOVA(Analysis of Variance) Problem - Question 11 - The Genius Blog

10 months ago

<…> Read about one-way ANOVA and the steps hereWatch the video here for step by step explanationSolutions StepsAs usual, we would transfer the table of data into MS Excel so it becomes easier to work with. The excel table is given below. <…>

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