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Analysis of Variance [ANOVA] is a statistical method used to test for the difference between two or more average values of multiple samples. The purpose of ANOVA is to determine the extent to which an independent variable can affect a major factor. Are in search of an expert data analyst? We have professionals who offer factorial ANOVA analysis using Statistical Package of Social Sciences (SPSS). Our experts have exceptional skills in analyzing data with years of experience. Contact us any time to make inquiries, as we are available 24/7.

Factorial ANOVA is a branch of the statistical methods used to compare two or more factors based on a single variable. It is used to identify whether there is an interaction between multiple variables and a factor and how the variables affect it. This article contains detailed examples of factorial ANOVA and step by step guide for carrying out factorial ANOVA using SPSS.

Examples of Use of Factorial ANOVA

Below are examples of how factorial ANOVA is used in real scenarios.

Example 1:

An employer may want to know how training programs and time shifts may affect employee productivity. They subject the employees to different training programs, with some having physical training and others having online training. They also give different employees distinct time shifts, with others working in the morning hours and others during the evening. After a while, they record the productivity rate of each employee.

In this example, the variables are:

Factors: Training programs, time shifts

Single variable: Employee productivity

The employee could use factorial ANOVA for the analysis to understand how the two factors affect the single variable.

Example 2:

A professor wants to know if administering multiple tests, teaching methods, and class time affects student performance. She administers random tests to 15 students within three weeks and alternates between online and physical classes in the early morning and evening during the same period. After the duration ends, they take note of the results of each student.

In the example above, the variables are:

Factors: Tests, teaching methods, class time
Single variable: Student performance

The professor could use factorial ANOVA analysis to know how the three factors affect the single variable.

Example of Factorial ANOVA Analysis

The table below shows an example of factorial ANOVA analysis.

Factors	WEEK 1	WEEK 2	WEEK 3
TESTS	5 5 5 4 8	3 4 6 1 5	14 13 12 9 16
TEACHING METHODS	11 14 13 14 15	7 7 6 2 5	10 11 12 13 12
CLASS TIMES	12 12 14 15 16	11 8 9 8 9	12 18 16 17 17

The marginal means during the three weeks of the students are:

Taking tests= 12.933

Using different teaching methods= 10.133

Different class time= 7.333

Week 1= 10.867

Week 2= 6.067

Week 3= 13.467

The sums are:

Taking tests= 194

Using different teaching methods= 152

Different class time= 110

Week 1= 163

Week 2= 91

Week 3= 202

The grand mean is 10.13333

Total is 456

∑y²=5514

Now, we test for hypothesis and perform the factorial ANOVA using SPSS. Before performing factorial ANOVA in SPSS, certain assumptions need to be met.

Assumptions made before performing factorial ANOVA in SPSS

Assumption #1- Lack of outliers. Outliers are odd measures that are much smaller or much larger than the rest of the observations. For example, in the data above, the mean score is 10.133, with a small variation between the scores of the students; if one student recorded a score of 25, then that would have been an outlier.

Assumption #2- The dependent variable should be continuous. For instance, in our example above, time is measured in weeks, so it is a continuous variable that is in intervals.

Assumption #3- The independent variables should comprise multiple independent groups. For example, our independent variables are different factors, such as time, methods, and tests.

Assumption #4- There should be no relation between the variables in the data set.

Assumption #5- There should be homogeneity of variances in the independent variables. A common way of checking for this assumption is using Levene’s test, which can be found in the SPSS software.

Carrying Out Factorial ANOVA Using SPSS: Step by Step

After ensuring all the assumptions are met, you can now run the factorial ANOVA test in SPSS.

• Step 1: Click on Analyze>General Linear Model>Univariate. A univariate dialogue box appears.
• Step 2: Transfer the dependent variable, such as, in our case, student scores, into the Dependent variable box, and the independent variables, tests, time, and methods, into the Fixed factors
• Step 3: Click on the Plots tab where the Univariate: Profile Plots box appears.
• Step 4: Transfer the dependent variable from the Factors box to the Separate lines box and the independent variable to the horizontal axis
• Step 5: Click on the Add This step adds the variables to the Plots box.
• Step 6: Click on the Continue tab which takes you back to the Univariate dialogue box.
• Step 7: Click the Options A Univariate-options box is presented.
• Step 8: Transfer the variables from the Factors box to the Display Means box, then click on the descriptive statistics
• Step 9: Click on the Continue tab where you will return to the Univariate dialogue box.
• Step 10: Run a poc hoc test. Poc hoc tests in factorial ANOVA test if the difference between each variable is statistically significant.
• Step 11: Click on Continue then Ok to run the analysis.

After the analysis is complete, SPSS generates a couple of tables showcasing the output. It can generate a descriptive statistics table, a Test of between-subjects table, or a sketch plot of the results.

Why Should I Hire an ANOVA Expert?

• ANOVA analysis enables you to understand whether two occurrences have a meaningful pattern or are just out of chance. It gives you a detailed explanation of the relation between two variables and how much they affect each other.
• Research and analysis experts conduct an ANOVA analysis and detect patterns visible in the data set. The output of this analysis is crucial for decision-making. For example, a business can hire these experts to find the relationship between sales and advertising methods.
• ANOVA experts can help in the interpretation of the analysis results and offer advice on how to work with the results for your benefit.
• Research and analysis experts offer customized solutions according to your research needs. Whether you need help with the analysis or interpretation, they handle it.

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Summary

Factorial ANOVA is a branch of the statistical methods ANOVA that analyzes how two or more factors affect a single variable. It is used by researchers to find out whether there is a relationship between variables and how much they affect each other. It can be used in various fields, such as business, sociology, or medicine. Researchers can use SPSS to conduct factorial ANOVA analysis. Before carrying out the analysis, they must ensure the five assumptions are met. Hiring an ANOVA expert to carry out the analysis assures you of a quality analysis perfect for decision-making. If you are looking for a statistical data analysis expert, contact us today or view our order page to get started. We have quality assurance personnel to ensure that the product delivered is of high quality with no errors and delivered on time.