Two-Way Analysis of Variance: Examining Influence of Two Factors on Criterion Variable
A two-way analysis of variance is a design with two factors where we intend to compare the effect of multiple levels of two factors simultaneously on criterion variable. The two-way ANOVA is applied in two situations: first, where there is one observation
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Two-Way Analysis of Variance: Examining Influence of Two Factors on Criterion Variable
Learning Objectives After completing this chapter, you should be able to do the following: • • • • • • • • • •
Explain the importance of two-way analysis of variance (ANOVA) in research. Understand different designs where two-way ANOVA can be used. Describe the assumptions used in two-way analysis of variance. Learn to construct various hypotheses to be tested in two-way analysis of variance. Interpret various terms involved in two-way analysis of variance. Learn to apply two-way ANOVA manually in your data. Understand the procedure of analyzing the interaction between two factors. Know the procedure of using SPSS for two-way ANOVA. Learn the model way of writing the results in two-way analysis of variance by using the output obtained in the SPSS. Interpret the output obtained in two-way analysis of variance.
Introduction A two-way analysis of variance is a design with two factors where we intend to compare the effect of multiple levels of two factors simultaneously on criterion variable. The two-way ANOVA is applied in two situations: first, where there is one observation per cell and, second, where there is more than one observation per cell. In a situation where there is more than one observation per cell, it is mandatory that the number of observations in each cell must be equal. Using two-way ANOVA with n observations per cell facilitates us to test if there is any interaction between the two factors. Two-way analysis of variance is in fact an extension of one-way ANOVA. In one-way ANOVA, the effect of one factor is studied on the criterion variable, whereas in two-way ANOVA, the effect of two factors on the criterion variable is J.P. Verma, Data Analysis in Management with SPSS Software, DOI 10.1007/978-81-322-0786-3_8, # Springer India 2013
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studied simultaneously. An additional advantage in two-way ANOVA is to study the interaction effect between the two factors. One of the important advantages of two-way analysis of variance design is that there are two sources of assignable causes of variation, and this helps to reduce the error variance and thus making this design more efficient. Consider an experiment where a personal manger is interested to know whether the job satisfaction of the employees in different age categories is same or not irrespective of an employee being male or female. In testing this hypothesis, 15 employees may be randomly selected in each of three age categories: 20–30, 31–40, and 41–50 years, and one-way ANOVA experiment may be planned. Since in making the groups male and female employees were selected at random, and, therefore, if any difference in the satisfaction level is observed in different age categories, it may not be truly attributed due to the age category only. The variation might be because of their gender difference as well. Now, the same experiment may be planned in two-way ANOVA with one factor as ag
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