TwoWay ANOVA  Definition
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TwoWay ANOVA Definition
A twoway ANOVA is a oneway ANOVAs extension, a statistical test used to examine the effect of two different variables on one continuous dependent variable. Besides assessing the main effect of each independent variable, ANOVA also assesses to find out if, between the two variables, there is any kind of interaction.
A Little More on What is twoway ANOVA
A twoway ANOVA is a test that analyzes the independent variables effect on the anticipated outcome, along with its outcomes relationship. When it comes to random factors, they are usually considered to have no statistical influence on a set of data. It is contrary to the systematic factors where their statistical are found to be of significance. A researcher may use a twoway ANOVA when he or she wants to have one measurement variable as well as two nominal variables. Note that the nominal variable (also known as factors), exists in all possible combinations. By using a twoway ANOVA, as a researcher, you can be able to find out whether the outcomes variability is as a result of the factors in the analysis or by chance. Individuals can apply ANOVA in different fields, such as economics, finance, social science, and medicine.
TwoWay ANOVA Assumptions
Generally, a twoway ANOVA test is an extension of the onewayANOVA test. The twoway ANOVA test has got two independent variables hence the term twoway. Note that there as several assumptions that relate to the twoway analysis of variance. They are as follows:
 The sample population must be approximately normally or normally distributed
 It is mandatory for the samples to be independent
 It is mandatory that the populations variances be equal
 The sample size of the groups must be the same
A TwoWat ANOVA Hypotheses
The twoway ANOVA has several sets to hypotheses. The null hypotheses are as follows:
 The first factors population means are equal. It is is the same as the oneway ANOVA when it comes to the row factor)
 The second factors population means are equal. It is is the same as the oneway ANOVA when it comes to column factor)
 Between the two factors, no interaction exists. It is the same as administering a test for independence using contingency tables.
Twoway ANOVA Uses
When you want to identify which factors are influencing a particular outcome, you will first have to apply the ANOVA test. By performing the test, a tester may be in a position to help you do more analysis on the methodical factors that are contributing to the variability of the data set in a statistical manner. Also, a twoway ANOVA test will tell you the outcome of the two independent variables on a dependent variable. The results from the ANOVA test can be used in an Ftest to determine its significance on the regression formula overall. It is helpful when you want to test the effects of variables on each other. It is the same as that of multiple twosample ttests. Nonetheless, it is suitable for a range of issues because it usually results in fewer type 1 errors. ANOVA can also be used to group differences where it compares each groups means, including spreading out the variance into different sources. It is usually used together with subjects, test groups either between or within groups.
A TwoWay ANOVA vs. ANOVA
Analysis of variance exists in two types: onewar and twoway which is also known as unidirectional and bidirectional respectively. The two analyses of variance refer to independent variables number in the analysis of variance test. OneWay ANOVA It is a type of analysis of variance used to evaluate the sole factors impact on a single response variable. It also tests the samples to find out if they are equal. In addition, it can be used to determine whether, between the means of three or more unrelated groups, there are significant differences in the statistics. TwoWay ANOVA There are two independent variables in this type of analysis of variance. With the twoway variables test, a company can easily compare the productivity of its workers, based on two independent variables such as skills and salary. It can utilize the test to observe how those two factors interact with each other. It also tests the two factors effect simultaneously. Key Takeaways
 A twoway ANOVA is a oneway ANOVAs extension, a statistical test used to examine the effect of two different variables on one continuous dependent variable.
 The twoway ANOVA test has two independent variables hence the term twoway.
 The twoway ANOVA can be applied in different fields, such as economics, finance, social science, and medicine.
References for TwoWay ANOVA
https://statistics.laerd.com/spsstutorials/twowayanovausingspssstatistics.phphttps://en.wikipedia.org/wiki/Twoway_analysis_of_variancehttps://www.investopedia.com Business Business Leaders Math & Statistics
Academic research for TwoWay ANOVA
Twoway ANOVA with unequal cell frequencies and unequal variances, Ananda, M. M., & Weerahandi, S. (1997). Twoway ANOVA with unequal cell frequencies and unequal variances. Statistica Sinica, 631646. Nonparametric competitors to the twoway ANOVA, Toothaker, L. E., & Newman, D. (1994). Nonparametric competitors to the twoway ANOVA. Journal of Educational Statistics, 19(3), 237273. Twoway ANOVA models with unbalanced data, Fujikoshi, Y. (1993). Twoway ANOVA models with unbalanced data. Discrete Mathematics, 116(13), 315334. [HTML] A parametric bootstrap approach for twoway ANOVA in presence of possible interactions with unequal variances, Xu, L. W., Yang, F. Q., & Qin, S. (2013). A parametric bootstrap approach for twoway ANOVA in presence of possible interactions with unequal variances. Journal of Multivariate Analysis, 115, 172180. Adjusting for unequal variances when comparing means in oneway and twoway fixed effects ANOVA models, Wilcox, R. R. (1989). Adjusting for unequal variances when comparing means in oneway and twoway fixed effects ANOVA models. Journal of Educational Statistics, 14(3), 269278. Testing nonadditivity (interaction) in twoway ANOVA tables with no replication, Alin, A., & Kurt, S. (2006). Testing nonadditivity (interaction) in twoway ANOVA tables with no replication. Statistical methods in medical research, 15(1), 6385. Using twoway ANOVA and hypothesis test in evaluating crumb rubber modification (CRM) agitation effects on rheological properties of bitumen, Aflaki, S., & Memarzadeh, M. (2011). Using twoway ANOVA and hypothesis test in evaluating crumb rubber modification (CRM) agitation effects on rheological properties of bitumen. Construction and Building Materials, 25(4), 20942106. An approximate degrees of freedom test for heteroscedastic twoway ANOVA, Zhang, J. T. (2012). An approximate degrees of freedom test for heteroscedastic twoway ANOVA. Journal of Statistical Planning and Inference, 142(1), 336346. Testing for interaction in twoway ANOVA tables with no replication, Tusell, F. (1990). Testing for interaction in twoway ANOVA tables with no replication. Computational Statistics & Data Analysis, 10(1), 2945. Performance of twoway ANOVA procedures when cell frequencies and variances are unequal, Bao, P., & Ananda, M. M. (2001). Performance of twoway ANOVA procedures when cell frequencies and variances are unequal. Communications in StatisticsSimulation and Computation, 30(4), 805829.