One way and two way analysis of variance
Answers
When it comes to research, in the field of business, economics, psychology, sociology, biology, etc. the Analysis of Variance, shortly known as ANOVA is an extremely important tool for analysis of data. It is a technique employed by the researcher to make a comparison between more than two populations and help in performing simultaneous tests. There is a two-fold purpose of ANOVA. In one way ANOVA the researcher takes only one factor.
As against, in the case of two-way ANOVA, the researcher investigates two factors concurrently. For a layman these two concepts of statistics are synonymous. However, there is a difference between one-way and two-way ANOVA.
Content: One-Way ANOVA Vs Two-Way ANOVA
Comparison Chart
Definition
Key Differences
Conclusion
Comparison Chart
BASIS FOR COMPARISON ONE WAY ANOVA TWO WAY ANOVA
Meaning One way ANOVA is a hypothesis test, used to test the equality of three of more population means simultaneously using variance. Two way ANOVA is a statistical technique wherein, the interaction between factors, influencing variable can be studied.
Independent Variable One Two
Compares Three or more levels of one factor. Effect of multiple level of two factors.
Number of Observation Need not to be same in each group. Need to be equal in each group.
Design of experiments Need to satisfy only two principles. All three principles needs to be satisfied.
Definition of One-Way ANOVA
One way Analysis of Variance (ANOVA) is a hypothesis test in which only one categorical variable or single factor is considered. It is a technique which enables us to make a comparison of means of three or more samples with the help of F-distribution. It is used to find out the difference among its different categories having several possible values.
The null hypothesis (H0) is the equality in all population means, while alternative hypothesis (H1) will be the difference in at least one mean.
One way ANOVA is based on the following assumptions:
Normal distribution of the population from which the samples are drawn.
Measurement of the dependent variable is at interval or ratio level.
Two or more than two categorical independent groups in an independent variable.
Independence of samples
Homogeneity of the variance of the population.
Definition of Two-Way ANOVA
Two-way ANOVA as its name signifies, is a hypothesis test wherein the classification of data is based on two factors. For instance, the two bases of classification for the sales made by the firm is first on the basis of sales by the different salesman and second by sales in the various regions. It is a statistical technique used by the researcher to compare several levels (condition) of the two independent variables involving multiple observations at each level.
Two-way ANOVA examines the effect of the two factors on the continuous dependent variable. It also studies the inter-relationship between independent variables influencing the values of the dependent variable, if any.