 So, we did ANOVA one-way ANOVA by hand, which is quite cumbersome or there are quite a few calculations in it, but it is important to do it by hand. Why? Because you need to understand what is the logic behind ANOVA, what actually is doing, how it is doing. Sites always provide you tools, but you should be intelligent enough to use which tool, when and why. Understanding logic of ANOVA, understanding how it is doing, what it is doing, what it is telling me is important because once you know the logic and the reason behind and the philosophy behind, it's just a one-click game in SPSS. SPSS will calculate the output in all the values that we did in like 15 minutes. It will do in less than 15 seconds, but for us is it important to understand the output in which value is corresponding to what and how to interpret those values. So, I will do SPSS in ANOVA in SPSS. One way between group ANOVA is used when there is one independent grouping variable with three or more levels or two or more levels and one dependent continuous variable. We are clear about it here. One factor, one independent variable which is categorical with more than two levels, at least three or more levels. We will be opting for one-way ANOVA. For example, in comparing the effectiveness of three different teaching styles on students math scores, you will have one factor teaching style. Of course, it has three levels. Number one, whole class, number two, small group activity, number three, self-paced computer activity. There are three different teaching styles and what we want to see, what is the dependent variable? That is the scores on a math test or students performance or students performance on the math score. So, one independent variable, categorical, one dependent variable, continuous, which will be running score, which will be interval scale variable. One way ANOVA tells whether there are significant differences in the mean scores on the dependent variable across the three groups. ANOVA just tells us whether their mean scores are different or not, whether the three groups are same or different by using or utilizing the variability or variance in the three groups. Post-hoc test can then be used to find out whether there are further differences. We just talked about the significant differences in the two groups. To run in SPSS, we need one categorical dependent variable with three or more levels, with one dependent variable which is continuous and we can do it. But we can also add one more variable to it. Then we call it factorial ANOVA. As I just talked about, if we add age to it, what is age of participants, age would be another variable. And then we can do grouping further. That can be divided into three age categories, 29 in junger between 30 and 44 and 45 for above. We can do grouping. So, now I have two independent variable, number one teaching style with three levels, age with the three levels and dependent variable is a continuous variable which is a score. So, this will become two-way ANOVA and we can also call it factorial ANOVA. And we write it as three by three. That means I have three by three factorial ANOVA which means I have ANOVA which is two-way with two independent variables. There are three levels of the first independent variable and three levels of the second independent variable. Now we stick to one-way ANOVA where we have only one independent variable and it has three levels. This is an example again from Gravator. Human factor psychologist studied T-computer keyboard designs. T samples of individuals were given material to type on a particular keyboard and the number of errors committed by each participant was recorded. Data shown in the table are these data sufficient to conclude that there are significant differences in typing performance among the three keyboard designs at an alpha level of 0.05. So, what is typing performance? You have to see which is a dependent variable which is measured by a continuous score in which there are so many errors. And we have an independent variable type of keyboard and three types of keyboards are A, B, C and we have to see the role of the key board and how many percent variants are there. We will explain that.