Spss - One - Way anova

In this video I will show you how to conduct a One-Way analysis of variance in SPSS. This data set includes three variables. The first one, called ID is just a numerical identifier for all of the individuals in the data set. And this data set consists of 75 students. The second variable is a categorical variable, called Instruction which shows the type of instruction that students receive, and we have three categories, for this variable. If we go to the Variable View tab, we can see that the Instruction variable takes the value 1 for online instruction, the value 2 for hybrid courses, which consists of both, online and face-to-face meetings, and the value 3 for traditional instruction, or face-to-face courses. The third variable, Post-test, includes students' test scores, after instruction was delivered, regardless of the instructional method used. The no hypothesis here, is that there is no significant difference between the average scores of the three groups. To conduct the analysis of variance, we have to go to the Analyze Menu, and choose Compare Means, and then One-Way ANOVA. On the left side, we have a list of all the variables in the data set, and we have to select the variable that we are testing across the three groups. In our case, this variable is the Post-test variable because we are comparing test scores between the three groups, so this would be our dependent variable, Then, we have to select the variable that shows to which group each individual belongs to. And in our case, this variable is the instruction variable, and we have to select it, and then move it in this area called Factor. We also want to see the actual means and standard deviations and sample sizes for each group. And for that, we have to go to the Option Menu, and then choose the box next to Descriptive Statistics, and then click Continue. If the test statistic is significant, we also want to see where the significant differences occur so, we want to conduct some post-hoc analysis. To do that, we have to go to the post-hoc button, And from this list I am going to choose the Tukey procedure. And then click Continue. And then click OK. In my output window I have three tables. The first one is the descriptives table that I've requested. So, for each category, online instruction, hybrid and traditional instruction, we have the sample size. We can see here that we have 25 students in each group, and a total of 75 students. The mean for each group, we can already see here that, the students in hybrid group, had the highest means, followed by the students in the online cohort, and then students in the traditional instruction cohort. We also have standard deviations, standard errors, the 95% confidence interval, for this means, and also the minimum and the maximum values in each group. The second table is the one that is the most important, because it provides the results of the test of significance. Because we have three groups, the between groups degrees of freedom is equal to 2. 3 minus 1 is equal to 2. The within groups degrees of freedom are equal to the sample size minus the number of groups so, 75 minus 3 is 72. And the total degrees of freedom is 74. This is the result of subtracting 1 from the sample size, 75 minus 1. The test statistic F, is the result of dividing the between groups mean square, by the within groups mean square, which is also called the error term. The p value for this test statistic is .001, which tells us that, the differences between these 3 means are statistically significant, because the p value is lower than alpha of .05. Now that we know that the differences between the three groups are statistically significant, the next question is: Where do these differences that are statistically significant occurred, between which groups? Are all the differences significant, or only some of them? To respond to this question we have to look at the results of the post-hoc analysis. The Tukey procedure computes differences between all of the groups, and tests whether or not these differences are statistically significant. In this table we have, for instance, the differences between online instruction and hybrid instruction, online instruction and traditional instruction. In the first column we have the actual differences between the groups. Then we have the standard error for these differences, and the p value, for all of these differences. The p values that are statistically significant at the .05 level, are marked within asterix. So, we can see in our example, that hybrid instruction and traditional instruction are statistically different. The other difference, that is marked as significant is actually the same difference, between traditional instruction and hybrid instruction. The Tukey procedure also creates subsets of groups that are similar, to subsets include the groups that did not have means that were statistically significant. In our case the first subset consists of the traditional instruction and online instruction group, which were not significantly different, and the second subsets consists of the online instruction and the hybrid instruction group, which were not significantly different.