One Way ANOVA

The video begins with an introduction to conducting a one-way ANOVA manually, aiming to clarify the steps and calculations involved when using software like SPSS. The fundamental goal of a one-way ANOVA is to compare the means across at least three different conditions or groups in an experiment. The presenter outlines a five-step process and uses a simple dataset with three groups and three scores per group to demonstrate the process. The data set includes scores of 1, 2, and 5 for the first group; 2, 4, and 2 for the second; and 2, 3, and 4 for the third group.

The second paragraph delves into the formulation of hypotheses for the one-way ANOVA, emphasizing the importance of doing so a priori. The null hypothesis (H₀) posits that there is no difference between the means of the three conditions, while the alternative hypothesis suggests at least one mean differs. The video specifies an alpha level of 0.05, a common choice in statistical analysis, to determine the critical F-value using the F-distribution, which requires calculating degrees of freedom between and within groups. The degrees of freedom between groups is calculated as K - 1, where K is the number of conditions, and the within groups as the total number of scores (N) minus K.

This paragraph explains the process of calculating degrees of freedom for both between and within groups to find the critical F-value for the ANOVA test. The total degrees of freedom is the sum of the degrees of freedom between and within groups. Using an F-distribution table, the critical F-value is determined by looking up the degrees of freedom between groups (2) and within groups (6), resulting in a critical value of 5.14. This value is crucial for comparing against the calculated F-statistic to make a decision about the null hypothesis.

The heart of the process, as described in the fourth paragraph, is the detailed calculation of the sum of squares for total variability, within groups, and between groups. This involves calculating the mean for each group, the grand mean for all scores, and then using these means to compute the sum of squared deviations from the grand mean (total sum of squares). The sum of squares within is calculated by summing the squared deviations of each score from its group mean. The sum of squares between is derived by subtracting the sum of squares within from the total sum of squares, providing a measure of variability due to differences between group means.

The final paragraph wraps up the process by calculating the mean square between and within groups, which are essentially the variances between and within groups, by dividing the respective sum of squares by their degrees of freedom. The F-statistic is then calculated by dividing the mean square between by the mean square within, resulting in an F-value of 0.5. This F-value is compared to the critical F-value (5.14) to determine whether to reject the null hypothesis. Since the calculated F-value is less than the critical value, the null hypothesis is not rejected, indicating no significant difference between the group means.