The overall fit of a linear model is tested using the F-statistic. The F-statistic is used to test whether groups are significantly different and then specific model parameters (the bs) are used to show which groups are different. The F-statistic gives an associated p-value as well. A p-value which is smaller than 0.05 (or any set alpha) stands for a significant difference between the group means. The downside of the F-test is that it does not tell us which groups are different. Associated t-tests can show which groups are significantly different. The null hypothesis if the F-statistic is that the group means are equal and the alternative hypothesis is that the group means are not equal. If the null hypothesis is true, then the b-coefficients should be zero. The F-statistic can also be described as the ratio of explained to the unexplained variation. The total sum of squares is the total amount of variation within the data. This can be calculated by using the following formula:It is the difference between each observed data point and the grand mean squared. The grand variance is the total sum of squares of all observations. It is the variation between all scores, regardless of the group from which the scores come. The model sum of squares is calculated by taking the difference between the values predicted by the model and the grand mean. It tells us how much of the variation can be explained using the model. It uses the following formula:It is the difference of the group mean and the grand mean squared. This value is multiplied with the number of participants in this group and these values for each group are added together. The residual sum of squares tells us how much of the variation cannot be explained by the model. It is calculated by looking at the difference between the score obtained by a person and the mean of the group to which the person belongs. It uses the following formula:It is the squared difference between the...

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