Could someone let me know if I did this correctly?
Source Sum of Squares (degrees of freedom [df]) Mean Square Fobt. Fcrit.
Gender 68.15 1.07 68.15/63.685 0.59 1.07,1,2
Marital Status 127.37 3.04 63.685/20.95 0.75 3.04,2,2
Gender * Marital Status (A x B) 41.90 2.28 20.95/9.2 0.89 2.28,2.94
Error (Within) 864.82 94 9.2 NA NA
Total 1102.24 99 NA NA NA
Based on the information provided, it seems like you are trying to interpret the results of an ANOVA (Analysis of Variance) table. To determine if you did it correctly, we need to understand the information in the table and the calculations involved.
Let's break down the ANOVA table:
Source: This column indicates the source or factor being analyzed. In this case, the factors are Gender, Marital Status, and the interaction between Gender and Marital Status (A x B). The last row, labeled "Error (Within)", represents the residual or unexplained variation.
Sum of Squares: This column shows the sum of squared deviations from the mean. These values represent the variation explained by each factor and the remaining unexplained variation (Error).
Degrees of Freedom (df): This column shows the degrees of freedom associated with each factor. Degrees of freedom are used to estimate the population values from a sample. In ANOVA, the df for a factor is usually the number of levels minus one. The "Error (Within)" row represents the total degrees of freedom.
Mean Square: This column represents the sum of squares divided by the corresponding degrees of freedom. Mean square values provide an estimate of the average amount of variation accounted for by each factor.
Fobt: This column represents the calculated F-value for each factor. The F-value is a ratio of the mean squares for the factor and the mean squares for the error. It assesses whether the factor's effect is statistically significant.
Fcrit: This column represents the critical F-value. It is the threshold value that is compared to the Fobt to determine statistical significance. If Fobt is equal to or higher than Fcrit, the factor's effect is considered significant.
To check if you did it correctly, make sure you have performed the ANOVA calculations accurately. Calculate each factor's Mean Square by dividing the corresponding Sum of Squares by its degrees of freedom. Verify that you calculated the F-value correctly by dividing the Mean Square of each factor by the Mean Square of the Error. Finally, check if the Fobt values you calculated match the given values in the table.
Comparing your calculated Fobt values to the Fcrit values, you can determine if there is a statistically significant effect for each factor or interaction. If Fobt is equal to or higher than Fcrit, then the factor's effect is considered significant.
Remember, without knowing the specific research question, sample size, or significance level, it is not possible to provide a definitive answer regarding the correctness of your calculations.