The Three Way ANOVA Calculator is a powerful tool used in statistical analysis to examine the influence of three categorical independent variables on a continuous dependent variable. It helps researchers and analysts understand the variation within their data and determine the significance of each factor and their interactions.
Formula of Three Way ANOVA Calculator
The calculator utilizes the following formulas:
SS_total = SS_between_A + SS_between_B + SS_between_C + SS_between_AB + SS_between_AC + SS_between_BC + SS_between_AB*C + SS_within
df_total = df_between_A + df_between_B + df_between_C + df_between_AB + df_between_AC + df_between_BC + df_between_AB*C + df_within
MS_total = SS_total / df_total
F_A = (SS_between_A / df_between_A) / MS_within F_B = (SS_between_B / df_between_B) / MS_within F_C = (SS_between_C / df_between_C) / MS_within F_A_B = (SS_between_AB / df_between_AB) / MS_within F_A_C = (SS_between_AC / df_between_AC) / MS_within F_B_C = (SS_between_BC / df_between_BC) / MS_within F_A_B_C = (SS_between_ABC / df_between_ABC) / MS_within
p_value_A = p-value from F-distribution with df_between_A and df_within p_value_B = p-value from F-distribution with df_between_B and df_within p_value_C = p-value from F-distribution with df_between_C and df_within p_value_A_B = p-value from F-distribution with df_between_AB and df_within p_value_A_C = p-value from F-distribution with df_between_AC and df_within p_value_B_C = p-value from F-distribution with df_between_BC and df_within p_value_A_B_C = p-value from F-distribution with df_between_AB*C and df_within
In these formulas:
SS: sum of squares
df: degrees of freedom
MS: mean squares
F: F-statistic
p_value: p-value associated with each factor and interaction
General Terms Table
| Term | Description |
|---|---|
| SS | Sum of squares |
| df | Degrees of freedom |
| MS | Mean squares |
| F | F-statistic |
| p-value | Associated probability value |
Example of Three Way ANOVA Calculator
Suppose we have a study analyzing the effects of three different types of exercise (A, B, and C) on cardiovascular health. Using the Three Way ANOVA Calculator, we can determine if there are significant differences in cardiovascular health among the exercise types, while also considering potential interactions between them.
Most Common FAQs
A: The calculator helps researchers analyze the influence of multiple categorical independent variables on a continuous dependent variable, providing insights into their significance and interactions.
A: The calculator provides F-statistics and p-values for each factor and interaction, indicating their significance. A lower p-value suggests a higher significance level.
A: No, the calculator requires complete data for accurate analysis.
A: The calculator is best suited for balanced experimental designs with categorical independent variables.