Use-of-ANOVA-to-find-effect-of-treatments-on-child-s-growth

• Checking if there is any significant effect of different treatments on child's growth using One Way ANOVA test
• I have done ANOVA test manually from scratch without using built in Statsmodels library and just using simple pandas functions and ANOVA test steps :
• Step 1) Find means of all 4 individual treatment groups (xi_bar)
• Step 2) Find grand mean of all 4 treatment groups (xi_bar_bar)
• Step 3) Sum of Squares Between the groups (SSB) = n * sum(xi_bar - xi_bar_bar)^2 , (where, n = no. of observations per treatment group, i = (1,2,3,4))
• Step 4) Sum of Squares Within the group (SSWi) = sum(xi - xi_bar)^2 , (where, xi = individual obervations) in the group, i = (1,2,3,4)) SSW = SSW1 + SSW2 + SSW3 + SSW4
• Step 5) Variance Between Group (VBG) = SSB / k - 1, where k = no. of groups / treatments
• Step 6) Vraince Within Gropus (VWG) = SSW / nk - k
• Step 7) F-stat = SSB/SSW and R2 = SSB/SST (to determine how much variation in treatment groups is explained by ANOVA test)
• Analyzing F-stat to analyze hypothesis of ANOVA and infering the result to our problem statement