The Health Company, which provides various diet plans to lose weight, conducted a market test experiment to test three different levels of diets (A, B, C). Each diet had a different impact on the weight after following the diet for 6 weeks. I was given a dataset of 78 observations who are provided with either of the diet plans - A, B, or C, along with their weights before and 6 weeks after taking the diet. The information is recorded in the columns 'diet', 'preweight', and 'weight6weeks'.
Statistical evidence to check whether the mean weight losses with respect to the three diet plans are significantly different.
First, Check if data follows a normal distribution using Shapiro's Wilk Test
Second, check for equality of variance using the Levene Test.
Third, calculate the p-value using One-way Anova Test.