Answer to Question #241159 in Statistics and Probability for darv

Question

The weighs in kilograms of 3 groups of 5 each are shown in below. Is there unusual variation among the groups?

1^st member: 1^st group is 50, 2^nd group is 60, 3^rd group is 53

  2^nd member: 1^st group is 48, 2^nd group is 40, 3^rd group is 55

 3^rd member: 1^st group is 55, 2^nd group is 50, 3^rd group is 40

 4^th member: 1^st group is 50, 2^nd group is 60, 3^rd group is 40

5^th member: 1^st group is 46, 2^nd group is 52, 3^rd group is 47

 

 

Answer 1

One-Way ANOVA test

using online calculator https://goodcalculators.com/, we get:

H₀: µ₁ = µ₂ = µ₃    ("all 3 population means are equal")

H₁: At least one µ_i different ("at least one of the 3 population means is not equal to the others")

test statistic:

computed as

$F=\frac{MSR}{MSE}$

where MSR = SSR/df_r = the regression mean square,

MSE = SSE/df_e = the mean square error,

SSR = the regression sum of squares,

SSE = the error sum of squares,

SST = the total sum of squares (SST = SSR + SSE),

df_r = the model degrees of freedom (equal to df_r = k - 1),

df_e = the error degrees of freedom (equal to df_e = n - k - 1)

k = the total number of groups (levels of the independent variable)

n = the total number of valid observations,

df_T = the total degrees of freedom (equal to df_T = df_r + df_e = n - 1)

for $\alpha=0.05$ :

p-value > 0.05

so, we can conclude that there is no unusual variation among the groups