Answer to Question #241126 in Statistics and Probability for darv

Question

The mathematical scores of 6 groups of 4 students each are shown below. Test whether the differences in scores may be attributed to chance, at .01 significance level.

 Group 1: Student1 84, Student2 88, Student3 70, Student4 80. Group 2: Student1 90, Student2 95, Student3 93, Student4 80. Group 3: Student1 70, Student2 73, Student3 85, Student4 90. Group 4: Student1 95, Student2 96, Student3 90, Student4 90. Group 6: Student1 85, Student2 78, Student3 75, Student4 90. Group 6: Student1 93, Student2 85, Student3 80, Student4 90.

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)

p-value > 0.01

so, we can conclude that the differences in scores may be attributed to chance