Imagine an experiment having three conditions and 20 subjects within each condition. The mean and variances of each condition are listed bel

Question

Imagine an experiment having three conditions and 20 subjects within each condition. The mean and variances of each condition are listed below.

Condition Mean Variance
Condition 1 3.2 14.3
Condition 2 4.2 17.2
Condition 3 7.6 16.7
1. What’s the valueof mean squares between groups (MSB)?
2.What’s the value of mean square error (MSE)?
3. Whats the value of F?
4. What’s the probability value of this result?

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5 days 2021-09-15T22:54:28+00:00 1 Answer 0

Answers ( )

    0
    2021-09-15T22:56:23+00:00

    Answer:

    1. Mean square B= 5.32

    2. Mean square E= 16.067

    3. F= 0.33

    4. p-value: 0.28

    Step-by-step explanation:

    Hello!

    You have the information of 3 groups of people.

    Group 1

    n₁= 20

    X[bar]₁= 3.2

    S₁²= 14.3

    Group 2

    n₂= 20

    X[bar]₂= 4.2

    S₂²= 17.2

    Group 3

    n₃= 20

    X[bar]₃= 7.6

    S₃²= 16.7

    1. To manually calculate the mean square between the groups you have to calculate the sum of square between conditions and divide it by the degrees of freedom.

    Df B= k-1 = 3-1= 2

    Sum Square B is:

    ∑ni(Ÿi – Ÿ..)²

    Ÿi= sample mean of sample i ∀ i= 1,2,3

    Ÿ..= general mean is the mean that results of all the groups together.

    General mean:

    Ÿ..= (Ÿ₁ + Ÿ₂ + Ÿ₃)/ 3 = (3.2+4.2+7.6)/3 = 5

    Sum Square B (Ÿ₁ – Ÿ..)² + (Ÿ₂ – Ÿ..)² + (Ÿ₃ – Ÿ..)²= (3.2 – 5)² + (4.2 – 5)² + (7.6 – 5)²= 10.64

    Mean square B= Sum Square B/Df B= 10.64/2= 5.32

    2. The mean square error (MSE) is the estimation of the variance error (σ_{e}^2S_{e} ^{2}), you have to use the following formula:

    Se²= (n₁-1)S₁² + -(n₂-1)S₂² + (n₃-1)S₃²

                            n₁+n₂+n₃-k

    Se²= 19*14.3 + 19*17.2 + 19*16.7 =  915.8    = 16.067

                     20+20+20-3                  57

    DfE= N-k = 60-3= 57

    3. To calculate the value of the statistic you have to divide the MSB by MSE

    F= \frac{Mean square B}{Mean square E} = \frac{5.32}{16.067} = 0.33

    4. P(F_{2; 57} ≤ F) = P(F_{2; 57} ≤ 0.33) = 0.28

    I hope you have a SUPER day!

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