Question

Recitation Exercise: Repeated Measures ANOVA Answer the following questions. You are allowed to work in groups, but everyone must show All of their work. Round to the hundredth decimal place at every step and Jeel free to attach an additional sheet of paper 1.) A researcher has randomly selected a sample of 5 adults to participate in a memory study. Each adult is exposed to different types of music to see if the presence of lyrics in the music influences memory when studying. Participants were exposed to different types of music while studying lists of words and then given a memory test. The scores are recorded below on the table. Participant No music Instrumental Rock/Pop 4 ni G= - no music x 2 instrum rock/pop a. Complete the ANOVA summary table below to help determine whether these data indicate any significant mean differences among the treatments. MS Source Between Treatments Within Treatments Between Subjects Error Total b. Testing at an alpha level of a 05, is there a significant difference among the treatment conditions? What is your Forilical value? crit

Answer 1

Participants	No music	Instrumental	Rock/Pop		P	P2	P2/k
A	8	6	3		17	289	96.33
B	5	8	5		18	324	108
C	7	6	2		15	225	75
D	5	3	3		11	121	40.33
E	8	4	4		16	256	85.33

N = 15, n1 = 5, n2 = 5, n3 = 5, k= 3

Grand total, G = 77

Sum of treatment 1, T1 = 8+5+7+5+8 = 33

Sum of treatment 2, T2 = 27

Sum of treatment 3, T3 = 17

$\dpi{100} \frac{G^2}{N} = \frac{77^2}{15}= \textbf{395.267}$

$\dpi{100} \frac{T_1^2}{n_1} = \frac{33^2}{5} = \textbf{217.8}$

$\dpi{100} \frac{T_2^2}{n_2} = \frac{27^2}{5}= \textbf{145.8}$

$\dpi{100} \frac{T_3^2}{n_3} = \frac{17^2}{5} = \textbf{57.8}$

$\dpi{100} \Sigma X^2 = 8^2+ 6^2 + 3^2+.....+8^2+ 4^2+4^2 = \textbf{451}$

$\dpi{100} \Sigma x^2_{no\ music} = 8^2+ 5^2 + 7^2+5^2+8^2=\textbf{227}$

$\dpi{100} \Sigma x^2_{instrument} = 6^2+ 8^2 + 6^2+3^2+4^2=\textbf{161}$

$\dpi{100} \Sigma x^2_{rock/pop} = 3^2+ 5^2 + 2^2+3^2+4^2=\textbf{63}$

Sum of square for treatment 1, SS1 = 9.2

Sum of square for treatment 2, SS2 = 15.2

Sum of square for treatment 3, SS3 = 5.2

a) ANOVA table:

Source of Variation		SS	df	MS	F
Between Treatment		$\dpi{100} =\frac{T_1^2}{n_1}+\frac{T_2^2}{n_2}+\frac{T_3^2}{n_3}+\frac{G^2}{N} =\textbf{ 26.133 }$	k-1 = 2	$\dpi{100} =\frac{26.133}{2} =\textbf{ 13.067}$	$\dpi{100} =\frac{13.067}{2.483} = \textbf{5.263}$
Within Treatment		$\dpi{100} =SS1+SS2+SS3 = \textbf{29.6}$	(n-1)*k = 12
Between Subjects		$\dpi{100} =\sum \frac{P^2}{k}-\frac{G^2}{N} =\textbf{9.733}$	n-1 = 4
Error		$\dpi{100} =SS_{within\ treatment} - SS_{between\ subjects}= \textbf{19.867}$	(k-1)(n-1) = 8	$\dpi{100} =\frac{19.867}{2} = \textbf{2.483}$
Total		$\dpi{100} =\sum X^2-\frac{G^2}{N} =\textbf{55.733}$	N-1 = 14

b) $\dpi{100} F_{crit} =\textbf{3.885}$